Session: Stability and Robustness in Statistical Learning
Chair: Louis Chen
Cluster: Optimization Under Uncertainty and Data-driven Optimization
Talk 1: A Stability Principle for Learning under Non-Stationarity
Speaker: Kaizheng Wang
Abstract: We develop a versatile framework for statistical learning in non-stationary environments. In each time period, our approach applies a stability principle to select a look-back window that maximizes the utilization of historical data while keeping the cumulative bias within an acceptable range relative to the stochastic error. Our theory showcases the adaptability of this approach to unknown non-stationarity. The regret bound is minimax optimal up to logarithmic factors when the population losses are strongly convex, or Lipschitz only. At the heart of our analysis lie two novel components: a measure of similarity between functions and a segmentation technique for dividing the non-stationary data sequence into quasi-stationary pieces. The talk is based on joint work with Chengpiao Huang.
Talk 2: On the Adversarial Robustness of Benjamini Hochberg
Speaker: Louis Chen
Abstract: The Benjamini-Hochberg (BH) procedure is widely used to control the false detection rate (FDR) in multiple testing. Applications of this control abound in drug discovery, forensics, anomaly detection, and, in particular, machine learning, ranging from nonparametric outlier detection to out-of-distribution detection and one-class classification methods. Considering this control's place in critical safety/security contexts, we investigate its adversarial robustness. More precisely, we study under what conditions BH does and does not exhibit adversarial robustness, we present a class of simple and easily implementable adversarial test-perturbation algorithms, and we perform computational experiments. With our algorithms, we demonstrate that there are conditions under which BH's control can be significantly broken with relatively few (even just one) test score perturbation(s), and provide non-asymptotic guarantees on the expected adversarial-adjustment to FDR. Our technical analysis involves a combinatorial reframing of the BH procedure as a ``balls into bins'' process, and drawing a connection to generalized ballot problems to facilitate an information-theoretic approach for deriving non-asymptotic lower bounds.
Talk 3: Estimating the Direction-of-Arrival of a Signal Under Impulsive Noise
Speaker: Robert Bassett
Abstract: We consider the problem of estimating a signal subspace in the presence of interference that contaminates some proportion of the received observations. Our emphasis is on detecting the contaminated observations so that the signal subspace can be estimated with the contaminated observations discarded. We employ a signal model which explicitly includes an interference term that is distinct from environmental noise. To detect when the interference term is nonzero, we estimate the interference term using an optimization problem with a sparsity-inducing group SLOPE penalty which accounts for simultaneous sparsity across all channels of the multichannel signal. We propose an iterative algorithm which efficiently computes the observations estimated to contain interference. Theoretical support for the accuracy of our interference estimator is provided by bounding its false discovery rate. Finally, we demonstrate the empirical performance of our contributions in a number of simulated experiments.
