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arXiv · 1712.06695

Accurate Inference for Adaptive Linear Models

Yash Deshpande·Lester Mackey·Vasilis Syrgkanis·Matt Taddy
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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.

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Yash Deshpande, Lester Mackey, Vasilis Syrgkanis, Matt Taddy. 2017-12-18. Accurate Inference for Adaptive Linear Models. https://arxiv.org/abs/1712.06695

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