Martin J. Wainwright’s research while affiliated with University of California, Berkeley and other places

Panel data consists of a collection of N units that are observed over T units of time. A policy or treatment is subject to staggered adoption if different units take on treatment at different times and remains treated (or never at all). Assessing the effectiveness of such a policy requires estimating the treatment effect, corresponding to the difference between outcomes for treated versus untreated units. We develop inference procedures that build upon a computationally efficient matrix estimator for treatment effects in panel data. Our routines return confidence intervals (CIs) both for individual treatment effects, as well as for more general bilinear functionals of treatment effects, with prescribed coverage guarantees. We apply these inferential methods to analyze the effectiveness of Medicaid expansion portion of the Affordable Care Act. Based on our analysis, Medicaid expansion has led to substantial reductions in uninsurance rates, has reduced infant mortality rates, and has had no significant effects on healthcare expenditures.

We study a class of prediction problems in which relatively few observations have associated responses, but all observations include both standard covariates as well as additional "helper" covariates. While the end goal is to make high-quality predictions using only the standard covariates, helper covariates can be exploited during training to improve prediction. Helper covariates arise in many applications, including forecasting in time series; incorporation of biased or mis-calibrated predictions from foundation models; and sharing information in transfer learning. We propose "prediction aided by surrogate training" ($\texttt{PAST}$), a class of methods that exploit labeled data to construct a response estimator based on both the standard and helper covariates; and then use the full dataset with pseudo-responses to train a predictor based only on standard covariates. We establish guarantees on the prediction error of this procedure, with the response estimator allowed to be constructed in an arbitrary way, and the final predictor fit by empirical risk minimization over an arbitrary function class. These upper bounds involve the risk associated with the oracle data set (all responses available), plus an overhead that measures the accuracy of the pseudo-responses. This theory characterizes both regimes in which $\texttt{PAST}$ accuracy is comparable to the oracle accuracy, as well as more challenging regimes where it behaves poorly. We demonstrate its empirical performance across a range of applications, including forecasting of societal ills over time with future covariates as helpers; prediction of cardiovascular risk after heart attacks with prescription data as helpers; and diagnosing pneumonia from chest X-rays using machine-generated predictions as helpers.

Resampling methods are especially well-suited to inference with estimators that provide only "black-box'' access. Jackknife is a form of resampling, widely used for bias correction and variance estimation, that is well-understood under classical scaling where the sample size n grows for a fixed problem. We study its behavior in application to estimating functionals using high-dimensional Z-estimators, allowing both the sample size n and problem dimension d to diverge. We begin showing that the plug-in estimator based on the Z-estimate suffers from a quadratic breakdown: while it is $\sqrt{n}$-consistent and asymptotically normal whenever $n \gtrsim d^2$, it fails for a broad class of problems whenever $n \lesssim d^2$. We then show that under suitable regularity conditions, applying a jackknife correction yields an estimate that is $\sqrt{n}$-consistent and asymptotically normal whenever $n\gtrsim d^{3/2}$. This provides strong motivation for the use of jackknife in high-dimensional problems where the dimension is moderate relative to sample size. We illustrate consequences of our general theory for various specific Z-estimators, including non-linear functionals in linear models; generalized linear models; and the inverse propensity score weighting (IPW) estimate for the average treatment effect, among others.

We provide a non-asymptotic analysis of the linear instrumental variable estimator allowing for the presence of exogeneous covariates. In addition, we introduce a novel measure of the strength of an instrument that can be used to derive non-asymptotic confidence intervals. For strong instruments, these non-asymptotic intervals match the asymptotic ones exactly up to higher order corrections; for weaker instruments, our intervals involve adaptive adjustments to the instrument strength, and thus remain valid even when asymptotic predictions break down. We illustrate our results via an analysis of the effect of PM2.5 pollution on various health conditions, using wildfire smoke exposure as an instrument. Our analysis shows that exposure to PM2.5 pollution leads to statistically significant increases in incidence of health conditions such as asthma, heart disease, and strokes.

We study stochastic approximation procedures for approximately solving a d -dimen­sional linear fixed-point equation based on observing a trajectory of length n from an ergodic Markov chain. We first exhibit a non-asymptotic bound of the order t_{\mathrm{mix}}\frac{d}{n} on the squared error of the last iterate of a standard scheme, where t_{\mathrm{mix}} is a mixing time. We then prove a non-asymptotic instance-dependent bound on a suitably averaged sequence of iterates, with a leading term that matches the local asymptotic minimax limit, including sharp dependence on the parameters (d, t_{\mathrm{mix}}) in the higher-order terms. We complement these upper bounds with a non-asymptotic minimax lower bound that establishes the instance-optimality of the averaged SA estimator. We derive corollaries of these results for policy evaluation with Markov noise—covering the \mathrm{TD}(\lambda) family of algorithms for all \lambda \in [0, 1) —and linear autoregressive models. Our instance-dependent characterizations open the door to the design of fine-grained model selection procedures for hyperparameter tuning (e.g., choosing the value of \lambda when running the \mathrm{TD}(\lambda) algorithm).

Various algorithms in reinforcement learning exhibit dramatic variability in their convergence rates and ultimate accuracy as a function of the problem structure. Such instance-specific behavior is not captured by existing global minimax bounds, which are worst-case in nature. We analyze the problem of estimating optimal Q -state-action value functions for a discounted Markov decision process with discrete states and actions; our main result is to identify an instance-dependent functional that controls the difficulty of estimation in the ℓ _∞ -norm. Using a local minimax framework, we show that this functional arises in lower bounds on the accuracy on any estimation procedure. We establish the sharpness of these lower bounds, up to factors logarithmic in the state and action spaces, by analyzing a variance-reduced version of Q -learning. Our theory provides a precise way of distinguishing “easy” problems from “hard” ones in the context of Q -learning, as illustrated by an ensemble with a continuum of difficulty.

Anecdotally, using an estimated propensity score is superior to the true propensity score in estimating the average treatment effect based on observational data. However, this claim comes with several qualifications: it holds only if propensity score model is correctly specified and the number of covariates d is small relative to the sample size n. We revisit this phenomenon by studying the inverse propensity score weighting (IPW) estimator based on a logistic model with a diverging number of covariates. We first show that the IPW estimator based on the estimated propensity score is consistent and asymptotically normal with smaller variance than the oracle IPW estimator (using the true propensity score) if and only if $n \gtrsim d^2$. We then propose a debiased IPW estimator that achieves the same guarantees in the regime $n \gtrsim d^{3/2}$. Our proofs rely on a novel non-asymptotic decomposition of the IPW error along with careful control of the higher order terms.