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The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
The manifold hypothesis says that natural high-dimensional data lie on or around a low-dimensional manifold. The recent success of statistical and learning-based methods in very high dimensions empirically supports this hypothesis,…
We extend the restrictiveness measure of Fudenberg, Gao & Liang (2026) to functional and structural econometric settings using Gaussian process priors. We find that models evaluated over continuum domains appear more restrictive than when…
Many recent loss functions in deep metric learning are expressed with logarithmic and exponential forms, and they involve margin and scale as essential hyper-parameters. Since each data class has an intrinsic characteristic, several…
In the recent years, branch-and-cut algorithms have been the target of data-driven approaches designed to enhance the decision making in different phases of the algorithm such as branching, or the choice of cutting planes (cuts). In…
We establish new upper and lower bounds on the number of queries required to test convexity of functions over various discrete domains. 1. We provide a simplified version of the non-adaptive convexity tester on the line. We re-prove the…
We show how to control the generalization error of time series models wherein past values of the outcome are used to predict future values. The results are based on a generalization of standard i.i.d. concentration inequalities to dependent…
The paper deals with regression problems, in which the nonsmooth target is assumed to switch between different operating modes. Specifically, piecewise smooth (PWS) regression considers target functions switching deterministically via a…
We discuss the asymptotic behaviour of models of lattice polygons, mainly on the square lattice. In particular, we focus on limiting area laws in the uniform perimeter ensemble where, for fixed perimeter, each polygon of a given area occurs…
We prove a new generalization bound that shows for any class of linear predictors in Gaussian space, the Rademacher complexity of the class and the training error under any continuous loss $\ell$ can control the test error under all Moreau…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
Similarity learning has received a large amount of interest and is an important tool for many scientific and industrial applications. In this framework, we wish to infer the distance (similarity) between points with respect to an arbitrary…
Deep neural networks often contain far more parameters than training examples, yet they still manage to generalize well in practice. Classical complexity measures such as VC-dimension or PAC-Bayes bounds usually become vacuous in this…
Margin-based learning, exemplified by linear and kernel methods, is one of the few classical settings where generalization guarantees are independent of the number of parameters. This makes it a central case study in modern highly…
Inspired by recent strides in empirical efficacy of implicit learning in many robotics tasks, we seek to understand the theoretical benefits of implicit formulations in the face of nearly discontinuous functions, common characteristics for…
Aimed at explaining the surprisingly good generalization behavior of overparameterized deep networks, recent works have developed a variety of generalization bounds for deep learning, all based on the fundamental learning-theoretic…
We study the diversity of the features learned by a two-layer neural network trained with the least squares loss. We measure the diversity by the average $L_2$-distance between the hidden-layer features and theoretically investigate how…
Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and…
We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove…
Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…