From 799e4517b0f3f475ad256920c1d737a068da216b Mon Sep 17 00:00:00 2001
From: Pat Alt <55311242+pat-alt@users.noreply.github.com>
Date: Wed, 13 Sep 2023 16:50:30 +0200
Subject: [PATCH] just missing section 6
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paper/body.tex | 81 +-
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-@TechReport{kingma2017adam,
- author = {Kingma, Diederik P. and Ba, Jimmy},
- date = {2017-01},
- institution = {arXiv},
- title = {Adam: {A} {Method} for {Stochastic} {Optimization}},
- doi = {10.48550/arXiv.1412.6980},
- note = {arXiv:1412.6980 [cs] type: article},
- url = {http://arxiv.org/abs/1412.6980},
- urldate = {2023-05-17},
- abstract = {We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.},
- annotation = {Comment: Published as a conference paper at the 3rd International Conference for Learning Representations, San Diego, 2015},
- file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1412.6980.pdf:application/pdf},
- keywords = {Computer Science - Machine Learning},
- shorttitle = {Adam},
-}
-
-@TechReport{xiao2017fashion,
- author = {Xiao, Han and Rasul, Kashif and Vollgraf, Roland},
- date = {2017-09},
- institution = {arXiv},
- title = {Fashion-{MNIST}: a {Novel} {Image} {Dataset} for {Benchmarking} {Machine} {Learning} {Algorithms}},
- doi = {10.48550/arXiv.1708.07747},
- note = {arXiv:1708.07747 [cs, stat] type: article},
- url = {http://arxiv.org/abs/1708.07747},
- urldate = {2023-05-10},
- abstract = {We present Fashion-MNIST, a new dataset comprising of 28x28 grayscale images of 70,000 fashion products from 10 categories, with 7,000 images per category. The training set has 60,000 images and the test set has 10,000 images. Fashion-MNIST is intended to serve as a direct drop-in replacement for the original MNIST dataset for benchmarking machine learning algorithms, as it shares the same image size, data format and the structure of training and testing splits. The dataset is freely available at https://github.com/zalandoresearch/fashion-mnist},
- annotation = {Comment: Dataset is freely available at https://github.com/zalandoresearch/fashion-mnist Benchmark is available at http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/},
- file = {:xiao2017fashion - Fashion MNIST_ a Novel Image Dataset for Benchmarking Machine Learning Algorithms.pdf:PDF},
- keywords = {Computer Science - Machine Learning, Computer Science - Computer Vision and Pattern Recognition, Statistics - Machine Learning},
- shorttitle = {Fashion-{MNIST}},
-}
-
-@Online{mw2023fidelity,
- author = {Merriam-Webster},
- title = {"Fidelity"},
- url = {https://www.merriam-webster.com/dictionary/fidelity},
- language = {en},
- organization = {Merriam-Webster},
- urldate = {2023-03-23},
- abstract = {the quality or state of being faithful; accuracy in details : exactness; the degree to which an electronic device (such as a record player, radio, or television) accurately reproduces its effect (such as sound or picture)… See the full definition},
-}
-
-@InProceedings{altmeyer2023endogenous,
- author = {Altmeyer, Patrick and Angela, Giovan and Buszydlik, Aleksander and Dobiczek, Karol and van Deursen, Arie and Liem, Cynthia},
- booktitle = {First {IEEE} {Conference} on {Secure} and {Trustworthy} {Machine} {Learning}},
- title = {Endogenous {Macrodynamics} in {Algorithmic} {Recourse}},
- file = {:altmeyerendogenous - Endogenous Macrodynamics in Algorithmic Recourse.pdf:PDF},
- year = {2023},
-}
-
-%% This BibTeX bibliography file was created using BibDesk.
-%% https://bibdesk.sourceforge.io/
-
-%% Created for Anonymous Author at 2022-12-13 12:58:22 +0100
-
-
-%% Saved with string encoding Unicode (UTF-8)
-
-
-
-@Article{abadie2002instrumental,
- author = {Abadie, Alberto and Angrist, Joshua and Imbens, Guido},
- title = {Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings},
- number = {1},
- pages = {91--117},
- volume = {70},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Econometrica : journal of the Econometric Society},
- shortjournal = {Econometrica},
- year = {2002},
-}
-
-@Article{abadie2003economic,
- author = {Abadie, Alberto and Gardeazabal, Javier},
- title = {The Economic Costs of Conflict: {{A}} Case Study of the {{Basque Country}}},
- number = {1},
- pages = {113--132},
- volume = {93},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {American economic review},
- year = {2003},
-}
-
-@InProceedings{ackerman2021machine,
- author = {Ackerman, Samuel and Dube, Parijat and Farchi, Eitan and Raz, Orna and Zalmanovici, Marcel},
- booktitle = {2021 {{IEEE}}/{{ACM Third International Workshop}} on {{Deep Learning}} for {{Testing}} and {{Testing}} for {{Deep Learning}} ({{DeepTest}})},
- title = {Machine {{Learning Model Drift Detection Via Weak Data Slices}}},
- pages = {1--8},
- publisher = {{IEEE}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2021},
-}
-
-@Article{allen2017referencedependent,
- author = {Allen, Eric J and Dechow, Patricia M and Pope, Devin G and Wu, George},
- title = {Reference-Dependent Preferences: {{Evidence}} from Marathon Runners},
- number = {6},
- pages = {1657--1672},
- volume = {63},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Management Science},
- year = {2017},
-}
-
-@Article{altmeyer2018option,
- author = {Altmeyer, Patrick and Grapendal, Jacob Daniel and Pravosud, Makar and Quintana, Gand Derry},
- title = {Option Pricing in the {{Heston}} Stochastic Volatility Model: An Empirical Evaluation},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2018},
-}
-
-@Article{altmeyer2021deep,
- author = {Altmeyer, Patrick and Agusti, Marc and Vidal-Quadras Costa, Ignacio},
- title = {Deep {{Vector Autoregression}} for {{Macroeconomic Data}}},
- url = {https://thevoice.bse.eu/wp-content/uploads/2021/07/ds21-project-agusti-et-al.pdf},
- bdsk-url-1 = {https://thevoice.bse.eu/wp-content/uploads/2021/07/ds21-project-agusti-et-al.pdf},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2021},
-}
-
-@Book{altmeyer2021deepvars,
- author = {Altmeyer, Patrick},
- title = {Deepvars: {{Deep Vector Autoregession}}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2021},
-}
-
-@Misc{altmeyer2022counterfactualexplanations,
- author = {Altmeyer, Patrick},
- title = {{{CounterfactualExplanations}}.Jl - a {{Julia}} Package for {{Counterfactual Explanations}} and {{Algorithmic Recourse}}},
- url = {https://github.com/pat-alt/CounterfactualExplanations.jl},
- bdsk-url-1 = {https://github.com/pat-alt/CounterfactualExplanations.jl},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2022},
-}
-
-@Software{altmeyerCounterfactualExplanationsJlJulia2022,
- author = {Altmeyer, Patrick},
- title = {{{CounterfactualExplanations}}.Jl - a {{Julia}} Package for {{Counterfactual Explanations}} and {{Algorithmic Recourse}}},
- url = {https://github.com/pat-alt/CounterfactualExplanations.jl},
- version = {0.1.2},
- bdsk-url-1 = {https://github.com/pat-alt/CounterfactualExplanations.jl},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2022},
-}
-
-@Unpublished{angelopoulos2021gentle,
- author = {Angelopoulos, Anastasios N. and Bates, Stephen},
- title = {A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {2107.07511},
- eprinttype = {arxiv},
- file = {:/Users/FA31DU/Zotero/storage/RKSUMYZG/Angelopoulos and Bates - 2021 - A gentle introduction to conformal prediction and .pdf:;:/Users/FA31DU/Zotero/storage/PRUEKRR3/2107.html:},
- year = {2021},
-}
-
-@Misc{angelopoulos2022uncertainty,
- author = {Angelopoulos, Anastasios and Bates, Stephen and Malik, Jitendra and Jordan, Michael I.},
- title = {Uncertainty {{Sets}} for {{Image Classifiers}} Using {{Conformal Prediction}}},
- eprint = {2009.14193},
- eprinttype = {arxiv},
- abstract = {Convolutional image classifiers can achieve high predictive accuracy, but quantifying their uncertainty remains an unresolved challenge, hindering their deployment in consequential settings. Existing uncertainty quantification techniques, such as Platt scaling, attempt to calibrate the network's probability estimates, but they do not have formal guarantees. We present an algorithm that modifies any classifier to output a predictive set containing the true label with a user-specified probability, such as 90\%. The algorithm is simple and fast like Platt scaling, but provides a formal finite-sample coverage guarantee for every model and dataset. Our method modifies an existing conformal prediction algorithm to give more stable predictive sets by regularizing the small scores of unlikely classes after Platt scaling. In experiments on both Imagenet and Imagenet-V2 with ResNet-152 and other classifiers, our scheme outperforms existing approaches, achieving coverage with sets that are often factors of 5 to 10 smaller than a stand-alone Platt scaling baseline.},
- archiveprefix = {arXiv},
- bdsk-url-1 = {http://arxiv.org/abs/2009.14193},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- file = {:/Users/FA31DU/Zotero/storage/5BYIRBR2/Angelopoulos et al. - 2022 - Uncertainty Sets for Image Classifiers using Confo.pdf:;:/Users/FA31DU/Zotero/storage/2QJAKFKV/2009.html:},
- keywords = {Computer Science - Computer Vision and Pattern Recognition, Mathematics - Statistics Theory, Statistics - Machine Learning},
- month = sep,
- number = {arXiv:2009.14193},
- primaryclass = {cs, math, stat},
- publisher = {{arXiv}},
- year = {2022},
-}
-
-@Article{angelucci2009indirect,
- author = {Angelucci, Manuela and De Giorgi, Giacomo},
- title = {Indirect Effects of an Aid Program: How Do Cash Transfers Affect Ineligibles' Consumption?},
- number = {1},
- pages = {486--508},
- volume = {99},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {American economic review},
- year = {2009},
-}
-
-@Article{angrist1990lifetime,
- author = {Angrist, Joshua D},
- title = {Lifetime Earnings and the {{Vietnam}} Era Draft Lottery: Evidence from Social Security Administrative Records},
- pages = {313--336},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {The American Economic Review},
- year = {1990},
-}
-
-@Unpublished{antoran2020getting,
- author = {Antor{\'a}n, Javier and Bhatt, Umang and Adel, Tameem and Weller, Adrian and Hern{\'a}ndez-Lobato, Jos{\'e} Miguel},
- title = {Getting a Clue: {{A}} Method for Explaining Uncertainty Estimates},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {2006.06848},
- eprinttype = {arxiv},
- year = {2020},
-}
-
-@Article{arcones1992bootstrap,
- author = {Arcones, Miguel A and Gine, Evarist},
- title = {On the Bootstrap of {{U}} and {{V}} Statistics},
- pages = {655--674},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {The Annals of Statistics},
- year = {1992},
-}
-
-@Article{ariely2003coherent,
- author = {Ariely, Dan and Loewenstein, George and Prelec, Drazen},
- title = {``{{Coherent}} Arbitrariness'': {{Stable}} Demand Curves without Stable Preferences},
- number = {1},
- pages = {73--106},
- volume = {118},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {The Quarterly journal of economics},
- year = {2003},
-}
-
-@Article{ariely2006tom,
- author = {Ariely, Dan and Loewenstein, George and Prelec, Drazen},
- title = {Tom {{Sawyer}} and the Construction of Value},
- number = {1},
- pages = {1--10},
- volume = {60},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Journal of Economic Behavior \& Organization},
- year = {2006},
-}
-
-@Article{arrieta2020explainable,
- author = {Arrieta, Alejandro Barredo and Diaz-Rodriguez, Natalia and Del Ser, Javier and Bennetot, Adrien and Tabik, Siham and Barbado, Alberto and Garcia, Salvador and Gil-Lopez, Sergio and Molina, Daniel and Benjamins, Richard and others},
- title = {Explainable {{Artificial Intelligence}} ({{XAI}}): {{Concepts}}, Taxonomies, Opportunities and Challenges toward Responsible {{AI}}},
- pages = {82--115},
- volume = {58},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Information Fusion},
- year = {2020},
-}
-
-@Article{auer2002finitetime,
- author = {Auer, Peter and Cesa-Bianchi, Nicolo and Fischer, Paul},
- title = {Finite-Time Analysis of the Multiarmed Bandit Problem},
- number = {2},
- pages = {235--256},
- volume = {47},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Machine learning},
- year = {2002},
-}
-
-@Article{barabasi2016network,
- author = {Barab{\'a}si, Albert-L{\'a}szl{\'o}},
- title = {Network {{Science}}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Network Science},
- year = {2016},
-}
-
-@Unpublished{bastounis2021mathematics,
- author = {Bastounis, Alexander and Hansen, Anders C and Vla{\v c}i{\'c}, Verner},
- title = {The Mathematics of Adversarial Attacks in {{AI}}--{{Why}} Deep Learning Is Unstable despite the Existence of Stable Neural Networks},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {2109.06098},
- eprinttype = {arxiv},
- year = {2021},
-}
-
-@Article{bechara1997deciding,
- author = {Bechara, Antoine and Damasio, Hanna and Tranel, Daniel and Damasio, Antonio R},
- title = {Deciding Advantageously before Knowing the Advantageous Strategy},
- number = {5304},
- pages = {1293--1295},
- volume = {275},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Science (New York, N.Y.)},
- shortjournal = {Science},
