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Normalization is ubiquitous in economics, and a growing literature shows that ``normalizations'' can matter for interpretation, counterfactual analysis, misspecification, and inference. This paper provides a general framework for these…

Several recent works have shown that state-of-the-art classifiers are vulnerable to worst-case (i.e., adversarial) perturbations of the datapoints. On the other hand, it has been empirically observed that these same classifiers are…

Inspired by the work of Tsiamis et al. \cite{tsiamis2022learning}, in this paper we study the statistical hardness of learning to stabilize linear time-invariant systems. Hardness is measured by the number of samples required to achieve a…

Among the different possible strategies for evaluating the reliability of individual predictions of classifiers, robustness quantification stands out as a method that evaluates how much uncertainty a classifier could cope with before…

There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high-dimensionality of the data, high codimension in the ambient space of the data manifolds of interest, and…

The problem of adversarial examples has highlighted the need for a theory of regularisation that is general enough to apply to exotic function classes, such as universal approximators. In response, we give a very general equality result…

Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating…

Standardness is a popular assumption in the literature on set estimation. It also appears in statistical approaches to topological data analysis, where it is common to assume that the data were sampled from a probability measure that…

Robustness of machine learning models to various adversarial and non-adversarial corruptions continues to be of interest. In this paper, we introduce the notion of the boundary thickness of a classifier, and we describe its connection with…

We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the $\ell\_p$ ball for $p \in [1, \infty]$ and Gaussian noise with an arbitrary covariance matrix. We…

In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…

We provide a thorough study of stability of the 1-D continuity equation, which models many physical conservation laws. In our system-theoretic perspective, the velocity is considered to be an input. An additional input appears in the…

We examine the stability of loss-minimizing training processes that are used for deep neural networks (DNN) and other classifiers. While a classifier is optimized during training through a so-called loss function, the performance of…

Machine learning (ML) robustness and domain generalization are fundamentally correlated: they essentially concern data distribution shifts under adversarial and natural settings, respectively. On one hand, recent studies show that more…

This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…

Generalization is the ability of a model to predict on unseen domains and is a fundamental task in machine learning. Several generalization bounds, both theoretical and empirical have been proposed but they do not provide tight bounds .In…

Robustness is widely regarded as a fundamental problem in the analysis of machine learning (ML) models. Most often robustness equates with deciding the non-existence of adversarial examples, where adversarial examples denote situations…

In many scientific and data-driven applications, machine learning models are increasingly used as measurement instruments, rather than merely as predictors of predefined labels. When the measurement function is learned from data, the…

Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…

The goal of this paper is to analyze an intriguing phenomenon recently discovered in deep networks, namely their instability to adversarial perturbations (Szegedy et. al., 2014). We provide a theoretical framework for analyzing the…