Representer Point Selection for Explaining Regularized High-dimensional Models

Che-Ping Tsai, Jiong Zhang, Hsiang-Fu Yu, Eli Chien, Cho-Jui Hsieh, Pradeep Kumar Ravikumar
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:34469-34490, 2023.

Abstract

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model’s prediction. We derive consequences for the canonical instances of $\ell_1$ regularized sparse models and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-tsai23a, title = {Representer Point Selection for Explaining Regularized High-dimensional Models}, author = {Tsai, Che-Ping and Zhang, Jiong and Yu, Hsiang-Fu and Chien, Eli and Hsieh, Cho-Jui and Ravikumar, Pradeep Kumar}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {34469--34490}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/tsai23a/tsai23a.pdf}, url = {https://proceedings.mlr.press/v202/tsai23a.html}, abstract = {We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model’s prediction. We derive consequences for the canonical instances of $\ell_1$ regularized sparse models and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.} }
Endnote
%0 Conference Paper %T Representer Point Selection for Explaining Regularized High-dimensional Models %A Che-Ping Tsai %A Jiong Zhang %A Hsiang-Fu Yu %A Eli Chien %A Cho-Jui Hsieh %A Pradeep Kumar Ravikumar %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-tsai23a %I PMLR %P 34469--34490 %U https://proceedings.mlr.press/v202/tsai23a.html %V 202 %X We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model’s prediction. We derive consequences for the canonical instances of $\ell_1$ regularized sparse models and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.
APA
Tsai, C., Zhang, J., Yu, H., Chien, E., Hsieh, C. & Ravikumar, P.K.. (2023). Representer Point Selection for Explaining Regularized High-dimensional Models. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:34469-34490 Available from https://proceedings.mlr.press/v202/tsai23a.html.

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