- year = {1997},
-}
-
-@Book{berlinet2011reproducing,
- author = {Berlinet, Alain and Thomas-Agnan, Christine},
- title = {Reproducing Kernel {{Hilbert}} Spaces in Probability and Statistics},
- publisher = {{Springer Science \& Business Media}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2011},
-}
-
-@Misc{bernanke1990federal,
- author = {Bernanke, Ben S},
- title = {The Federal Funds Rate and the Channels of Monetary Transnission},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- publisher = {{National Bureau of Economic Research Cambridge, Mass., USA}},
- year = {1990},
-}
-
-@Article{besbes2014stochastic,
- author = {Besbes, Omar and Gur, Yonatan and Zeevi, Assaf},
- title = {Stochastic Multi-Armed-Bandit Problem with Non-Stationary Rewards},
- pages = {199--207},
- volume = {27},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Advances in neural information processing systems},
- year = {2014},
-}
-
-@Article{bholat2020impact,
- author = {Bholat, D and Gharbawi, M and Thew, O},
- title = {The {{Impact}} of {{Covid}} on {{Machine Learning}} and {{Data Science}} in {{UK Banking}}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Bank of England Quarterly Bulletin, Q4},
- year = {2020},
-}
-
-@Book{bishop2006pattern,
- author = {Bishop, Christopher M},
- title = {Pattern Recognition and Machine Learning},
- publisher = {{springer}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2006},
-}
-
-@Article{blaom2020mlj,
- author = {Blaom, Anthony D. and Kiraly, Franz and Lienart, Thibaut and Simillides, Yiannis and Arenas, Diego and Vollmer, Sebastian J.},
- title = {{{MLJ}}: {{A Julia}} Package for Composable Machine Learning},
- doi = {10.21105/joss.02704},
- issn = {2475-9066},
- number = {55},
- pages = {2704},
- urldate = {2022-10-27},
- volume = {5},
- abstract = {Blaom et al., (2020). MLJ: A Julia package for composable machine learning. Journal of Open Source Software, 5(55), 2704, https://doi.org/10.21105/joss.02704},
- bdsk-url-1 = {https://joss.theoj.org/papers/10.21105/joss.02704},
- bdsk-url-2 = {https://doi.org/10.21105/joss.02704},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- file = {:/Users/FA31DU/Zotero/storage/7AY87FGP/Blaom et al. - 2020 - MLJ A Julia package for composable machine learni.pdf:;:/Users/FA31DU/Zotero/storage/D69YSMVF/joss.html:},
- journal = {Journal of Open Source Software},
- langid = {english},
- month = nov,
- shorttitle = {{{MLJ}}},
- year = {2020},
-}
-
-@InProceedings{blundell2015weight,
- author = {Blundell, Charles and Cornebise, Julien and Kavukcuoglu, Koray and Wierstra, Daan},
- booktitle = {International Conference on Machine Learning},
- title = {Weight Uncertainty in Neural Network},
- pages = {1613--1622},
- publisher = {{PMLR}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2015},
-}
-
-@Article{borch2022machine,
- author = {Borch, Christian},
- title = {Machine Learning, Knowledge Risk, and Principal-Agent Problems in Automated Trading},
- pages = {101852},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Technology in Society},
- year = {2022},
-}
-
-@Unpublished{borisov2021deep,
- author = {Borisov, Vadim and Leemann, Tobias and Se{\ss}ler, Kathrin and Haug, Johannes and Pawelczyk, Martin and Kasneci, Gjergji},
- title = {Deep Neural Networks and Tabular Data: {{A}} Survey},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {2110.01889},
- eprinttype = {arxiv},
- year = {2021},
-}
-
-@Article{bramoulle2009identification,
- author = {Bramoull{\'e}, Yann and Djebbari, Habiba and Fortin, Bernard},
- title = {Identification of Peer Effects through Social Networks},
- number = {1},
- pages = {41--55},
- volume = {150},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Journal of econometrics},
- year = {2009},
-}
-
-@Article{bramoulle2020peer,
- author = {Bramoull{\'e}, Yann and Djebbari, Habiba and Fortin, Bernard},
- title = {Peer Effects in Networks: {{A}} Survey},
- pages = {603--629},
- volume = {12},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Annual Review of Economics},
- year = {2020},
-}
-
-@Unpublished{branco2015survey,
- author = {Branco, Paula and Torgo, Luis and Ribeiro, Rita},
- title = {A Survey of Predictive Modelling under Imbalanced Distributions},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {1505.01658},
- eprinttype = {arxiv},
- year = {2015},
-}
-
-@Book{brock1991nonlinear,
- author = {Brock, William Allen and Brock, William A and Hsieh, David Arthur and LeBaron, Blake Dean and Brock, William E},
- title = {Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence},
- publisher = {{MIT press}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {1991},
-}
-
-@InProceedings{buolamwini2018gender,
- author = {Buolamwini, Joy and Gebru, Timnit},
- booktitle = {Conference on Fairness, Accountability and Transparency},
- title = {Gender Shades: {{Intersectional}} Accuracy Disparities in Commercial Gender Classification},
- pages = {77--91},
- publisher = {{PMLR}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2018},
-}
-
-@Unpublished{bussmann2020neural,
- author = {Bussmann, Bart and Nys, Jannes and Latr{\'e}, Steven},
- title = {Neural {{Additive Vector Autoregression Models}} for {{Causal Discovery}} in {{Time Series Data}}},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {2010.09429},
- eprinttype = {arxiv},
- year = {2020},
-}
-
-@Report{card1993minimum,
- author = {Card, David and Krueger, Alan B},
- title = {Minimum Wages and Employment: {{A}} Case Study of the Fast Food Industry in {{New Jersey}} and {{Pennsylvania}}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- school = {{National Bureau of Economic Research}},
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- journal = {Psychological science},
- year = {2013},
-}
-
-@Article{list2004neoclassical,
- author = {List, John A},
- title = {Neoclassical Theory versus Prospect Theory: {{Evidence}} from the Marketplace},
- number = {2},
- pages = {615--625},
- volume = {72},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Econometrica : journal of the Econometric Society},
- shortjournal = {Econometrica},
- year = {2004},
-}
-
-@Article{lucas1976econometric,
- author = {Lucas, JR},
- title = {Econometric Policy Evaluation: A Critique `, in {{K}}. {{Brunner}} and {{A Meltzer}}, {{The Phillips}} Curve and Labor Markets, {{North Holland}}},
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- title = {A Unified Approach to Interpreting Model Predictions},
- pages = {4768--4777},
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- year = {2017},
-}
-
-@Book{lutkepohl2005new,
- author = {L{\"u}tkepohl, Helmut},
- title = {New Introduction to Multiple Time Series Analysis},
- publisher = {{Springer Science \& Business Media}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2005},
-}
-
-@Article{madrian2001power,
- author = {Madrian, Brigitte C and Shea, Dennis F},
- title = {The Power of Suggestion: {{Inertia}} in 401 (k) Participation and Savings Behavior},
- number = {4},
- pages = {1149--1187},
- volume = {116},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {The Quarterly journal of economics},
- year = {2001},
-}
-
-@Book{manning2008introduction,
- author = {Manning, Christopher D and Sch{\"u}tze, Hinrich and Raghavan, Prabhakar},
- title = {Introduction to Information Retrieval},
- publisher = {{Cambridge university press}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2008},
-}
-
-@misc{manokhin2022awesome,
- author = {Manokhin, Valery},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- title = {Awesome Conformal Prediction}}
-
-@Article{manski1993identification,
- author = {Manski, Charles F},
- title = {Identification of Endogenous Social Effects: {{The}} Reflection Problem},
- number = {3},
- pages = {531--542},
- volume = {60},
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- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {The review of economic studies},
- year = {1993},
-}
-
-@Article{markle2018goals,
- author = {Markle, Alex and Wu, George and White, Rebecca and Sackett, Aaron},
- title = {Goals as Reference Points in Marathon Running: {{A}} Novel Test of Reference Dependence},
- number = {1},
- pages = {19--50},
- volume = {56},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Journal of Risk and Uncertainty},
- year = {2018},
-}
-
-@Article{masini2021machine,
- author = {Masini, Ricardo P and Medeiros, Marcelo C and Mendes, Eduardo F},
- title = {Machine Learning Advances for Time Series Forecasting},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Journal of Economic Surveys},
- year = {2021},
-}
-
-@Article{mccracken2016fredmd,
- author = {McCracken, Michael W and Ng, Serena},
- title = {{{FRED-MD}}: {{A}} Monthly Database for Macroeconomic Research},
- number = {4},
- pages = {574--589},
- volume = {34},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Journal of Business \& Economic Statistics},
- year = {2016},
-}
-
-@Article{mcculloch1990logical,
- author = {McCulloch, Warren S and Pitts, Walter},
- title = {A Logical Calculus of the Ideas Immanent in Nervous Activity},
- number = {1},
- pages = {99--115},
- volume = {52},
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- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Bulletin of mathematical biology},
- year = {1990},
-}
-
-@Article{migut2015visualizing,
- author = {Migut, MA and Worring, Marcel and Veenman, Cor J},
- title = {Visualizing Multi-Dimensional Decision Boundaries in {{2D}}},
- number = {1},
- pages = {273--295},
- volume = {29},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Data Mining and Knowledge Discovery},
- year = {2015},
-}
-
-@Article{miller2019explanation,
- author = {Miller, Tim},
- title = {Explanation in Artificial Intelligence: {{Insights}} from the Social Sciences},
- pages = {1--38},
- volume = {267},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Artificial intelligence},
- year = {2019},
-}
-
-@InProceedings{miller2020strategic,
- author = {Miller, John and Milli, Smitha and Hardt, Moritz},
- booktitle = {Proceedings of the 37th {{International Conference}} on {{Machine Learning}}},
- title = {Strategic {{Classification}} Is {{Causal Modeling}} in {{Disguise}}},
- eventtitle = {International {{Conference}} on {{Machine Learning}}},
- pages = {6917--6926},
- publisher = {{PMLR}},
- url = {https://proceedings.mlr.press/v119/miller20b.html},
- urldate = {2022-11-03},
- abstract = {Consequential decision-making incentivizes individuals to strategically adapt their behavior to the specifics of the decision rule. While a long line of work has viewed strategic adaptation as gaming and attempted to mitigate its effects, recent work has instead sought to design classifiers that incentivize individuals to improve a desired quality. Key to both accounts is a cost function that dictates which adaptations are rational to undertake. In this work, we develop a causal framework for strategic adaptation. Our causal perspective clearly distinguishes between gaming and improvement and reveals an important obstacle to incentive design. We prove any procedure for designing classifiers that incentivize improvement must inevitably solve a non-trivial causal inference problem. We show a similar result holds for designing cost functions that satisfy the requirements of previous work. With the benefit of hindsight, our results show much of the prior work on strategic classification is causal modeling in disguise.},
- bdsk-url-1 = {https://proceedings.mlr.press/v119/miller20b.html},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- file = {:/Users/FA31DU/Zotero/storage/46I2QMPI/Miller et al. - 2020 - Strategic Classification is Causal Modeling in Dis.pdf:;:/Users/FA31DU/Zotero/storage/NWREET6B/Miller et al. - 2020 - Strategic Classification is Causal Modeling in Dis.pdf:},
- issn = {2640-3498},
- langid = {english},
- month = nov,
- year = {2020},
-}
-
-@Article{mischel1988nature,
- author = {Mischel, Walter and Shoda, Yuichi and Peake, Philip K},
- title = {The Nature of Adolescent Competencies Predicted by Preschool Delay of Gratification.},
- number = {4},
- pages = {687},
- volume = {54},
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-@InProceedings{mittelstadt2019explaining,
- author = {Mittelstadt, Brent and Russell, Chris and Wachter, Sandra},
- booktitle = {Proceedings of the Conference on Fairness, Accountability, and Transparency},
- title = {Explaining Explanations in {{AI}}},
- pages = {279--288},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2019},
-}
-
-@Book{molnar2020interpretable,
- author = {Molnar, Christoph},
- title = {Interpretable Machine Learning},
- publisher = {{Lulu. com}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2020},
-}
-
-@Book{morgan2015counterfactuals,
- author = {Morgan, Stephen L and Winship, Christopher},
- title = {Counterfactuals and Causal Inference},
- publisher = {{Cambridge University Press}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2015},
-}
-
-@Article{mosteller1951experimental,
- author = {Mosteller, Frederick and Nogee, Philip},
- title = {An Experimental Measurement of Utility},
- number = {5},
- pages = {371--404},
- volume = {59},
