相关论文: Set structured global empirical risk minimizers ar…

Stochastic convex optimization is one of the most well-studied models for learning in modern machine learning. Nevertheless, a central fundamental question in this setup remained unresolved: "How many data points must be observed so that…

In this work, we study the weighted empirical risk minimization (weighted ERM) schema, in which an additional data-dependent weight function is incorporated when the empirical risk function is being minimized. We show that under a general…

Surveys of microbial biodiversity such as the Earth Microbiome Project (EMP) and the Human Microbiome Project (HMP) have revealed robust ecological patterns across different environments. A major goal in ecology is to leverage these…

Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d.\ test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such…

Empirical risk minimization (ERM) is sensitive to spurious correlations in the training data, which poses a significant risk when deploying systems trained under this paradigm in high-stake applications. While the existing literature…

Networked data, in which every training example involves two objects and may share some common objects with others, is used in many machine learning tasks such as learning to rank and link prediction. A challenge of learning from networked…

Self-referential learning -- training a model on data it generated itself -- promises boundless scalability but chronically suffers from model collapse: language models degenerate into repetitive text, GANs drop modes, and…

Uncertainty is ubiquitous in real-world data, and the assumptions underlying classical linear regression models are often violated in practice. Inspired by the theory of sublinear expectation, we consider a linear regression model where the…

The purpose of this paper is to pursue our study of rho-estimators built from i.i.d. observations that we defined in Baraud et al. (2014). For a \rho-estimator based on some model S (which means that the estimator belongs to S) and a true…

Understanding the limiting behavior of eigenvalues of random matrices is the central problem of random matrix theory. Classical limit results are known for many models, and there has been significant recent progress in obtaining more…

We introduce the entropic measure transform (EMT) problem for a general process and prove the existence of a unique optimal measure characterizing the solution. The density process of the optimal measure is characterized using a…

In the context of Structural Risk Minimization, one is presented a sequence of classes $\{\mathcal{G}_j\}$ from which, given a random sample $(X_i,Y_i)$ one wants to choose a strongly consistent estimator. For certain types of classes of…

Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…

We present an extension of Vapnik's classical empirical risk minimizer (ERM) where the empirical risk is replaced by a median-of-means (MOM) estimator, the new estimators are called MOM minimizers. While ERM is sensitive to corruption of…

Entropy regularized algorithms such as Soft Q-learning and Soft Actor-Critic, recently showed state-of-the-art performance on a number of challenging reinforcement learning (RL) tasks. The regularized formulation modifies the standard RL…

The exponential random graph model (ERGM) is a central object in the study of clustering properties in social networks as well as canonical ensembles in statistical physics. Despite some breakthrough works in the mathematical understanding…

Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…

In order to circumvent statistical and computational hardness results in sequential decision-making, recent work has considered smoothed online learning, where the distribution of data at each time is assumed to have bounded likeliehood…

Envelope methods perform dimension reduction of predictors or responses in multivariate regression, exploiting the relationship between them to improve estimation efficiency. While most research on envelopes has focused on their estimation…

In this paper, we focus on the high-dimensional double sparse structure, where the parameter of interest simultaneously encourages group-wise sparsity and element-wise sparsity in each group. By combining the Gilbert-Varshamov bound and its…