相关论文: Double Descent Risk and Volume Saturation Effects:…

While state-of-the-art diffusion models (DMs) excel in image generation, concerns regarding their security persist. Earlier research highlighted DMs' vulnerability to data poisoning attacks, but these studies placed stricter requirements…

The double descent curve is one of the most intriguing properties of deep neural networks. It contrasts the classical bias-variance curve with the behavior of modern neural networks, occurring where the number of samples nears the number of…

In nature, submarine slope failures usually carry thousands of cubic-meters of sediments across extremely long distances and cause tsunamis and damages to offshore structures. This paper uses the granular column collapse experiment to…

We study the sample complexity of the best-case Empirical Risk Minimizer in the setting of stochastic convex optimization. We show that there exists an instance in which the sample size is linear in the dimension, learning is possible, but…

The concentration of measure phenomena were discovered as the mathematical background of statistical mechanics at the end of the XIX - beginning of the XX century and were then explored in mathematics of the XX-XXI centuries. At the…

Popular statistical software provides Bayesian information criterion (BIC) for multilevel models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to…

In the well known logistic map, the parameter of interest is weighted by a coefficient that decreases linearly when this parameter increases. Since such a linear decrease forms a specific case, we consider the more general case where this…

This paper generalizes results concerning strong convexity of two-stage mean-risk models with linear recourse to distortion risk measures. Introducing the concept of (restricted) partial strong convexity, we conduct an in-depth analysis of…

We prove risk bounds for binary classification in high-dimensional settings when the sample size is allowed to be smaller than the dimensionality of the training set observations. In particular, we prove upper bounds for both 'compressive…

Doubly stochastic learning algorithms are scalable kernel methods that perform very well in practice. However, their generalization properties are not well understood and their analysis is challenging since the corresponding learning…

The support vector machine (SVM) and minimum Euclidean norm least squares regression are two fundamentally different approaches to fitting linear models, but they have recently been connected in models for very high-dimensional data through…

We study the learning performance of gradient descent when the empirical risk is weakly convex, namely, the smallest negative eigenvalue of the empirical risk's Hessian is bounded in magnitude. By showing that this eigenvalue can control…

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…

Let $n>m$, and let $A$ be an $(m\times n)$-matrix of full rank. Then obviously the estimate $\|Ax\|\leq\|A\|\|x\|$ holds for the euclidean norm of $x$ and $Ax$ and the spectral norm as the assigned matrix norm. We study the sets of all $x$…

The definition of a double-scaling limit represents an important goal in the development of tensor models. We take the first steps towards this goal by extracting and analysing the next-to-leading order contributions, in the 1/N expansion,…

Machine unlearning, an emerging research topic focusing on compliance with data privacy regulations, enables trained models to remove the information learned from specific data. While many existing methods indirectly address this issue by…

We present a fast and efficient method for studying vacuum stability constraints in multi-scalar theories beyond the Standard Model. This method is designed for a reliable use in large scale parameter scans. The minimization of the scalar…

In this contribution, the use of discrete simulations to formulate an anisotropic damage model is investigated. It is proposed to use a beam-particle model to perform numerical characterization tests. Indeed, this discrete model explicitly…

Bayesian Deep Learning (BDL) gives access not only to aleatoric uncertainty, as standard neural networks already do, but also to epistemic uncertainty, a measure of confidence a model has in its own predictions. In this article, we show…

Precision matrix estimation is a cornerstone concept in statistics, economics, and finance. Despite advances in recent years, estimation methods that are simultaneously (i) dense, (ii) consistent, and (iii) model-free are lacking. While…