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- year = {1951},
-}
-
-@InProceedings{mothilal2020explaining,
- author = {Mothilal, Ramaravind K and Sharma, Amit and Tan, Chenhao},
- booktitle = {Proceedings of the 2020 {{Conference}} on {{Fairness}}, {{Accountability}}, and {{Transparency}}},
- title = {Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations},
- pages = {607--617},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2020},
-}
-
-@Book{murphy2012machine,
- author = {Murphy, Kevin P},
- title = {Machine Learning: A Probabilistic Perspective},
- publisher = {{MIT press}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2012},
-}
-
-@Book{murphy2012machine,
- author = {Murphy, Kevin P},
- title = {Machine Learning: {{A}} Probabilistic Perspective},
- publisher = {{MIT press}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2012},
-}
-
-@Book{murphy2022probabilistic,
- author = {Murphy, Kevin P},
- title = {Probabilistic {{Machine Learning}}: {{An}} Introduction},
- publisher = {{MIT Press}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2022},
-}
-
-@Article{nagel1995unraveling,
- author = {Nagel, Rosemarie},
- title = {Unraveling in Guessing Games: {{An}} Experimental Study},
- number = {5},
- pages = {1313--1326},
- volume = {85},
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- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {The American Economic Review},
- year = {1995},
-}
-
-@Unpublished{navarro-martinez2021bridging,
- author = {Navarro-Martinez, Daniel and Wang, Xinghua},
- title = {Bridging the Gap between the Lab and the Field: {{Dictator}} Games and Donations},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2021},
-}
-
-@InProceedings{nelson2015evaluating,
- author = {Nelson, Kevin and Corbin, George and Anania, Mark and Kovacs, Matthew and Tobias, Jeremy and Blowers, Misty},
- booktitle = {2015 {{IEEE Symposium}} on {{Computational Intelligence}} for {{Security}} and {{Defense Applications}} ({{CISDA}})},
- title = {Evaluating Model Drift in Machine Learning Algorithms},
- pages = {1--8},
- publisher = {{IEEE}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2015},
-}
-
-@Book{nocedal2006numerical,
- author = {Nocedal, Jorge and Wright, Stephen},
- title = {Numerical Optimization},
- publisher = {{Springer Science \& Business Media}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2006},
-}
-
-@Misc{oecd2021artificial,
- author = {{OECD}},
- title = {Artificial {{Intelligence}}, {{Machine Learning}} and {{Big Data}} in {{Finance}}: {{Opportunities}}, {{Challenges}} and {{Implications}} for {{Policy Makers}}},
- url = {https://www.oecd.org/finance/financial-markets/Artificial-intelligence-machine-learning-big-data-in-finance.pdf},
- bdsk-url-1 = {https://www.oecd.org/finance/financial-markets/Artificial-intelligence-machine-learning-big-data-in-finance.pdf},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2021},
-}
-
-@Online{oecdArtificialIntelligenceMachine2021,
- author = {{OECD}},
- title = {Artificial {{Intelligence}}, {{Machine Learning}} and {{Big Data}} in {{Finance}}: {{Opportunities}}, {{Challenges}} and {{Implications}} for {{Policy Makers}}},
- url = {https://www.oecd.org/finance/financial-markets/Artificial-intelligence-machine-learning-big-data-in-finance.pdf},
- bdsk-url-1 = {https://www.oecd.org/finance/financial-markets/Artificial-intelligence-machine-learning-big-data-in-finance.pdf},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- publisher = {{OECD}},
- year = {2021},
-}
-
-@Book{oneil2016weapons,
- author = {O'Neil, Cathy},
- title = {Weapons of Math Destruction: {{How}} Big Data Increases Inequality and Threatens Democracy},
- publisher = {{Crown}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2016},
-}
-
-@Article{pace1997sparse,
- author = {Pace, R Kelley and Barry, Ronald},
- title = {Sparse Spatial Autoregressions},
- number = {3},
- pages = {291--297},
- volume = {33},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Statistics \& Probability Letters},
- year = {1997},
-}
-
-@Unpublished{parr2018matrix,
- author = {Parr, Terence and Howard, Jeremy},
- title = {The Matrix Calculus You Need for Deep Learning},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {1802.01528},
- eprinttype = {arxiv},
- year = {2018},
-}
-
-@Unpublished{pawelczyk2021carla,
- author = {Pawelczyk, Martin and Bielawski, Sascha and van den Heuvel, Johannes and Richter, Tobias and Kasneci, Gjergji},
- title = {Carla: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {2108.00783},
- eprinttype = {arxiv},
- year = {2021},
-}
-
-@Book{pearl2018book,
- author = {Pearl, Judea and Mackenzie, Dana},
- title = {The Book of Why: The New Science of Cause and Effect},
- publisher = {{Basic books}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2018},
-}
-
-@Article{pearl2019seven,
- author = {Pearl, Judea},
- title = {The Seven Tools of Causal Inference, with Reflections on Machine Learning},
- number = {3},
- pages = {54--60},
- volume = {62},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Communications of the ACM},
- year = {2019},
-}
-
-@Article{pedregosa2011scikitlearn,
- author = {Pedregosa, Fabian and Varoquaux, Ga{\"e}l and Gramfort, Alexandre and Michel, Vincent and Thirion, Bertrand and Grisel, Olivier and Blondel, Mathieu and Prettenhofer, Peter and Weiss, Ron and Dubourg, Vincent and others},
- title = {Scikit-Learn: {{Machine}} Learning in {{Python}}},
- pages = {2825--2830},
- volume = {12},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {the Journal of machine Learning research},
- year = {2011},
-}
-
-@Book{perry2010economic,
- author = {Perry, George L and Tobin, James},
- title = {Economic {{Events}}, {{Ideas}}, and {{Policies}}: The 1960s and After},
- publisher = {{Brookings Institution Press}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2010},
-}
-
-@Article{pfaff2008var,
- author = {Pfaff, Bernhard and others},
- title = {{{VAR}}, {{SVAR}} and {{SVEC}} Models: {{Implementation}} within {{R}} Package Vars},
- number = {4},
- pages = {1--32},
- volume = {27},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Journal of Statistical Software},
- year = {2008},
-}
-
-@Book{pindyck2014microeconomics,
- author = {Pindyck, Robert S and Rubinfeld, Daniel L},
- title = {Microeconomics},
- publisher = {{Pearson Education}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2014},
-}
-
-@Article{pope2011numbers,
- author = {Pope, Devin and Simonsohn, Uri},
- title = {Round Numbers as Goals: {{Evidence}} from Baseball, {{SAT}} Takers, and the Lab},
- number = {1},
- pages = {71--79},
- volume = {22},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Psychological science},
- year = {2011},
-}
-
-@InProceedings{poyiadzi2020face,
- author = {Poyiadzi, Rafael and Sokol, Kacper and Santos-Rodriguez, Raul and De Bie, Tijl and Flach, Peter},
- booktitle = {Proceedings of the {{AAAI}}/{{ACM Conference}} on {{AI}}, {{Ethics}}, and {{Society}}},
- title = {{{FACE}}: {{Feasible}} and Actionable Counterfactual Explanations},
- pages = {344--350},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2020},
-}
-
-@Article{qu2015estimating,
- author = {Qu, Xi and Lee, Lung-fei},
- title = {Estimating a Spatial Autoregressive Model with an Endogenous Spatial Weight Matrix},
- number = {2},
- pages = {209--232},
- volume = {184},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Journal of Econometrics},
- year = {2015},
-}
-
-@Article{rabanser2019failing,
- author = {Rabanser, Stephan and G{\"u}nnemann, Stephan and Lipton, Zachary},
- title = {Failing Loudly: {{An}} Empirical Study of Methods for Detecting Dataset Shift},
- volume = {32},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Advances in Neural Information Processing Systems},
- year = {2019},
-}
-
-@Unpublished{raghunathan2019adversarial,
- author = {Raghunathan, Aditi and Xie, Sang Michael and Yang, Fanny and Duchi, John C and Liang, Percy},
- title = {Adversarial Training Can Hurt Generalization},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {1906.06032},
- eprinttype = {arxiv},
- year = {2019},
-}
-
-@Unpublished{raj2017taming,
- author = {Raj, Vishnu and Kalyani, Sheetal},
- title = {Taming Non-Stationary Bandits: {{A Bayesian}} Approach},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {1707.09727},
- eprinttype = {arxiv},
- year = {2017},
-}
-
-@InProceedings{rasmussen2003gaussian,
- author = {Rasmussen, Carl Edward},
- booktitle = {Summer School on Machine Learning},
- title = {Gaussian Processes in Machine Learning},
- pages = {63--71},
- publisher = {{Springer}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2003},
-}
-
-@InProceedings{ribeiro2016why,
- author = {Ribeiro, Marco Tulio and Singh, Sameer and Guestrin, Carlos},
- booktitle = {Proceedings of the 22nd {{ACM SIGKDD}} International Conference on Knowledge Discovery and Data Mining},
- title = {"{{Why}} Should i Trust You?" {{Explaining}} the Predictions of Any Classifier},
- pages = {1135--1144},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2016},
-}
-
-@Article{romer1989does,
- author = {Romer, Christina D and Romer, David H},
- title = {Does Monetary Policy Matter? {{A}} New Test in the Spirit of {{Friedman}} and {{Schwartz}}},
- pages = {121--170},
- volume = {4},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {NBER macroeconomics annual},
- year = {1989},
-}
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-@Article{rudin2019stop,
- author = {Rudin, Cynthia},
- title = {Stop Explaining Black Box Machine Learning Models for High Stakes Decisions and Use Interpretable Models Instead},
- number = {5},
- pages = {206--215},
- volume = {1},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Nature Machine Intelligence},
- year = {2019},
-}
-
-@Article{sacerdote2001peer,
- author = {Sacerdote, Bruce},
- title = {Peer Effects with Random Assignment: {{Results}} for {{Dartmouth}} Roommates},
- number = {2},
- pages = {681--704},
- volume = {116},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {The Quarterly journal of economics},
- year = {2001},
-}
-
-@Article{sadinle2019least,
- author = {Sadinle, Mauricio and Lei, Jing and Wasserman, Larry},
- title = {Least Ambiguous Set-Valued Classifiers with Bounded Error Levels},
- number = {525},
- pages = {223--234},
- volume = {114},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- file = {:/Users/FA31DU/Zotero/storage/YXQ8N76A/Sadinle et al. - 2019 - Least ambiguous set-valued classifiers with bounde.pdf:;:/Users/FA31DU/Zotero/storage/ZHB56F3V/01621459.2017.html:},
- journal = {Journal of the American Statistical Association},
- publisher = {{Taylor \& Francis}},
- year = {2019},
-}
-
-@InProceedings{satopaa2011finding,
- author = {Satopaa, Ville and Albrecht, Jeannie and Irwin, David and Raghavan, Barath},
- booktitle = {2011 31st International Conference on Distributed Computing Systems Workshops},
- title = {Finding a" Kneedle" in a Haystack: {{Detecting}} Knee Points in System Behavior},
- pages = {166--171},
- publisher = {{IEEE}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2011},
-}
-
-@InProceedings{schut2021generating,
- author = {Schut, Lisa and Key, Oscar and Mc Grath, Rory and Costabello, Luca and Sacaleanu, Bogdan and Gal, Yarin and others},
- booktitle = {International {{Conference}} on {{Artificial Intelligence}} and {{Statistics}}},
- title = {Generating {{Interpretable Counterfactual Explanations By Implicit Minimisation}} of {{Epistemic}} and {{Aleatoric Uncertainties}}},
- pages = {1756--1764},
- publisher = {{PMLR}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2021},
-}
-
-@Book{schutze2008introduction,
- author = {Sch{\"u}tze, Hinrich and Manning, Christopher D and Raghavan, Prabhakar},
- title = {Introduction to Information Retrieval},
- publisher = {{Cambridge University Press Cambridge}},
- volume = {39},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2008},
-}
-
-@Article{shafir1993reasonbased,
- author = {Shafir, Eldar and Simonson, Itamar and Tversky, Amos},
- title = {Reason-Based Choice},
- number = {1-2},
- pages = {11--36},
- volume = {49},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Cognition},
- year = {1993},
-}
-
-@Article{simonson1989choice,
- author = {Simonson, Itamar},
- title = {Choice Based on Reasons: {{The}} Case of Attraction and Compromise Effects},
- number = {2},
- pages = {158--174},
- volume = {16},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Journal of consumer research},
- year = {1989},
-}
-
-@Article{sims1986are,
- author = {Sims, Christopher A and others},
- title = {Are Forecasting Models Usable for Policy Analysis?},
- issue = {Win},
- pages = {2--16},
- volume = {10},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Quarterly Review},
- year = {1986},
-}
-
-@InProceedings{slack2020fooling,
- author = {Slack, Dylan and Hilgard, Sophie and Jia, Emily and Singh, Sameer and Lakkaraju, Himabindu},
- booktitle = {Proceedings of the {{AAAI}}/{{ACM Conference}} on {{AI}}, {{Ethics}}, and {{Society}}},
- title = {Fooling Lime and Shap: {{Adversarial}} Attacks on Post Hoc Explanation Methods},
- pages = {180--186},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2020},
