14:00 – 15:00 Henry Reeve

Title: Subgroup selection in non-parametric regimes  

Abstract: In this work we consider the challenge of subgroup selection in non-parametric regimes. The goal here is to output a large subset of the feature space which satisfies the following Type 1 error guarantee: On the selected set, the regression function (the conditional expectation of the response given the covariates) is uniformly above some pre-specified threshold, with high probability. We begin by considering a flexible regime where our distributional classes are characterised by the Holder continuity of the regression function on the level set. We then turn to a more benign setting in which we replace smoothness with shape constraints. In particular, we consider a setting in which the regression function is monotonic with respect to a natural partial ordering on the feature space. In this setting we build upon ideas from the multiple testing literature to construct an adaptive procedure with a near-optimal, high probability regret guarantee.

15:30 – 16:30 Peter Orbanz

Title: Statistical implications of group invariance of distributions

Abstract: Consider a large random structure — a random graph, a stochastic process on the line, a random field on the grid — and a function that depends only on a small part of the structure. Now use a family of transformations to ‘move’ the domain of the function over the

structure, collect each function value, and average. Under suitable conditions, the law of large numbers generalizes to such averages; that is one of the deep insights of modern ergodic theory. My own recent work with Morgane Austern (Harvard) shows that central limit theorems and other higher-order properties also hold. Loosely speaking, if the i.i.d. assumption of classical statistics is substituted by suitable properties formulated in terms of groups, the fundamental theorems of inference still hold.

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