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Abstract: This talk discusses uncertainty quantification and inference using ensemble methods. Recent theoretical developments inspired by random forests have cast bagging-type methods as U-statistics when bootstrap samples are replaced by subsamples, resulting in a central limit theorem and hence the potential for inference. However, to carry this out requires estimating a variance for which all proposed estimators exhibit substantial upward bias. In this talk, we convert subsamples without replacement to subsamples with replacement resulting in V-statistics for which we prove…

Abstract: One of the central objects in the theory of optimal transport is the Brenier map: the unique monotone transformation which pushes forward an absolutely continuous probability law onto any other given law. Recent work has identified a class of plugin estimators of Brenier maps which achieve the minimax L^2 risk, and are simple to compute. In this talk, we show that such estimators obey pointwise central limit theorems. This provides a first step toward the question of performing statistical…

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Abstract: From clinical trials to corporate strategy, randomized experiments are a reliable methodological tool for estimating causal effects. In recent years, there has been a growing interest in causal inference under interference, where treatment given to one unit can affect outcomes of other units. While the literature on interference has focused primarily on unbiased and consistent estimation, designing randomized network experiments to insure tight rates of convergence is relatively under-explored for many settings. In this talk, we study the problem…

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Abstract:  We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. By integrating concepts and tools from cross-validation and differential privacy, we develop a test statistic that is asymptotically normal even in high-dimensional settings, and allows for arbitrarily many ties in the population mean vector. The key technical ingredient is a central limit theorem for globally dependent data characterized…