-}
-
-@Article{slack2021counterfactual,
- author = {Slack, Dylan and Hilgard, Anna and Lakkaraju, Himabindu and Singh, Sameer},
- title = {Counterfactual Explanations Can Be Manipulated},
- volume = {34},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Advances in Neural Information Processing Systems},
- year = {2021},
-}
-
-@Article{slovic1974who,
- author = {Slovic, Paul and Tversky, Amos},
- title = {Who Accepts {{Savage}}'s Axiom?},
- number = {6},
- pages = {368--373},
- volume = {19},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Behavioral science},
- year = {1974},
-}
-
-@Unpublished{spooner2021counterfactual,
- author = {Spooner, Thomas and Dervovic, Danial and Long, Jason and Shepard, Jon and Chen, Jiahao and Magazzeni, Daniele},
- title = {Counterfactual {{Explanations}} for {{Arbitrary Regression Models}}},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {2106.15212},
- eprinttype = {arxiv},
- shortjournal = {arXiv preprint arXiv:2106.15212},
- year = {2021},
-}
-
-@Article{srivastava2014dropout,
- author = {Srivastava, Nitish and Hinton, Geoffrey and Krizhevsky, Alex and Sutskever, Ilya and Salakhutdinov, Ruslan},
- title = {Dropout: A Simple Way to Prevent Neural Networks from Overfitting},
- number = {1},
- pages = {1929--1958},
- volume = {15},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {The journal of machine learning research},
- year = {2014},
-}
-
-@Unpublished{stanton2022bayesian,
- author = {Stanton, Samuel and Maddox, Wesley and Wilson, Andrew Gordon},
- title = {Bayesian {{Optimization}} with {{Conformal Coverage Guarantees}}},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {2210.12496},
- eprinttype = {arxiv},
- file = {:/Users/FA31DU/Zotero/storage/XFGZAB9J/Stanton et al. - 2022 - Bayesian Optimization with Conformal Coverage Guar.pdf:;:/Users/FA31DU/Zotero/storage/RPWYDPVW/2210.html:},
- year = {2022},
-}
-
-@Article{sturm2014simple,
- author = {Sturm, Bob L},
- title = {A Simple Method to Determine If a Music Information Retrieval System Is a ``Horse''},
- number = {6},
- pages = {1636--1644},
- volume = {16},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {IEEE Transactions on Multimedia},
- year = {2014},
-}
-
-@Article{sunstein2003libertarian,
- author = {Sunstein, Cass R and Thaler, Richard H},
- title = {Libertarian Paternalism Is Not an Oxymoron},
- pages = {1159--1202},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {The University of Chicago Law Review},
- year = {2003},
-}
-
-@Book{sutton2018reinforcement,
- author = {Sutton, Richard S and Barto, Andrew G},
- title = {Reinforcement Learning: {{An}} Introduction},
- publisher = {{MIT press}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2018},
-}
-
-@Unpublished{szegedy2013intriguing,
- author = {Szegedy, Christian and Zaremba, Wojciech and Sutskever, Ilya and Bruna, Joan and Erhan, Dumitru and Goodfellow, Ian and Fergus, Rob},
- title = {Intriguing Properties of Neural Networks},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {1312.6199},
- eprinttype = {arxiv},
- year = {2013},
-}
-
-@Article{thaler1981empirical,
- author = {Thaler, Richard},
- title = {Some Empirical Evidence on Dynamic Inconsistency},
- number = {3},
- pages = {201--207},
- volume = {8},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Economics letters},
- year = {1981},
-}
-
-@Article{thaler2004more,
- author = {Thaler, Richard H and Benartzi, Shlomo},
- title = {Save More Tomorrow{\texttrademark}: {{Using}} Behavioral Economics to Increase Employee Saving},
- number = {S1},
- pages = {S164--S187},
- volume = {112},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Journal of political Economy},
- year = {2004},
-}
-
-@Article{tversky1981framing,
- author = {Tversky, Amos and Kahneman, Daniel},
- title = {The Framing of Decisions and the Psychology of Choice},
- number = {4481},
- pages = {453--458},
- volume = {211},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Science (New York, N.Y.)},
- shortjournal = {science},
- year = {1981},
-}
-
-@Article{ungemach2011how,
- author = {Ungemach, Christoph and Stewart, Neil and Reimers, Stian},
- title = {How Incidental Values from the Environment Affect Decisions about Money, Risk, and Delay},
- number = {2},
- pages = {253--260},
- volume = {22},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Psychological Science},
- year = {2011},
-}
-
-@Unpublished{upadhyay2021robust,
- author = {Upadhyay, Sohini and Joshi, Shalmali and Lakkaraju, Himabindu},
- title = {Towards {{Robust}} and {{Reliable Algorithmic Recourse}}},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {2102.13620},
- eprinttype = {arxiv},
- year = {2021},
-}
-
-@InProceedings{ustun2019actionable,
- author = {Ustun, Berk and Spangher, Alexander and Liu, Yang},
- booktitle = {Proceedings of the {{Conference}} on {{Fairness}}, {{Accountability}}, and {{Transparency}}},
- title = {Actionable Recourse in Linear Classification},
- pages = {10--19},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2019},
-}
-
-@Article{vanboven2000egocentric,
- author = {Van Boven, Leaf and Dunning, David and Loewenstein, George},
- title = {Egocentric Empathy Gaps between Owners and Buyers: Misperceptions of the Endowment Effect.},
- number = {1},
- pages = {66},
- volume = {79},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Journal of personality and social psychology},
- year = {2000},
-}
-
-@Book{varshney2022trustworthy,
- author = {Varshney, Kush R.},
- title = {Trustworthy {{Machine Learning}}},
- publisher = {{Independently Published}},
- address = {{Chappaqua, NY, USA}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2022},
-}
-
-@Unpublished{verma2020counterfactual,
- author = {Verma, Sahil and Dickerson, John and Hines, Keegan},
- title = {Counterfactual Explanations for Machine Learning: {{A}} Review},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {2010.10596},
- eprinttype = {arxiv},
- year = {2020},
-}
-
-@Article{verstyuk2020modeling,
- author = {Verstyuk, Sergiy},
- title = {Modeling Multivariate Time Series in Economics: {{From}} Auto-Regressions to Recurrent Neural Networks},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Available at SSRN 3589337},
- year = {2020},
-}
-
-@Article{wachter2017counterfactual,
- author = {Wachter, Sandra and Mittelstadt, Brent and Russell, Chris},
- title = {Counterfactual Explanations without Opening the Black Box: {{Automated}} Decisions and the {{GDPR}}},
- pages = {841},
- volume = {31},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Harv. JL \& Tech.},
- year = {2017},
-}
-
-@Article{wang2018optimal,
- author = {Wang, HaiYing and Zhu, Rong and Ma, Ping},
- title = {Optimal Subsampling for Large Sample Logistic Regression},
- number = {522},
- pages = {829--844},
- volume = {113},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Journal of the American Statistical Association},
- year = {2018},
-}
-
-@Book{wasserman2006all,
- author = {Wasserman, Larry},
- title = {All of Nonparametric Statistics},
- publisher = {{Springer Science \& Business Media}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2006},
-}
-
-@Book{wasserman2013all,
- author = {Wasserman, Larry},
- title = {All of Statistics: A Concise Course in Statistical Inference},
- publisher = {{Springer Science \& Business Media}},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- year = {2013},
-}
-
-@Article{widmer1996learning,
- author = {Widmer, Gerhard and Kubat, Miroslav},
- title = {Learning in the Presence of Concept Drift and Hidden Contexts},
- number = {1},
- pages = {69--101},
- volume = {23},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Machine learning},
- year = {1996},
-}
-
-@Unpublished{wilson2020case,
- author = {Wilson, Andrew Gordon},
- title = {The Case for {{Bayesian}} Deep Learning},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {2001.10995},
- eprinttype = {arxiv},
- year = {2020},
-}
-
-@Article{witten2009penalized,
- author = {Witten, Daniela M and Tibshirani, Robert and Hastie, Trevor},
- title = {A Penalized Matrix Decomposition, with Applications to Sparse Principal Components and Canonical Correlation Analysis},
- number = {3},
- pages = {515--534},
- volume = {10},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Biostatistics (Oxford, England)},
- shortjournal = {Biostatistics},
- year = {2009},
-}
-
-@Article{xu2020epidemiological,
- author = {Xu, Bo and Gutierrez, Bernardo and Mekaru, Sumiko and Sewalk, Kara and Goodwin, Lauren and Loskill, Alyssa and Cohn, Emily and Hswen, Yulin and Hill, Sarah C. and Cobo, Maria M and Zarebski, Alexander and Li, Sabrina and Wu, Chieh-Hsi and Hulland, Erin and Morgan, Julia and Wang, Lin and O'Brien, Katelynn and Scarpino, Samuel V. and Brownstein, John S. and Pybus, Oliver G. and Pigott, David M. and Kraemer, Moritz U. G.},
- title = {Epidemiological Data from the {{COVID-19}} Outbreak, Real-Time Case Information},
- doi = {doi.org/10.1038/s41597-020-0448-0},
- number = {106},
- volume = {7},
- bdsk-url-1 = {https://doi.org/10.1038/s41597-020-0448-0},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Scientific Data},
- year = {2020},
-}
-
-@Article{yeh2009comparisons,
- author = {Yeh, I-Cheng and Lien, Che-hui},
- title = {The Comparisons of Data Mining Techniques for the Predictive Accuracy of Probability of Default of Credit Card Clients},
- number = {2},
- pages = {2473--2480},
- volume = {36},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Expert systems with applications},
- year = {2009},
-}
-
-@Article{zhang1998forecasting,
- author = {Zhang, Guoqiang and Patuwo, B Eddy and Hu, Michael Y},
- title = {Forecasting with Artificial Neural Networks:: {{The}} State of the Art},
- number = {1},
- pages = {35--62},
- volume = {14},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {International journal of forecasting},
- year = {1998},
-}
-
-@Article{zhang2003time,
- author = {Zhang, G Peter},
- title = {Time Series Forecasting Using a Hybrid {{ARIMA}} and Neural Network Model},
- pages = {159--175},
- volume = {50},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {Neurocomputing},
- year = {2003},
-}
-
-@Unpublished{zheng2018dags,
- author = {Zheng, Xun and Aragam, Bryon and Ravikumar, Pradeep and Xing, Eric P},
- title = {Dags with No Tears: {{Continuous}} Optimization for Structure Learning},
- archiveprefix = {arXiv},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- eprint = {1803.01422},
- eprinttype = {arxiv},
- year = {2018},
-}
-
-@Article{zhu2015optimal,
- author = {Zhu, Rong and Ma, Ping and Mahoney, Michael W and Yu, Bin},
- title = {Optimal Subsampling Approaches for Large Sample Linear Regression},
- pages = {arXiv--1509},
- date-added = {2022-12-13 12:58:01 +0100},
- date-modified = {2022-12-13 12:58:01 +0100},
- journal = {arXiv},
- year = {2015},
-}
-
-@Article{barber2021predictive,
- author = {Barber, Rina Foygel and Candès, Emmanuel J. and Ramdas, Aaditya and Tibshirani, Ryan J.},
- title = {Predictive inference with the jackknife+},
- doi = {10.1214/20-AOS1965},
- issn = {0090-5364, 2168-8966},
- number = {1},
- pages = {486--507},
- urldate = {2022-12-13},
- volume = {49},
- abstract = {This paper introduces the jackknife+, which is a novel method for constructing predictive confidence intervals. Whereas the jackknife outputs an interval centered at the predicted response of a test point, with the width of the interval determined by the quantiles of leave-one-out residuals, the jackknife+ also uses the leave-one-out predictions at the test point to account for the variability in the fitted regression function. Assuming exchangeable training samples, we prove that this crucial modification permits rigorous coverage guarantees regardless of the distribution of the data points, for any algorithm that treats the training points symmetrically. Such guarantees are not possible for the original jackknife and we demonstrate examples where the coverage rate may actually vanish. Our theoretical and empirical analysis reveals that the jackknife and the jackknife+ intervals achieve nearly exact coverage and have similar lengths whenever the fitting algorithm obeys some form of stability. Further, we extend the jackknife+ to \$K\$-fold cross validation and similarly establish rigorous coverage properties. Our methods are related to cross-conformal prediction proposed by Vovk (Ann. Math. Artif. Intell. 74 (2015) 9–28) and we discuss connections.},
- file = {:Barber2021 - Predictive Inference with the Jackknife+.pdf:PDF},
- journal = {The Annals of Statistics},
- keywords = {62F40, 62G08, 62G09, conformal inference, cross-validation, distribution-free, jackknife, leave-one-out, stability},
- month = feb,
- publisher = {Institute of Mathematical Statistics},
- year = {2021},
-}
-
-@TechReport{chouldechova2018frontiers,
- author = {Chouldechova, Alexandra and Roth, Aaron},
- title = {The {Frontiers} of {Fairness} in {Machine} {Learning}},
- doi = {10.48550/arXiv.1810.08810},
- eprint = {1810.08810},
- note = {arXiv:1810.08810 [cs, stat] type: article},
