Papers › Accurate Inference for Adaptive Linear Models
Accurate Inference for Adaptive Linear Models
Yash Deshpande, Lester Mackey, Vasilis Syrgkanis, Matt Taddy
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 -- 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 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 𝐖-decorrelation procedure in two different adaptive data settings: the multi-armed bandit and the autoregressive time series.
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