Abstract: We consider after-study statistical inference for sequentially designed experiments wherein multiple units are assigned treatments for multiple time points using treatment policies that adapt over time. Our goal is to provide inference guarantees for the counterfactual mean at the smallest possible scale--mean outcome under different treatments for each unit and each time -- with minimal assumptions on the adaptive treatment policy. Without any structural assumptions on the counterfactual means, this challenging task is infeasible due to more unknowns than observed data points. To make progress, we introduce a latent factor model over the counterfactual means that serves as a non-parametric generalization of the non-linear mixed effects model and the bilinear latent factor model considered in prior works. For estimation, we use a non-parametric method, namely a variant of nearest neighbors, and establish a non-asymptotic high probability error bound for the counterfactual mean for each unit and each time. Under regularity conditions, this bound leads to asymptotically valid confidence intervals for the counterfactual mean as the number of units and time points grows to infinity. Finally, we also introduce a doubly robust variant of nearest neighbors that provides sharper error guarantees. We demonstrate the usefulness of our methods for a mobile health application to measure a mobile app's effectiveness in promoting a healthier lifestyle with limited data.

Bio: Raaz Dwivedi is currently a FODSI postdoc fellow advised by Prof. Susan Murphy and Prof. Devavrat Shah in CS and Statistics, at Harvard and EECS, MIT respectively. He will be starting as an assistant professor in Operations Research and Information Engineering, at Cornell University, at Cornell Tech in New York City in Spring 2024! He earned his Ph. D. at EECS, UC Berkeley, advised by Prof. Martin Wainwright and Prof. Bin Yu; and his bachelor's degree at EE, IIT Bombay, advised by Prof. Vivek Borkar. His research builds statistically and computationally efficient strategies for personalized decision-making with theory and methods spanning the areas of causal inference, reinforcement learning, random sampling, and high-dimensional statistics. He won the President of India Gold Medal at IIT Bombay, the Berkeley Fellowship, teaching awards at UC Berkeley and Harvard, and a best student paper award for his work on optimal compression.