- abstract = {The last few years have seen an explosion of academic and popular interest in algorithmic fairness. Despite this interest and the volume and velocity of work that has been produced recently, the fundamental science of fairness in machine learning is still in a nascent state. In March 2018, we convened a group of experts as part of a CCC visioning workshop to assess the state of the field, and distill the most promising research directions going forward. This report summarizes the findings of that workshop. Along the way, it surveys recent theoretical work in the field and points towards promising directions for research.},
- archiveprefix = {arxiv},
- file = {:chouldechova2018frontiers - The Frontiers of Fairness in Machine Learning.pdf:PDF},
- keywords = {Computer Science - Machine Learning, Computer Science - Data Structures and Algorithms, Computer Science - Computer Science and Game Theory, Statistics - Machine Learning},
- month = oct,
- school = {arXiv},
- year = {2018},
-}
-
-@Article{pawelczyk2022probabilistically,
- author = {Pawelczyk, Martin and Datta, Teresa and van-den-Heuvel, Johannes and Kasneci, Gjergji and Lakkaraju, Himabindu},
- title = {Probabilistically {Robust} {Recourse}: {Navigating} the {Trade}-offs between {Costs} and {Robustness} in {Algorithmic} {Recourse}},
- file = {:pawelczyk2022probabilistically - Probabilistically Robust Recourse_ Navigating the Trade Offs between Costs and Robustness in Algorithmic Recourse.pdf:PDF},
- journal = {arXiv preprint arXiv:2203.06768},
- shorttitle = {Probabilistically {Robust} {Recourse}},
- year = {2022},
-}
-
-@InProceedings{stutz2022learning,
- author = {Stutz, David and Dvijotham, Krishnamurthy Dj and Cemgil, Ali Taylan and Doucet, Arnaud},
- title = {Learning {Optimal} {Conformal} {Classifiers}},
- language = {en},
- url = {https://openreview.net/forum?id=t8O-4LKFVx},
- urldate = {2023-02-13},
- abstract = {Modern deep learning based classifiers show very high accuracy on test data but this does not provide sufficient guarantees for safe deployment, especially in high-stake AI applications such as medical diagnosis. Usually, predictions are obtained without a reliable uncertainty estimate or a formal guarantee. Conformal prediction (CP) addresses these issues by using the classifier's predictions, e.g., its probability estimates, to predict confidence sets containing the true class with a user-specified probability. However, using CP as a separate processing step after training prevents the underlying model from adapting to the prediction of confidence sets. Thus, this paper explores strategies to differentiate through CP during training with the goal of training model with the conformal wrapper end-to-end. In our approach, conformal training (ConfTr), we specifically "simulate" conformalization on mini-batches during training. Compared to standard training, ConfTr reduces the average confidence set size (inefficiency) of state-of-the-art CP methods applied after training. Moreover, it allows to "shape" the confidence sets predicted at test time, which is difficult for standard CP. On experiments with several datasets, we show ConfTr can influence how inefficiency is distributed across classes, or guide the composition of confidence sets in terms of the included classes, while retaining the guarantees offered by CP.},
- file = {:stutz2022learning - Learning Optimal Conformal Classifiers.pdf:PDF},
- month = may,
- year = {2022},
-}
-
-@InProceedings{grathwohl2020your,
- author = {Grathwohl, Will and Wang, Kuan-Chieh and Jacobsen, Joern-Henrik and Duvenaud, David and Norouzi, Mohammad and Swersky, Kevin},
- title = {Your classifier is secretly an energy based model and you should treat it like one},
- language = {en},
- url = {https://openreview.net/forum?id=Hkxzx0NtDB},
- urldate = {2023-02-13},
- abstract = {We propose to reinterpret a standard discriminative classifier of p(y{\textbar}x) as an energy based model for the joint distribution p(x, y). In this setting, the standard class probabilities can be easily computed as well as unnormalized values of p(x) and p(x{\textbar}y). Within this framework, standard discriminative architectures may be used and the model can also be trained on unlabeled data. We demonstrate that energy based training of the joint distribution improves calibration, robustness, and out-of-distribution detection while also enabling our models to generate samples rivaling the quality of recent GAN approaches. We improve upon recently proposed techniques for scaling up the training of energy based models and present an approach which adds little overhead compared to standard classification training. Our approach is the first to achieve performance rivaling the state-of-the-art in both generative and discriminative learning within one hybrid model.},
- file = {:grathwohl2020your - Your Classifier Is Secretly an Energy Based Model and You Should Treat It like One.pdf:PDF},
- month = mar,
- year = {2020},
-}
-
-@Book{murphy2023probabilistic,
- author = {Murphy, Kevin P.},
- date = {2023},
- title = {Probabilistic machine learning: {Advanced} topics},
- publisher = {MIT Press},
- shorttitle = {Probabilistic machine learning},
-}
-
-@TechReport{artelt2021evaluating,
- author = {Artelt, André and Vaquet, Valerie and Velioglu, Riza and Hinder, Fabian and Brinkrolf, Johannes and Schilling, Malte and Hammer, Barbara},
- date = {2021-07},
- institution = {arXiv},
- title = {Evaluating {Robustness} of {Counterfactual} {Explanations}},
- note = {arXiv:2103.02354 [cs] type: article},
- url = {http://arxiv.org/abs/2103.02354},
- urldate = {2023-03-24},
- abstract = {Transparency is a fundamental requirement for decision making systems when these should be deployed in the real world. It is usually achieved by providing explanations of the system's behavior. A prominent and intuitive type of explanations are counterfactual explanations. Counterfactual explanations explain a behavior to the user by proposing actions -- as changes to the input -- that would cause a different (specified) behavior of the system. However, such explanation methods can be unstable with respect to small changes to the input -- i.e. even a small change in the input can lead to huge or arbitrary changes in the output and of the explanation. This could be problematic for counterfactual explanations, as two similar individuals might get very different explanations. Even worse, if the recommended actions differ considerably in their complexity, one would consider such unstable (counterfactual) explanations as individually unfair. In this work, we formally and empirically study the robustness of counterfactual explanations in general, as well as under different models and different kinds of perturbations. Furthermore, we propose that plausible counterfactual explanations can be used instead of closest counterfactual explanations to improve the robustness and consequently the individual fairness of counterfactual explanations.},
- annotation = {Comment: Rewrite paper to make things more clear; Remove one theorem \& corollary due to buggy proof},
- file = {:artelt2021evaluating - Evaluating Robustness of Counterfactual Explanations.pdf:PDF},
- keywords = {Computer Science - Machine Learning, Computer Science - Artificial Intelligence},
-}
-
-@Article{guidotti2022counterfactual,
- author = {Guidotti, Riccardo},
- date = {2022-04},
- journaltitle = {Data Mining and Knowledge Discovery},
- title = {Counterfactual explanations and how to find them: literature review and benchmarking},
- doi = {10.1007/s10618-022-00831-6},
- issn = {1573-756X},
- language = {en},
- url = {https://doi.org/10.1007/s10618-022-00831-6},
- urldate = {2023-03-24},
- abstract = {Interpretable machine learning aims at unveiling the reasons behind predictions returned by uninterpretable classifiers. One of the most valuable types of explanation consists of counterfactuals. A counterfactual explanation reveals what should have been different in an instance to observe a diverse outcome. For instance, a bank customer asks for a loan that is rejected. The counterfactual explanation consists of what should have been different for the customer in order to have the loan accepted. Recently, there has been an explosion of proposals for counterfactual explainers. The aim of this work is to survey the most recent explainers returning counterfactual explanations. We categorize explainers based on the approach adopted to return the counterfactuals, and we label them according to characteristics of the method and properties of the counterfactuals returned. In addition, we visually compare the explanations, and we report quantitative benchmarking assessing minimality, actionability, stability, diversity, discriminative power, and running time. The results make evident that the current state of the art does not provide a counterfactual explainer able to guarantee all these properties simultaneously.},
- file = {Full Text PDF:https\://link.springer.com/content/pdf/10.1007%2Fs10618-022-00831-6.pdf:application/pdf},
- keywords = {Explainable AI, Counterfactual explanations, Contrastive explanations, Interpretable machine learning},
- shorttitle = {Counterfactual explanations and how to find them},
-}
-
-@TechReport{mahajan2020preserving,
- author = {Mahajan, Divyat and Tan, Chenhao and Sharma, Amit},
- date = {2020-06},
- institution = {arXiv},
- title = {Preserving {Causal} {Constraints} in {Counterfactual} {Explanations} for {Machine} {Learning} {Classifiers}},
- doi = {10.48550/arXiv.1912.03277},
- note = {arXiv:1912.03277 [cs, stat] type: article},
- url = {http://arxiv.org/abs/1912.03277},
- urldate = {2023-03-24},
- abstract = {To construct interpretable explanations that are consistent with the original ML model, counterfactual examples---showing how the model's output changes with small perturbations to the input---have been proposed. This paper extends the work in counterfactual explanations by addressing the challenge of feasibility of such examples. For explanations of ML models in critical domains such as healthcare and finance, counterfactual examples are useful for an end-user only to the extent that perturbation of feature inputs is feasible in the real world. We formulate the problem of feasibility as preserving causal relationships among input features and present a method that uses (partial) structural causal models to generate actionable counterfactuals. When feasibility constraints cannot be easily expressed, we consider an alternative mechanism where people can label generated CF examples on feasibility: whether it is feasible to intervene and realize the candidate CF example from the original input. To learn from this labelled feasibility data, we propose a modified variational auto encoder loss for generating CF examples that optimizes for feasibility as people interact with its output. Our experiments on Bayesian networks and the widely used ''Adult-Income'' dataset show that our proposed methods can generate counterfactual explanations that better satisfy feasibility constraints than existing methods.. Code repository can be accessed here: {\textbackslash}textit\{https://github.com/divyat09/cf-feasibility\}},
- annotation = {Comment: 2019 NeurIPS Workshop on Do the right thing: Machine learning and Causal Inference for improved decision making},
- file = {:mahajan2020preserving - Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers.pdf:PDF},
- keywords = {Computer Science - Machine Learning, Computer Science - Artificial Intelligence, Statistics - Machine Learning},
-}
-
-@TechReport{antoran2023sampling,
- author = {Antorán, Javier and Padhy, Shreyas and Barbano, Riccardo and Nalisnick, Eric and Janz, David and Hernández-Lobato, José Miguel},
- date = {2023-03},
- institution = {arXiv},
- title = {Sampling-based inference for large linear models, with application to linearised {Laplace}},
- note = {arXiv:2210.04994 [cs, stat] type: article},
- url = {http://arxiv.org/abs/2210.04994},
- urldate = {2023-03-25},
- abstract = {Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost associated with Bayesian linear models constrains this method's application to small networks, small output spaces and small datasets. We address this limitation by introducing a scalable sample-based Bayesian inference method for conjugate Gaussian multi-output linear models, together with a matching method for hyperparameter (regularisation) selection. Furthermore, we use a classic feature normalisation method (the g-prior) to resolve a previously highlighted pathology of the linearised Laplace method. Together, these contributions allow us to perform linearised neural network inference with ResNet-18 on CIFAR100 (11M parameters, 100 outputs x 50k datapoints), with ResNet-50 on Imagenet (50M parameters, 1000 outputs x 1.2M datapoints) and with a U-Net on a high-resolution tomographic reconstruction task (2M parameters, 251k output{\textasciitilde}dimensions).},
- annotation = {Comment: Published at ICLR 2023. This latest Arxiv version is extended with a demonstration of the proposed methods on the Imagenet dataset},
- file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2210.04994.pdf:application/pdf},
