Accurate Inference for Adaptive Linear Models

Yash Deshpande, Lester Mackey, Vasilis Syrgkanis, Matt Taddy
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:1194-1203, 2018.

Abstract

Estimators computed from adaptively collected data do not behave like their non-adaptive brethren.Rather, the sequential dependence of the collection policy can lead to severe distributional biases that persist even in the infinite data limit. We develop a general method – $\mathbf{W}$-decorrelation – for transforming the bias of adaptive linear regression estimators into variance. The method uses only coarse-grained information about the data collection policy and does not need access to propensity scores or exact knowledge of the policy.We bound the finite-sample bias and variance of the $\mathbf{W}$-estimator and develop asymptotically correct confidence intervals based on a novel martingale central limit theorem. We then demonstrate the empirical benefits of the generic $\mathbf{W}$-decorrelation procedure in two different adaptive data settings: the multi-armed bandit and the autoregressive time series.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-deshpande18a, title = {Accurate Inference for Adaptive Linear Models}, author = {Deshpande, Yash and Mackey, Lester and Syrgkanis, Vasilis and Taddy, Matt}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {1194--1203}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/deshpande18a/deshpande18a.pdf}, url = {https://proceedings.mlr.press/v80/deshpande18a.html}, abstract = {Estimators computed from adaptively collected data do not behave like their non-adaptive brethren.Rather, the sequential dependence of the collection policy can lead to severe distributional biases that persist even in the infinite data limit. We develop a general method – $\mathbf{W}$-decorrelation – for transforming the bias of adaptive linear regression estimators into variance. The method uses only coarse-grained information about the data collection policy and does not need access to propensity scores or exact knowledge of the policy.We bound the finite-sample bias and variance of the $\mathbf{W}$-estimator and develop asymptotically correct confidence intervals based on a novel martingale central limit theorem. We then demonstrate the empirical benefits of the generic $\mathbf{W}$-decorrelation procedure in two different adaptive data settings: the multi-armed bandit and the autoregressive time series.} }
Endnote
%0 Conference Paper %T Accurate Inference for Adaptive Linear Models %A Yash Deshpande %A Lester Mackey %A Vasilis Syrgkanis %A Matt Taddy %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-deshpande18a %I PMLR %P 1194--1203 %U https://proceedings.mlr.press/v80/deshpande18a.html %V 80 %X Estimators computed from adaptively collected data do not behave like their non-adaptive brethren.Rather, the sequential dependence of the collection policy can lead to severe distributional biases that persist even in the infinite data limit. We develop a general method – $\mathbf{W}$-decorrelation – for transforming the bias of adaptive linear regression estimators into variance. The method uses only coarse-grained information about the data collection policy and does not need access to propensity scores or exact knowledge of the policy.We bound the finite-sample bias and variance of the $\mathbf{W}$-estimator and develop asymptotically correct confidence intervals based on a novel martingale central limit theorem. We then demonstrate the empirical benefits of the generic $\mathbf{W}$-decorrelation procedure in two different adaptive data settings: the multi-armed bandit and the autoregressive time series.
APA
Deshpande, Y., Mackey, L., Syrgkanis, V. & Taddy, M.. (2018). Accurate Inference for Adaptive Linear Models. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:1194-1203 Available from https://proceedings.mlr.press/v80/deshpande18a.html.

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