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We address the general task of learning with a set of candidate models that is too large to have a uniform convergence of empirical estimates to true losses. While the common approach to such challenges is SRM (or regularization) based…

The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…

We investigate to which extent the relevant features of (static) Systemic Risk Measures can be extended to a conditional setting. After providing a general dual representation result, we analyze in greater detail Conditional Shortfall…

Information-theoretic (IT) generalization bounds have been used to study the generalization of learning algorithms. These bounds are intrinsically data- and algorithm-dependent so that one can exploit the properties of data and algorithm to…

Bagging is an important technique for stabilizing machine learning models. In this paper, we derive a finite-sample guarantee on the stability of bagging for any model. Our result places no assumptions on the distribution of the data, on…

Most generalization bounds in learning theory are based on some measure of the complexity of the hypothesis class used, independently of any algorithm. In contrast, the notion of algorithmic stability can be used to derive tight…

The purpose of this paper is to summarize the recent results on the stability of the parametric fundamental equation of information. Furthermore, by the help of a modification of a method we used in \cite{GM08} we shall give a unified proof…

Since the celebrated works of Russo and Zou (2016,2019) and Xu and Raginsky (2017), it has been well known that the generalization error of supervised learning algorithms can be bounded in terms of the mutual information between their input…

We present a new family of information-theoretic generalization bounds, in which the training loss and the population loss are compared through a jointly convex function. This function is upper-bounded in terms of the disintegrated,…

Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…

We present a unified information-theoretic framework elucidating the interplay between stability, privacy, and the generalization performance of quantum learning algorithms. We establish a bound on the expected generalization error in terms…

When a machine learning model is deployed, its predictions can alter its environment, as better informed agents strategize to suit their own interests. With such alterations in mind, existing approaches to uncertainty quantification break.…

Training modern neural networks often relies on large learning rates, operating at the edge of stability, where the optimization dynamics exhibit oscillatory and chaotic behavior. Empirically, this regime often yields improved…

Learning tasks play an increasingly prominent role in quantum information and computation. They range from fundamental problems such as state discrimination and metrology over the framework of quantum probably approximately correct (PAC)…

This paper takes an initial step to systematically investigate the generalization bounds of algorithms for solving nonconvex-(strongly)-concave (NC-SC/NC-C) stochastic minimax optimization measured by the stationarity of primal functions.…

Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an…

In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible…

Algorithmic stability is a key characteristic to ensure the generalization ability of a learning algorithm. Among different notions of stability, \emph{uniform stability} is arguably the most popular one, which yields exponential…

Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range…

We derive a novel information-theoretic analysis of the generalization property of meta-learning algorithms. Concretely, our analysis proposes a generic understanding of both the conventional learning-to-learn framework and the modern…