- keywords = {Statistics - Machine Learning, Computer Science - Artificial Intelligence, Computer Science - Machine Learning},
-}
-
-@Misc{altmeyer2022conformal,
- author = {Altmeyer, Patrick},
- date = {2022-10},
- title = {{Conformal} {Prediction} in {Julia}},
- language = {en},
- url = {https://www.paltmeyer.com/blog/posts/conformal-prediction/},
- urldate = {2023-03-27},
- abstract = {A (very) gentle introduction to Conformal Prediction in Julia using my new package ConformalPrediction.jl.},
-}
-
-@InProceedings{welling2011bayesian,
- author = {Welling, M. and Teh, Y.},
- date = {2011-06},
- title = {Bayesian {Learning} via {Stochastic} {Gradient} {Langevin} {Dynamics}},
- url = {https://www.semanticscholar.org/paper/Bayesian-Learning-via-Stochastic-Gradient-Langevin-Welling-Teh/aeed631d6a84100b5e9a021ec1914095c66de415},
- urldate = {2023-05-15},
- abstract = {In this paper we propose a new framework for learning from large scale datasets based on iterative learning from small mini-batches. By adding the right amount of noise to a standard stochastic gradient optimization algorithm we show that the iterates will converge to samples from the true posterior distribution as we anneal the stepsize. This seamless transition between optimization and Bayesian posterior sampling provides an inbuilt protection against overfitting. We also propose a practical method for Monte Carlo estimates of posterior statistics which monitors a "sampling threshold" and collects samples after it has been surpassed. We apply the method to three models: a mixture of Gaussians, logistic regression and ICA with natural gradients.},
- annotation = {[TLDR] This paper proposes a new framework for learning from large scale datasets based on iterative learning from small mini-batches by adding the right amount of noise to a standard stochastic gradient optimization algorithm and shows that the iterates will converge to samples from the true posterior distribution as the authors anneal the stepsize.},
- file = {:welling_bayesian_2011 - Bayesian Learning Via Stochastic Gradient Langevin Dynamics.html:URL;:welling2011bayesian - Bayesian Learning Via Stochastic Gradient Langevin Dynamics.pdf:PDF},
-}
-
-@Article{gill2010circular,
- author = {Gill, Jeff and Hangartner, Dominik},
- date = {2010},
- journaltitle = {Political Analysis},
- title = {Circular {Data} in {Political} {Science} and {How} to {Handle} {It}},
- doi = {10.1093/pan/mpq009},
- issn = {1047-1987, 1476-4989},
- language = {en},
- number = {3},
- pages = {316--336},
- url = {https://www.cambridge.org/core/journals/political-analysis/article/circular-data-in-political-science-and-how-to-handle-it/6DF2D9DA60C455E6A48FFB0FF011F747},
- urldate = {2023-05-15},
- volume = {18},
- abstract = {There has been no attention to circular (purely cyclical) data in political science research. We show that such data exist and are mishandled by models that do not take into account the inherently recycling nature of some phenomenon. Clock and calendar effects are the obvious cases, but directional data are observed as well. We describe a standard maximum likelihood regression modeling framework based on the von Mises distribution, then develop a general Bayesian regression procedure for the first time, providing an easy-to-use Metropolis-Hastings sampler for this approach. Applications include a chronographic analysis of U.S. domestic terrorism and directional party preferences in a two-dimensional ideological space for German Bundestag elections. The results demonstrate the importance of circular models to handle periodic and directional data in political science.},
- file = {Full Text PDF:https\://www.cambridge.org/core/services/aop-cambridge-core/content/view/6DF2D9DA60C455E6A48FFB0FF011F747/S1047198700012493a.pdf/div-class-title-circular-data-in-political-science-and-how-to-handle-it-div.pdf:application/pdf},
- publisher = {Cambridge University Press},
-}
-
-@InProceedings{liu2023goggle,
- author = {Liu, Tennison and Qian, Zhaozhi and Berrevoets, Jeroen and Schaar, Mihaela van der},
- date = {2023-02},
- title = {{GOGGLE}: {Generative} {Modelling} for {Tabular} {Data} by {Learning} {Relational} {Structure}},
- language = {en},
- url = {https://openreview.net/forum?id=fPVRcJqspu},
- urldate = {2023-05-15},
- abstract = {Deep generative models learn highly complex and non-linear representations to generate realistic synthetic data. While they have achieved notable success in computer vision and natural language processing, similar advances have been less demonstrable in the tabular domain. This is partially because generative modelling of tabular data entails a particular set of challenges, including heterogeneous relationships, limited number of samples, and difficulties in incorporating prior knowledge. Additionally, unlike their counterparts in image and sequence domain, deep generative models for tabular data almost exclusively employ fully-connected layers, which encode weak inductive biases about relationships between inputs. Real-world data generating processes can often be represented using relational structures, which encode sparse, heterogeneous relationships between variables. In this work, we learn and exploit relational structure underlying tabular data to better model variable dependence, and as a natural means to introduce regularization on relationships and include prior knowledge. Specifically, we introduce GOGGLE, an end-to-end message passing scheme that jointly learns the relational structure and corresponding functional relationships as the basis of generating synthetic samples. Using real-world datasets, we provide empirical evidence that the proposed method is effective in generating realistic synthetic data and exploiting domain knowledge for downstream tasks.},
- file = {Full Text PDF:https\://openreview.net/pdf?id=fPVRcJqspu:application/pdf},
- shorttitle = {{GOGGLE}},
-}
-
-@TechReport{du2020implicit,
- author = {Du, Yilun and Mordatch, Igor},
- date = {2020-06},
- institution = {arXiv},
- title = {Implicit {Generation} and {Generalization} in {Energy}-{Based} {Models}},
- doi = {10.48550/arXiv.1903.08689},
- note = {arXiv:1903.08689 [cs, stat] type: article},
- url = {http://arxiv.org/abs/1903.08689},
- urldate = {2023-05-16},
- abstract = {Energy based models (EBMs) are appealing due to their generality and simplicity in likelihood modeling, but have been traditionally difficult to train. We present techniques to scale MCMC based EBM training on continuous neural networks, and we show its success on the high-dimensional data domains of ImageNet32x32, ImageNet128x128, CIFAR-10, and robotic hand trajectories, achieving better samples than other likelihood models and nearing the performance of contemporary GAN approaches, while covering all modes of the data. We highlight some unique capabilities of implicit generation such as compositionality and corrupt image reconstruction and inpainting. Finally, we show that EBMs are useful models across a wide variety of tasks, achieving state-of-the-art out-of-distribution classification, adversarially robust classification, state-of-the-art continual online class learning, and coherent long term predicted trajectory rollouts.},
- file = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1903.08689.pdf:application/pdf},
- keywords = {Computer Science - Machine Learning, Computer Science - Computer Vision and Pattern Recognition, Statistics - Machine Learning},
-}
-
-@Comment{jabref-meta: databaseType:biblatex;}
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diff --git a/paper/aaai/paper.tex b/paper/aaai/paper.tex
index d481f00a..c1561ad4 100644
--- a/paper/aaai/paper.tex
+++ b/paper/aaai/paper.tex
@@ -117,8 +117,7 @@
% nouns, adverbs, adjectives should be capitalized, including both words in hyphenated terms, while
% articles, conjunctions, and prepositions are lower case unless they
% directly follow a colon or long dash
-\title{ECCCos from the Black Box:\\
-Faithful Explanations through\\
+\title{Faithful Model Explanations through\\
Energy-Constrained Conformal Counterfactuals}
\author{
%Authors
diff --git a/paper/appendix.tex b/paper/appendix.tex
index 9a44cb0e..623aa6c3 100644
--- a/paper/appendix.tex
+++ b/paper/appendix.tex
@@ -75,7 +75,7 @@ where $\hat{q}$ denotes the $(1-\alpha)$-quantile of $\mathcal{S}$ and $\alpha$
Observe from Equation~\ref{eq:scp} that Conformal Prediction works on an instance-level basis, much like CE are local. The prediction set for an individual instance $\mathbf{x}_i$ depends only on the characteristics of that sample and the specified error rate. Intuitively, the set is more likely to include multiple labels for samples that are difficult to classify, so the set size is indicative of predictive uncertainty. To see why this effect is exacerbated by small choices for $\alpha$ consider the case of $\alpha=0$, which requires that the true label is covered by the prediction set with probability equal to 1.
-\subsubsection{Differentiability}
+\subsubsection{Differentiability}\label{app:cp-diff}
The fact that conformal classifiers produce set-valued predictions introduces a challenge: it is not immediately obvious how to use such classifiers in the context of gradient-based counterfactual search. Put differently, it is not clear how to use prediction sets in Equation~\ref{eq:general}. Fortunately, \citet{stutz2022learning} have recently proposed a framework for Conformal Training that also hinges on differentiability. Specifically, they show how Stochastic Gradient Descent can be used to train classifiers not only for the discriminative task but also for additional objectives related to Conformal Prediction. One such objective is \textit{efficiency}: for a given target error rate $\alpha$, the efficiency of a conformal classifier improves as its average prediction set size decreases. To this end, the authors introduce a smooth set size penalty defined in Equation~\ref{eq:setsize} in the body of this paper. Formally, it is defined as $C_{\theta,\mathbf{y}}(\mathbf{x}_i;\alpha):=\sigma\left((s(\mathbf{x}_i,\mathbf{y})-\alpha) T^{-1}\right)$ for $\mathbf{y}\in\mathcal{Y}$, where $\sigma$ is the sigmoid function and $T$ is a hyper-parameter used for temperature scaling~\citep{stutz2022learning}.
diff --git a/paper/bib.bib b/paper/bib.bib
index f7795afd..fbc56554 100644
--- a/paper/bib.bib
+++ b/paper/bib.bib
@@ -3125,6 +3125,20 @@
keywords = {Computers / Data Science / Machine Learning, Computers / Image Processing, Computers / Computer Science, Computers / Machine Theory, Computers / Data Science / Neural Networks, Computers / Programming / General, Computers / Languages / Python, Computers / Data Science / Data Visualization},
}
+@Article{samoilescu2021model,
+ author = {Samoilescu, Robert-Florian and Van Looveren, Arnaud and Klaise, Janis},
+ title = {Model-agnostic and scalable counterfactual explanations via reinforcement learning},
+ journal = {arXiv preprint arXiv:2106.02597},
+ year = {2021},
+}
+
+@Article{chen2021seven,
+ author = {Chen, Jiahao and Storchan, Victor},
+ title = {Seven challenges for harmonizing explainability requirements},
+ journal = {arXiv preprint arXiv:2108.05390},
+ year = {2021},
+}
+
@Comment{jabref-meta: databaseType:biblatex;}
@Comment{jabref-meta: keypatterndefault:[auth:lower][year][veryshorttitle:lower];}
diff --git a/paper/body.tex b/paper/body.tex
index 750f31d5..46f4aa15 100644
--- a/paper/body.tex
+++ b/paper/body.tex
@@ -2,7 +2,7 @@
\begin{abstract}
- Counterfactual explanations offer an intuitive and straightforward way to explain black-box models and offer algorithmic recourse to individuals. To address the need for plausible explanations, existing work has primarily relied on surrogate models to learn how the input data is distributed. This effectively reallocates the task of learning realistic explanations for the data from the model itself to the surrogate. Consequently, the generated explanations may seem plausible to humans but need not necessarily describe the behaviour of the black-box model faithfully. We formalise this notion of faithfulness through the introduction of a tailored evaluation metric and propose a novel algorithmic framework for generating \textbf{E}nergy-\textbf{C}onstrained \textbf{C}onformal \textbf{Co}unterfactuals (ECCCos) that are only as plausible as the model permits. Through extensive empirical studies, we demonstrate that ECCCos reconcile the need for faithfulness and plausibility. In particular, we show that for models with gradient access, it is possible to achieve state-of-the-art performance without the need for surrogate models. To do so, our framework relies solely on properties defining the black-box model itself by leveraging recent advances in energy-based modelling and conformal prediction. To our knowledge, this is the first venture in this direction for generating faithful counterfactual explanations. Thus, we anticipate that ECCCos can serve as a baseline for future research. We believe that our work opens avenues for researchers and practitioners seeking tools to better distinguish trustworthy from unreliable models.
