Abstract: Regression discontinuity design (RDD) is a quasi-experimental impact evaluation method ubiquitous in the social- and applied health sciences. It aims to estimate average treatment effects of policy interventions by exploiting jumps in outcomes induced by cut-off assignment rules. Here, we establish a correspondence between the RDD setting and free discontinuity problems, in particular the celebrated Mumford-Shah model in image segmentation. The Mumford-Shah model is non-convex and hence admits local solutions in general. We circumvent this issue by relying on…

Abstract: This talk is based on two recent papers: 1. “On the Pointwise Behavior of Recursive Partitioning and Its Implications for Heterogeneous Causal Effect Estimation” and 2. “Convergence Rates of Oblique Regression Trees for Flexible Function Libraries” 1. Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of experiments, where tree estimation and inference is conducted at specific values of…

Abstract: In this talk, I will argue that it is sometimes possible to learn, with techniques originated from bandits, the "hints" on which learning-augmented algorithms rely to improve worst-case performances. We will describe this phenomenon, the combination of online learning with competitive analysis, on the example of stochastic online scheduling. We shall quantify the merits of this approach by computing and comparing non-asymptotic expected competitive ratios (the standard performance measure of algorithms) Bio: Vianney Perchet is a professor at the…

Abstract: The low-degree polynomial framework has emerged as a versatile tool for probing the computational complexity of statistical problems by studying the power and limitations of a restricted class of algorithms: low-degree polynomials. Focusing on the setting of hypothesis testing, I will discuss some extensions of this method that allow us to tackle finer-grained questions than the standard approach. First, for the task of detecting a planted clique in a random graph, we ask not merely when this can be…

Abstract: We consider estimation of parameters defined as linear functionals of solutions to linear inverse problems. Any such parameter admits a doubly robust representation that depends on the solution to a dual linear inverse problem, where the dual solution can be thought as a generalization of the inverse propensity function. We provide the first source condition double robust inference method that ensures asymptotic normality around the parameter of interest as long as either the primal or the dual inverse problem…

Abstract: We consider the Error-in-Operator (EiO) problem of recovering the source x signal from the noise observation Y given by the equation Y = A x + ε in the situation when the operator A is not precisely known. Instead, a pilot estimate \hat{A} is available. The study is motivated by Hoffmann & Reiss (2008), Trabs (2018) and by recent results on high dimensional regression with random design; see e.g., Tsigler, Bartlett (2020) (Benign overfitting in ridge regression; arXiv:2009.14286) Cheng, and Montanari (2022) (Dimension free ridge regression; arXiv:2210.08571), among many others. Examples of EiO include regression with error-in-variables and instrumental regression, stochastic diffusion, Markov time series, interacting particle…

Abstract: In this talk, we revisit classical results in the theory of statistical aggregation, focusing on the transition from global complexity to a more manageable local one. The goal of aggregation is to combine several base predictors to achieve a prediction nearly as accurate as the best one, without assumptions on the class structure or target. Though studied in both sequential and statistical settings, they traditionally use the same "global" complexity measure. We highlight the lesser-known PAC-Bayes localization enabling us…