Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models

Benjamin Lengerich, Sarah Tan, Chun-Hao Chang, Giles Hooker, Rich Caruana
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2402-2412, 2020.

Abstract

Models which estimate main effects of individual variables alongside interaction effects have an identifiability challenge: effects can be freely moved between main effects and interaction effects without changing the model prediction. This is a critical problem for interpretability because it permits “contradictory" models to represent the same function. To solve this problem, we propose pure interaction effects: variance in the outcome which cannot be represented by any subset of features. This definition has an equivalence with the Functional ANOVA decomposition. To compute this decomposition, we present a fast, exact algorithm that transforms any piecewise-constant function (such as a tree-based model) into a purified, canonical representation. We apply this algorithm to Generalized Additive Models with interactions trained on several datasets and show large disparity, including contradictions, between the apparent and the purified effects. These results underscore the need to specify data distributions and ensure identifiability before interpreting model parameters.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-lengerich20a, title = {Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models}, author = {Lengerich, Benjamin and Tan, Sarah and Chang, Chun-Hao and Hooker, Giles and Caruana, Rich}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {2402--2412}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/lengerich20a/lengerich20a.pdf}, url = {https://proceedings.mlr.press/v108/lengerich20a.html}, abstract = {Models which estimate main effects of individual variables alongside interaction effects have an identifiability challenge: effects can be freely moved between main effects and interaction effects without changing the model prediction. This is a critical problem for interpretability because it permits “contradictory" models to represent the same function. To solve this problem, we propose pure interaction effects: variance in the outcome which cannot be represented by any subset of features. This definition has an equivalence with the Functional ANOVA decomposition. To compute this decomposition, we present a fast, exact algorithm that transforms any piecewise-constant function (such as a tree-based model) into a purified, canonical representation. We apply this algorithm to Generalized Additive Models with interactions trained on several datasets and show large disparity, including contradictions, between the apparent and the purified effects. These results underscore the need to specify data distributions and ensure identifiability before interpreting model parameters.} }
Endnote
%0 Conference Paper %T Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models %A Benjamin Lengerich %A Sarah Tan %A Chun-Hao Chang %A Giles Hooker %A Rich Caruana %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-lengerich20a %I PMLR %P 2402--2412 %U https://proceedings.mlr.press/v108/lengerich20a.html %V 108 %X Models which estimate main effects of individual variables alongside interaction effects have an identifiability challenge: effects can be freely moved between main effects and interaction effects without changing the model prediction. This is a critical problem for interpretability because it permits “contradictory" models to represent the same function. To solve this problem, we propose pure interaction effects: variance in the outcome which cannot be represented by any subset of features. This definition has an equivalence with the Functional ANOVA decomposition. To compute this decomposition, we present a fast, exact algorithm that transforms any piecewise-constant function (such as a tree-based model) into a purified, canonical representation. We apply this algorithm to Generalized Additive Models with interactions trained on several datasets and show large disparity, including contradictions, between the apparent and the purified effects. These results underscore the need to specify data distributions and ensure identifiability before interpreting model parameters.
APA
Lengerich, B., Tan, S., Chang, C., Hooker, G. & Caruana, R.. (2020). Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:2402-2412 Available from https://proceedings.mlr.press/v108/lengerich20a.html.

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