Efficient nonparametric statistical inference on population feature importance using Shapley values

Brian Williamson, Jean Feng
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:10282-10291, 2020.

Abstract

The true population-level importance of a variable in a prediction task provides useful knowledge about the underlying data-generating mechanism and can help in deciding which measurements to collect in subsequent experiments. Valid statistical inference on this importance is a key component in understanding the population of interest. We present a computationally efficient procedure for estimating and obtaining valid statistical inference on the \textbf{S}hapley \textbf{P}opulation \textbf{V}ariable \textbf{I}mportance \textbf{M}easure (SPVIM). Although the computational complexity of the true SPVIM scales exponentially with the number of variables, we propose an estimator based on randomly sampling only $\Theta(n)$ feature subsets given $n$ observations. We prove that our estimator converges at an asymptotically optimal rate. Moreover, by deriving the asymptotic distribution of our estimator, we construct valid confidence intervals and hypothesis tests. Our procedure has good finite-sample performance in simulations, and for an in-hospital mortality prediction task produces similar variable importance estimates when different machine learning algorithms are applied.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-williamson20a, title = {Efficient nonparametric statistical inference on population feature importance using Shapley values}, author = {Williamson, Brian and Feng, Jean}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {10282--10291}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/williamson20a/williamson20a.pdf}, url = {https://proceedings.mlr.press/v119/williamson20a.html}, abstract = {The true population-level importance of a variable in a prediction task provides useful knowledge about the underlying data-generating mechanism and can help in deciding which measurements to collect in subsequent experiments. Valid statistical inference on this importance is a key component in understanding the population of interest. We present a computationally efficient procedure for estimating and obtaining valid statistical inference on the \textbf{S}hapley \textbf{P}opulation \textbf{V}ariable \textbf{I}mportance \textbf{M}easure (SPVIM). Although the computational complexity of the true SPVIM scales exponentially with the number of variables, we propose an estimator based on randomly sampling only $\Theta(n)$ feature subsets given $n$ observations. We prove that our estimator converges at an asymptotically optimal rate. Moreover, by deriving the asymptotic distribution of our estimator, we construct valid confidence intervals and hypothesis tests. Our procedure has good finite-sample performance in simulations, and for an in-hospital mortality prediction task produces similar variable importance estimates when different machine learning algorithms are applied.} }
Endnote
%0 Conference Paper %T Efficient nonparametric statistical inference on population feature importance using Shapley values %A Brian Williamson %A Jean Feng %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-williamson20a %I PMLR %P 10282--10291 %U https://proceedings.mlr.press/v119/williamson20a.html %V 119 %X The true population-level importance of a variable in a prediction task provides useful knowledge about the underlying data-generating mechanism and can help in deciding which measurements to collect in subsequent experiments. Valid statistical inference on this importance is a key component in understanding the population of interest. We present a computationally efficient procedure for estimating and obtaining valid statistical inference on the \textbf{S}hapley \textbf{P}opulation \textbf{V}ariable \textbf{I}mportance \textbf{M}easure (SPVIM). Although the computational complexity of the true SPVIM scales exponentially with the number of variables, we propose an estimator based on randomly sampling only $\Theta(n)$ feature subsets given $n$ observations. We prove that our estimator converges at an asymptotically optimal rate. Moreover, by deriving the asymptotic distribution of our estimator, we construct valid confidence intervals and hypothesis tests. Our procedure has good finite-sample performance in simulations, and for an in-hospital mortality prediction task produces similar variable importance estimates when different machine learning algorithms are applied.
APA
Williamson, B. & Feng, J.. (2020). Efficient nonparametric statistical inference on population feature importance using Shapley values. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:10282-10291 Available from https://proceedings.mlr.press/v119/williamson20a.html.

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