Related papers: Mitigating multiple descents: A model-agnostic fra…

This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…

We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…

In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk…

An evolving line of machine learning works observe empirical evidence that suggests interpolating estimators -- the ones that achieve zero training error -- may not necessarily be harmful. This paper pursues theoretical understanding for an…

In this paper, we studied two identically-trained neural networks (i.e. networks with the same architecture, trained on the same dataset using the same algorithm, but with different initialization) and found that their outputs discrepancy…

Risk sensitivity has become a central theme in reinforcement learning (RL), where convex risk measures and robust formulations provide principled ways to model preferences beyond expected return. Recent extensions to multi-agent RL (MARL)…

There remain theoretical gaps in deep neural network estimators for the nonparametric Cox proportional hazards model. In particular, it is unclear how gradient-based optimization error propagates to population risk under partial likelihood,…

We discuss a number of estimates of the hazard under the assumption that the hazard is monotone on an interval [0,a]. The usual isotonic least squares estimators of the hazard are inconsistent at the boundary points 0 and a. We use…

Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…

This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…

This paper considers an empirical risk minimization problem under heavy-tailed settings, where data does not have finite variance, but only has $p$-th moment with $p \in (1,2)$. Instead of using estimation procedure based on truncated…

Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much…

We study alternating minimization for matrix completion in the simplest possible setting: completing a rank-one matrix from a revealed subset of the entries. We bound the asymptotic convergence rate by the variational characterization of…

The risk of overparameterized models, in particular deep neural networks, is often double-descent shaped as a function of the model size. Recently, it was shown that the risk as a function of the early-stopping time can also be…

We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

Existing ordinal embedding methods usually follow a two-stage routine: outlier detection is first employed to pick out the inconsistent comparisons; then an embedding is learned from the clean data. However, learning in a multi-stage manner…

Flexible estimation of heterogeneous treatment effects lies at the heart of many statistical challenges, such as personalized medicine and optimal resource allocation. In this paper, we develop a general class of two-step algorithms for…

Variational algorithms have gained prominence over the past two decades as a scalable computational environment for Bayesian inference. In this article, we explore tools from the dynamical systems literature to study convergence of…