+ Counterfactual explanations offer an intuitive and straightforward way to explain black-box models and offer algorithmic recourse to individuals. To address the need for plausible explanations, existing work has primarily relied on surrogate models to learn how the input data is distributed. This effectively reallocates the task of learning realistic explanations for the data from the model itself to the surrogate. Consequently, the generated explanations may seem plausible to humans but need not necessarily describe the behaviour of the black-box model faithfully. We formalise this notion of faithfulness through the introduction of a tailored evaluation metric and propose a novel algorithmic framework for generating \textbf{E}nergy-\textbf{C}onstrained \textbf{C}onformal \textbf{Co}unterfactuals that are only as plausible as the model permits. Through extensive empirical studies, we demonstrate that \textit{ECCCo} reconciles the need for faithfulness and plausibility. In particular, we show that for models with gradient access, it is possible to achieve state-of-the-art performance without the need for surrogate models. To do so, our framework relies solely on properties defining the black-box model itself by leveraging recent advances in energy-based modelling and conformal prediction. To our knowledge, this is the first venture in this direction for generating faithful counterfactual explanations. Thus, we anticipate that \textit{ECCCo} can serve as a baseline for future research. We believe that our work opens avenues for researchers and practitioners seeking tools to better distinguish trustworthy from unreliable models.
\end{abstract}
\section{Introduction}\label{intro}
@@ -19,11 +19,11 @@ In this work, we draw closer attention to model faithfulness rather than fidelit
\begin{itemize}
\item We show that fidelity is an insufficient evaluation metric for counterfactuals (Section~\ref{fidelity}) and propose a definition of faithfulness that gives rise to more suitable metrics (Section~\ref{faithfulness}).
- \item We introduce a novel algorithmic approach aimed at generating Energy-Constrained Conformal Counterfactuals (ECCCos) that faithfully explain model behaviour in Section~\ref{meth}.
- \item We provide extensive empirical evidence demonstrating that ECCCos faithfully explain model behaviour and attain plausibility only when appropriate (Section~\ref{emp}).
+ \item We introduce a ECCCo: a novel algorithmic approach aimed at generating Energy-Constrained Conformal Counterfactuals that faithfully explain model behaviour in Section~\ref{meth}.
+ \item We provide extensive empirical evidence demonstrating that ecccos faithfully explain model behaviour and attain plausibility only when appropriate (Section~\ref{emp}).
\end{itemize}
-To our knowledge, this is the first venture in this direction for generating faithful counterfactuals. Thus, we anticipate that ECCCos can serve as a baseline for future research. We believe that our work opens avenues for researchers and practitioners seeking tools to better distinguish trustworthy from unreliable models.
+To our knowledge, this is the first venture in this direction for generating faithful counterfactuals. Thus, we anticipate that \textit{ECCCo} can serve as a baseline for future research. We believe that our work opens avenues for researchers and practitioners seeking tools to better distinguish trustworthy from unreliable models.
\section{Background}\label{background}
@@ -70,7 +70,7 @@ Since \textit{Wachter} is only concerned with proximity, the generated counterfa
So which of the counterfactuals most faithfully explains the behaviour of our image classifier? Fidelity cannot help us to make that judgement, because all of these counterfactuals have full fidelity. Thus, fidelity is an insufficient evaluation metric to assess the faithfulness of CE.
-\section{A New Notion of Faithfulness}\label{faithfulness}
+\section{Faithful first, Plausible second}\label{faithfulness}
Considering the limitations of fidelity as demonstrated in the previous section, analogous to Definition~\ref{def:plausible}, we introduce a new notion of faithfulness in the context of CE:
@@ -95,6 +95,33 @@ where $\mathbf{r}_j \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ is the stochastic t
Generating multiple samples using SGLD thus yields an empirical distribution $\widehat{\mathbf{X}}_{\theta,\mathbf{y}^+}$ that approximates what the model has learned about the input data. While in the context of EBM, this is usually done during training, we propose to repurpose this approach during inference in order to evaluate and generate faithful model explanations.
+\subsection{Quantifying the Model's Predictive Uncertainty}
+
+Faithful counterfactuals can be expected to also be plausible if the learned conditional distribution $\mathcal{X}_{\theta}|\mathbf{y}^+$ (Defintion~\ref{def:faithful}) is close to the true conditional distribution $\mathcal{X}|\mathbf{y}^+$ (Definition~\ref{def:plausible}). We can further improve plausibility of counterfactuals without the need for surrogate models that may interfer with faithfulness by minimizing predictive uncertainty~\citep{schut2021generating}.
+Unfortunately, this approach relies on the assumption that the model itself can provide predictive uncertainty estimates, which may be too restrictive in practice.
+
+To relax this assumption, we use conformal prediction (CP), an approach to predictive uncertainty quantification that has recently gained popularity~\citep{angelopoulos2021gentle,manokhin2022awesome}. Crucially for our intended application, CP is model-agnostic and can be applied during inference without placing any restrictions on model training. Intuitively, CP works under the premise of turning heuristic notions of uncertainty into rigorous uncertainty estimates by repeatedly sifting through the training data or a dedicated calibration dataset.
+
+Conformal classifiers produce prediction sets for individual inputs that include all output labels that can be reasonably attributed to the input. Finally, classification sets are formed as follows,
+
+\begin{equation}\label{eq:scp}
+ \begin{aligned}
+ C_{\theta}(\mathbf{x}_i;\alpha)=\{\mathbf{y}: s(\mathbf{x}_i,\mathbf{y}) \le \hat{q}\}
+ \end{aligned}
+\end{equation}
+
+where $\hat{q}$ denotes the $(1-\alpha)$-quantile of $\mathcal{S}$ and $\alpha$ is a predetermined error rate.
+
+These sets tend to be larger for inputs that do not conform with the training data and are characterized by high predictive uncertainty. To leverage this notion of predictive uncertainty in the context of gradient-based counterfactual search, we use a smooth set size penalty introduced by~\citet{stutz2022learning}:
+
+\begin{equation}\label{eq:setsize}
+ \begin{aligned}
+ \Omega(C_{\theta}(\mathbf{x};\alpha))&=\max \left(0, \sum_{\mathbf{y}\in\mathcal{Y}}C_{\theta,\mathbf{y}}(\mathbf{x}_i;\alpha) - \kappa \right)
+ \end{aligned}
+\end{equation}
+
+Here, $\kappa \in \{0,1\}$ is a hyper-parameter and $C_{\theta,\mathbf{y}}(\mathbf{x}_i;\alpha)$ can be interpreted as the probability of label $\mathbf{y}$ being included in the prediction set (see Appendix~\ref{app:cp-diff} for details). In order to compute this penalty for any black-box model we merely need to perform a single calibration pass through a holdout set $\mathcal{D}_{\text{cal}}$. Arguably, data is typically abundant and in most applications, practitioners tend to hold out a test data set anyway. Consequently, CP removes the restriction on the family of predictive models, at the small cost of reserving a subset of the available data for calibration. This particular case of conformal prediction is referred to as *split conformal prediction* (SCP) as it involves splitting the training data into a proper training dataset and a calibration dataset.
+
\subsection{Evaluating Plausibility and Faithfulness}
The parallels between our definitions of plausibility and faithfulness imply that we can also use similar evaluation metrics in both cases. Since existing work has focused heavily on plausibility, it offers a useful starting point. In particular,~\citet{guidotti2022counterfactual} have proposed an implausibility metric that measures the distance of the counterfactual from its nearest neighbour in the target class. As this distance is reduced, counterfactuals get more plausible under the assumption that the nearest neighbour itself is plausible in the sense of Definition~\ref{def:plausible}. In this work, we use the following adapted implausibility metric,
@@ -119,7 +146,7 @@ Specifically, we form this subset based on the $n_E$ generated samples with the
\section{Energy-Constrained Conformal Counterfactuals}\label{meth}
-Given our proposed notion of faithfulness, we now describe \textit{ECCCo}, our proposed framework for generating Energy-Constrained Conformal Counterfactuals (ECCCos). It is based on the premise that counterfactuals should first and foremost be faithful. Plausibility, as a secondary concern, is then still attainable, but only to the degree that the black-box model itself has learned plausible explanations for the underlying data.
+Given our proposed notion of faithfulness, we now describe \textit{ECCCo}, our proposed framework for generating Energy-Constrained Conformal Counterfactuals. It is based on the premise that counterfactuals should first and foremost be faithful. Plausibility, as a secondary concern, is then still attainable, but only to the degree that the black-box model itself has learned plausible explanations for the underlying data.
We begin by stating our proposed objective function, which involves tailored loss and penalty functions that we will explain in the following. In particular, we extend Equation~\ref{eq:general} as follows:
@@ -130,19 +157,7 @@ We begin by stating our proposed objective function, which involves tailored los
\end{aligned}
\end{equation}
-The first penalty term involving $\lambda_1$ induces proximity like in~\citet{wachter2017counterfactual}. Our default choice for $\text{dist}(\cdot)$ is the L1 Norm due to its sparsity-inducing properties. The second penalty term involving $\lambda_2$ induces faithfulness by constraining the energy of the generated counterfactual where $\text{unfaith}(\cdot)$ corresponds to the metric defined in Equation~\ref{eq:faith}. The third and final penalty term involving $\lambda_3$ introduces a new concept: it ensures that the generated counterfactual is associated with low predictive uncertainty. As mentioned in Section~\ref{background},~\citet{schut2021generating} have shown that plausible counterfactuals can be generated implicitly through predictive uncertainty minimization. Unfortunately, this relies on the assumption that the model itself can provide predictive uncertainty estimates, which may be too restrictive in practice.
-
-To relax this assumption, we leverage recent advances in conformal prediction (CP), an approach to predictive uncertainty quantification that has recently gained popularity~\citep{angelopoulos2021gentle,manokhin2022awesome}. Crucially for our intended application, CP is model-agnostic and can be applied during inference without placing any restrictions on model training. Intuitively, CP works under the premise of turning heuristic notions of uncertainty into rigorous uncertainty estimates by repeatedly sifting through the training data or a dedicated calibration dataset. Conformal classifiers produce prediction sets for individual inputs that include all output labels that can be reasonably attributed to the input. These sets tend to be larger for inputs that do not conform with the training data and are characterized by high predictive uncertainty.
-
-In order to generate counterfactuals that are associated with low predictive uncertainty, we use a smooth set size penalty introduced by~\citet{stutz2022learning} in the context of conformal training:
-
-\begin{equation}\label{eq:setsize}
- \begin{aligned}
- \Omega(C_{\theta}(\mathbf{x};\alpha))&=\max \left(0, \sum_{\mathbf{y}\in\mathcal{Y}}C_{\theta,\mathbf{y}}(\mathbf{x}_i;\alpha) - \kappa \right)
- \end{aligned}
-\end{equation}
-
-Here, $\kappa \in \{0,1\}$ is a hyper-parameter and $C_{\theta,\mathbf{y}}(\mathbf{x}_i;\alpha)$ can be interpreted as the probability of label $\mathbf{y}$ being included in the prediction set. In order to compute this penalty for any black-box model we merely need to perform a single calibration pass through a holdout set $\mathcal{D}_{\text{cal}}$. Arguably, data is typically abundant and in most applications, practitioners tend to hold out a test data set anyway. Consequently, CP removes the restriction on the family of predictive models, at the small cost of reserving a subset of the available data for calibration. This particular case of conformal prediction is referred to as *split conformal prediction* (SCP) as it involves splitting the training data into a proper training dataset and a calibration dataset. Further details are provided in Appendix~\ref{app:cp}.
+The first penalty term involving $\lambda_1$ induces proximity like in~\citet{wachter2017counterfactual}. Our default choice for $\text{dist}(\cdot)$ is the L1 Norm due to its sparsity-inducing properties. The second penalty term involving $\lambda_2$ induces faithfulness by constraining the energy of the generated counterfactual where $\text{unfaith}(\cdot)$ corresponds to the metric defined in Equation~\ref{eq:faith}. The third and final penalty term involving $\lambda_3$ ensures that the generated counterfactual is associated with low predictive uncertainty.
\begin{figure}
\centering
@@ -179,11 +194,11 @@ Algorithm~\ref{alg:eccco} describes how exactly \textit{ECCCo} works. For the sa
Our goal in this section is to shed light on the following research questions:
\begin{question}[Faithfulness]\label{rq:faithfulness}
- To what extent are ECCCos more faithful than counterfactuals produced by state-of-the-art generators?
