Abstract: Two of the fundamental problems in non-parametric statistical inference are goodness-of-fit and two-sample testing. These two problems have been extensively studied and several multivariate tests have been proposed over the last thirty years, many of which are based on geometric graphs. These include, among several others, the celebrated Friedman-Rafsky two-sample test based on the…

Abstract: For many causal effect parameters of interest, doubly robust machine learning (DRML) estimators ψ̂ 1 are the state-of-the-art, incorporating the good prediction performance of machine learning; the decreased bias of doubly robust estimators; and the analytic tractability and bias reduction of sample splitting with cross fitting. Nonetheless, even in the absence of confounding by unmeasured…

Abstract:  We consider sequential prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. We quantify relaxations of the classical i.i.d. assumption in terms of these constraint sets, with i.i.d. sequences at one extreme and adversarial mechanisms at the other. The Hedge algorithm, long known to be minimax…

Abstract: Mainstream machine learning, despite its recent successes, has a serious drawback: while its state-of-the-art algorithms often produce excellent predictions, they do not provide measures of their accuracy and reliability that would be both practically useful and provably valid. Conformal prediction adapts rank tests, popular in nonparametric statistics, to testing the IID assumption (the observations…