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Accurate Inference for Adaptive Linear Models
Yash Deshpande · Lester Mackey · Vasilis Syrgkanis · Matt Taddy

Fri Jul 13 09:15 AM -- 12:00 PM (PDT) @ Hall B #166
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 -- \emph{$\vect{W}$-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 $\vect{W}$-estimator and develop asymptotically correct confidence intervals based on a novel martingale central limit theorem. We then demonstrate the empirical benefits of the generic $\vect{W}$-decorrelation procedure in two different adaptive data settings: the multi-armed bandit and the autoregressive time series.

Author Information

Yash Deshpande (Massachusetts Institute of Technology)
Lester Mackey (Microsoft Research)
Vasilis Syrgkanis (Microsoft Research)
Matt Taddy (MICROSOFT)

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