相关论文: Stochastic Tverberg theorems and their application…

Statistical decision problems lie at the heart of statistical machine learning. The simplest problems are binary and multiclass classification and class probability estimation. Central to their definition is the choice of loss function,…

We use tools from random matrix theory to study the multi-spiked tensor model, i.e., a rank-$r$ deformation of a symmetric random Gaussian tensor. In particular, thanks to the nature of local optimization methods used to find the maximum…

In this paper we develop a statistical theory and an implementation of deep learning models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers optimises a deep learning objective. We allow…

Strassen's classical martingale coupling theorem states that two real-valued random variables are ordered in the convex (resp.\ increasing convex) stochastic order if and only if they admit a martingale (resp.\ submartingale) coupling. By…

We consider point clouds obtained as random samples of a measure on a Euclidean domain. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. Our goal is to…

We study stochastic nonconvex optimization under heavy-tailed noise. In this setting, the stochastic gradients only have bounded $p$-th central moment ($p$-BCM) for some $p \in (1,2]$. Building on the foundational work of Arjevani et al.…

Fitting a function by using linear combinations of a large number $N$ of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to…

We develop new approaches in multi-class settings for constructing proper scoring rules and hinge-like losses and establishing corresponding regret bounds with respect to the zero-one or cost-weighted classification loss. Our construction…

Data clustering is a fundamental problem with a wide range of applications. Standard methods, eg the $k$-means method, usually require solving a non-convex optimization problem. Recently, total variation based convex relaxation to the…

Providing generalization guarantees for stochastic optimization algorithms remains a key challenge in learning theory. Recently, numerous works demonstrated the impact of the geometric properties of optimization trajectories on…

This paper considers stochastic-constrained stochastic optimization where the stochastic constraint is to satisfy that the expectation of a random function is below a certain threshold. In particular, we study the setting where data samples…

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…

Understanding the generalization abilities of modern machine learning algorithms has been a major research topic over the past decades. In recent years, the learning dynamics of Stochastic Gradient Descent (SGD) have been related to…

Stochastic convex optimization, where the objective is the expectation of a random convex function, is an important and widely used method with numerous applications in machine learning, statistics, operations research and other areas. We…

We propose a simple yet powerful test statistic to quantify the discrepancy between two conditional distributions. The new statistic avoids the explicit estimation of the underlying distributions in highdimensional space and it operates on…

Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…

This paper studies multi-level stochastic approximation algorithms. Our aim is to extend the scope of the multilevel Monte Carlo method recently introduced by Giles (Giles 2008) to the framework of stochastic optimization by means of…