+ To what extent are counterfactuals generated by \textit{ECCCo} more faithful than those produced by state-of-the-art generators?
\end{question}
\begin{question}[Balancing Objectives]\label{rq:plausibility}
- Compared to state-of-the-art generators, how do ECCCos balance the two key objectives of faithfulness and plausibility?
+ Compared to state-of-the-art generators, how does \textit{ECCCo} balance the two key objectives of faithfulness and plausibility?
\end{question}
The second question is motivated by the intuition that faithfulness and plausibility should coincide for models that have learned plausible explanations of the data.
@@ -196,7 +211,7 @@ We use both synthetic and real-world datasets from different domains, all of whi
As for real-world data, we follow~\citet{schut2021generating} and use the \textit{MNIST}~\citep{lecun1998mnist} dataset containing images of handwritten digits such as the example shown above in Figure~\ref{fig:motiv}. From the social sciences domain, we include Give Me Some Credit (\textit{GMSC})~\citep{kaggle2011give}: a tabular dataset that has been studied extensively in the literature on algorithmic recourse~\citep{pawelczyk2021carla}. It consists of 11 numeric features that can be used to predict the binary outcome variable indicating whether retail borrowers experience financial distress.
-For the predictive modelling tasks, we use simple neural networks (\textit{MLP}) and Joint Energy Models (\textit{JEM}). For the more complex real-world datasets we also use ensembling in each case. Both joint-energy modelling and ensembling have been associated with improved generative properties and adversarial robustness~\citep{grathwohl2020your,lakshminarayanan2016simple}, so we expect this to be positively correlated with the plausibility of ECCCos. To account for stochasticity, we generate multiple counterfactuals for each target class, generator, model and dataset. Specifically, we randomly sample $n^{-}$ times from the subset of individuals for which the given model predicts the non-target class $\mathbf{y}^{-}$ given the current target. We set $n^{-}=25$ for all of our synthetic datasets, $n^{-}=10$ for \textit{GMSC} and $n^{-}=5$ for \textit{MNIST}. Full details concerning our parameter choices, training procedures and model performance can be found in Appendix~\ref{app:setup}.
+For the predictive modelling tasks, we use simple neural networks (\textit{MLP}) and Joint Energy Models (\textit{JEM}). For the more complex real-world datasets we also use ensembling in each case. Both joint-energy modelling and ensembling have been associated with improved generative properties and adversarial robustness~\citep{grathwohl2020your,lakshminarayanan2016simple}, so we expect this to be positively correlated with the plausibility of \textit{ECCCo}. To account for stochasticity, we generate multiple counterfactuals for each target class, generator, model and dataset. Specifically, we randomly sample $n^{-}$ times from the subset of individuals for which the given model predicts the non-target class $\mathbf{y}^{-}$ given the current target. We set $n^{-}=25$ for all of our synthetic datasets, $n^{-}=10$ for \textit{GMSC} and $n^{-}=5$ for \textit{MNIST}. Full details concerning our parameter choices, training procedures and model performance can be found in Appendix~\ref{app:setup}.
\subsection{Results for Synthetic Data}
@@ -204,7 +219,7 @@ Table~\ref{tab:results-synthetic} shows the key results for the synthetic datase
Starting with the high-level results for our \textit{Linearly Separable} data, we find that \textit{ECCCo} produces the most faithful counterfactuals for both black-box models. This is consistent with our design since \textit{ECCCo} directly enforces faithfulness through regularization. Crucially though, \textit{ECCCo} also produces the most plausible counterfactuals for both models. This dataset is so simple that even the \textit{MLP} has learned plausible explanations of the input data. Zooming in on the granular details for the \textit{Linearly Separable} data, the results for \textit{ECCCo (no CP)} and \textit{ECCCo (no EBM)} indicate that the positive results are dominated by the effect of quantifying and leveraging the model's generative property (EBM). Conformal prediction alone only leads to marginally improved faithfulness and plausibility.
-The findings for the \textit{Moons} dataset are broadly in line with the findings so far: for the \textit{JEM}, \textit{ECCCo} yields substantially more faithful and plausible counterfactuals than all other generators. For the \textit{MLP}, faithfulness is maintained but counterfactuals are not plausible. This high-level pattern is broadly consistent with other more complex datasets and supportive of our narrative, so it is worth highlighting: ECCCos consistently achieve high faithfulness, which---subject to the quality of the model itself---coincides with high plausibility. By comparison, \textit{REVISE} yields the most plausible counterfactuals for the \textit{MLP}, but it does so at the cost of faithfulness. We also observe that the best results for \textit{ECCCo} are achieved when using both penalties. Once again though, the generative component (EBM) has a stronger impact on the positive results for the \textit{JEM}.
+The findings for the \textit{Moons} dataset are broadly in line with the findings so far: for the \textit{JEM}, \textit{ECCCo} yields substantially more faithful and plausible counterfactuals than all other generators. For the \textit{MLP}, faithfulness is maintained but counterfactuals are not plausible. This high-level pattern is broadly consistent with other more complex datasets and supportive of our narrative, so it is worth highlighting: \textit{ECCCo} consistently achieves high faithfulness, which---subject to the quality of the model itself---coincides with high plausibility. By comparison, \textit{REVISE} yields the most plausible counterfactuals for the \textit{MLP}, but it does so at the cost of faithfulness. We also observe that the best results for \textit{ECCCo} are achieved when using both penalties. Once again though, the generative component (EBM) has a stronger impact on the positive results for the \textit{JEM}.
For the \textit{Circles} data, it appears that \textit{REVISE} performs well, but we note that it generates valid counterfactuals only half of the time (see Appendix~\ref{app:results} for a complete overview including additional common evaluation metrics). The underlying VAE with default parameters has not adequately learned the data-generating process. Of course, it is possible to improve generative performance through hyperparameter tuning but this example serves to illustrate that \textit{REVISE} depends on the quality of its surrogate. Independent of the outcome for \textit{REVISE}, however, the results do not seem to indicate that \textit{ECCCo} substantially improves faithfulness and plausibility for the \textit{Circles} data. We think this points to a limitation of our evaluation metrics rather than \textit{ECCCo} itself: computing average distances fails to account for the `wraparound' effect associated with circular data~\citep{gill2010circular}.
@@ -212,9 +227,9 @@ For the \textit{Circles} data, it appears that \textit{REVISE} performs well, bu
\subsection{Results for Real-World Data}
-The results for our real-world datasets are shown in Table~\ref{tab:results-real-world}. Once again the findings indicate that the plausibility of ECCCos is positively correlated with the capacity of the black-box model to distinguish plausible from implausible inputs. The case is very clear for \textit{MNIST}: ECCCos are consistently more faithful than the counterfactuals produced by our benchmark generators and their plausibility gradually improves through ensembling and joint-energy modelling. Interestingly, faithfulness also gradually improves for \textit{REVISE}. This indicates that as our models improve, their generative capacity approaches that of the surrogate VAE used by \textit{REVISE}. The VAE still outperforms our classifiers in this regard, as evident from the fact that \textit{ECCCo} never quite reaches the same level of plausibility as \textit{REVISE}. With reference to Appendix~\ref{app:results} we note that the results for \textit{Schut} need to be discounted as it rarely produces valid counterfactuals for \textit{MNIST}. Relatedly, we find that \textit{ECCCo} is the only generator that consistently achieves full validity. Finally, it is worth noting that \textit{ECCCo} produces counterfactual images with the lowest average predictive uncertainty for all models.
+The results for our real-world datasets are shown in Table~\ref{tab:results-real-world}. Once again the findings indicate that the plausibility attained by \textit{ECCCo} is positively correlated with the capacity of the black-box model to distinguish plausible from implausible inputs. The case is very clear for \textit{MNIST}: \textit{ECCCo} consistently generates more faithful counterfactuals than other generators and plausibility gradually improves through ensembling and joint-energy modelling. Interestingly, faithfulness also gradually improves for \textit{REVISE}. This indicates that as our models improve, their generative capacity approaches that of the surrogate VAE used by \textit{REVISE}. The VAE still outperforms our classifiers in this regard, as evident from the fact that \textit{ECCCo} never quite reaches the same level of plausibility as \textit{REVISE}. With reference to Appendix~\ref{app:results} we note that the results for \textit{Schut} need to be discounted as it rarely produces valid counterfactuals for \textit{MNIST}. Relatedly, we find that \textit{ECCCo} is the only generator that consistently achieves full validity. Finally, it is worth noting that \textit{ECCCo} produces counterfactual images with the lowest average predictive uncertainty for all models.
-For the tabular credit dataset (\textit{GMSC}) it is inherently challenging to use deep neural networks in order to achieve good discriminative performance~\citep{borisov2022deep,grinsztajn2022why} and generative performance~\citep{liu2023goggle}, respectively. In order to achieve high plausibility, \textit{ECCCo} effectively requires classifiers to achieve good performance for both tasks. Since this is a challenging task even for Joint Energy Models, it is not surprising to find that even though \textit{ECCCo} once again achieves state-of-the-art faithfulness, it is outperformed by \textit{REVISE} and \textit{Schut} with respect to plausibility.
+For the tabular credit dataset (\textit{GMSC}) it is inherently challenging to use deep neural networks in order to achieve good discriminative performance~\citep{borisov2022deep,grinsztajn2022why} and generative performance~\citep{liu2022goggle}, respectively. In order to achieve high plausibility, \textit{ECCCo} effectively requires classifiers to achieve good performance for both tasks. Since this is a challenging task even for Joint Energy Models, it is not surprising to find that even though \textit{ECCCo} once again achieves state-of-the-art faithfulness, it is outperformed by \textit{REVISE} and \textit{Schut} with respect to plausibility.
\subsection{Key Takeways}
@@ -224,12 +239,24 @@ To conclude this section, we summarize our findings with reference to the openin
\section{Limitations}
-Even though we have taken considerable measures to study our proposed methodology carefully, limitations can still be identified. In particular, we have found that the performance of \textit{ECCCo} is sensitive to hyperparameter choices. In order to achieve faithfulness, we generally had to penalise the distance from generated samples slightly more than the distance from factual values.
+Even though we have taken considerable measures to study our proposed methodology carefully, limitations can still be identified.
+
+\subsection{Evaluation Metrics}
+
+Our proposed distance-based evaluation metrics for plausibility and faithfulness may not be universally applicable to all types of data. In any case, they depend on choosing a distance metric on a case-by-base basis for different datasets. Arguably, commonly used metrics for measuring other desiderata such as closeness suffer from the same pitfall. We therefore think that future work on counterfactual explanations could benefit from defining universal evaluation metrics.
-Conversely, we have not found that strongly penalising prediction set sizes had any discernable effect. Our results indicate that CP alone is often not sufficient to achieve faithfulness and plausibility, although we acknowledge that this needs to be investigated more thoroughly through future work.
+\subsection{Experiments}
+
+While we have employed various datasets in our experiments that are commonly used in the related literature, we acknowledge that additional real-world data and application is needed to test \textit{ECCCo} and improve upon the ideas we have presented in this work. One challenge in this context is that counterfactual explanations do not scale very well to high-dimensional input data like images~\citep{samoilescu2021model,chen2021seven}. Consequently, we have limited ourselves to studying small image datasets only.
+
+\subsection{Generalizability}
While our approach is readily applicable to models with gradient access like deep neural networks, more work is needed to generalise it to other machine learning models such as decision trees. Relatedly, common challenges associated with energy-based modelling including sensitivity to scale, training instabilities and sensitivity to hyperparameters also apply to \textit{ECCCo}.
+\subsection{Ablation Studies}
+
+In our experiments we have used ablation to understand the roles of the different components of \textit{ECCCo}. Our results here indicate that conformal prediction alone is often not sufficient to achieve faithfulness and plausibility. To test this initial finding more throughly, future work could benefit from more extensive abalation studies that thoroughly tune hyperparameters and investigate different approaches to conformal prediction.
+
\section{Conclusion}
This work leverages recent advances in energy-based modelling and conformal prediction in the context of Explainable Artificial Intelligence. We have proposed a new way to generate counterfactuals that are maximally faithful to the black-box model they aim to explain. Our proposed generator, \textit{ECCCo}, produces plausible counterfactuals if and only if the black-box model itself has learned realistic explanations for the data, which we have demonstrated through rigorous empirical analysis. This should enable researchers and practitioners to use counterfactuals in order to discern trustworthy models from unreliable ones. While the scope of this work limits its generalizability, we believe that \textit{ECCCo} offers a solid baseline for future work on faithful counterfactual explanations.
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