相关论文: $\mathscr{H}$-Consistency Estimation Error of Surr…

A priori error bounds have been derived for different balancing-related model reduction methods. The most classical result is a bound for balanced truncation and singular perturbation approximation that is applicable for asymptotically…

Generalized linear mixed models are powerful tools for analyzing clustered data, where the unknown parameters are classically (and most commonly) estimated by the maximum likelihood and restricted maximum likelihood procedures. However,…

Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…

We suggest guaranteed, robust a posteriori error bounds for approximate solutions of the reaction-diffusion equations, modeled by the equation $-\Delta u+\sigma u= f$ in $\Omega$ with any $\sigma={\mathrm{const}}\ge 0$. We also term our…

When a system commits to a hypothesis, much of the evidential structure behind that commitment is lost to compression. Standard accounts assume that selected content and scalar confidence suffice for downstream control. This paper argues…

Empirical risk minimization (ERM) with a computationally feasible surrogate loss is a widely accepted approach for classification. Notably, the convexity and calibration (CC) properties of a loss function ensure consistency of ERM in…

This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…

This guide provides a reference for high-probability regret bounds in empirical risk minimization (ERM). The presentation is modular: we begin with intuition and general proof strategies, then state broadly applicable guarantees under…

In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network…

Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. These estimators provide attractive generalization guarantees: the robust objective obtained from the…

We establish risk bounds for Regularized Empirical Risk Minimizers (RERM) when the loss is Lipschitz and convex and the regularization function is a norm. In a first part, we obtain these results in the i.i.d. setup under subgaussian…

Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…

We establish an excess risk bound of O(H R_n^2 + R_n \sqrt{H L*}) for empirical risk minimization with an H-smooth loss function and a hypothesis class with Rademacher complexity R_n, where L* is the best risk achievable by the hypothesis…

We study data-driven least squares (LS) problems with semidefinite (SD) constraints and derive finite-sample guarantees on the spectrum of their optimal solutions when these constraints are relaxed. In particular, we provide a high…

We consider the problem of stochastic convex optimization with exp-concave losses using Empirical Risk Minimization in a convex class. Answering a question raised in several prior works, we provide a $O( d / n + \log( 1 / \delta) / n )$…

In multiclass classification over $n$ outcomes, the outcomes must be embedded into the reals with dimension at least $n-1$ in order to design a consistent surrogate loss that leads to the "correct" classification, regardless of the data…

Penalized empirical risk minimization with a surrogate loss function is often used to learn a high-dimensional linear decision rule in classification problems. Although much of the literature focus on the generalization error, there is a…

M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well understood when the loss satisfies some smoothness…

For several styles of fidelity constraints -- guaranteed distortion, conditional excess distortion, excess distortion -- we show mutual information upper bounds on the minimum expected description length needed to represent a random…

Stochastic majorization-minimization (SMM) is a class of stochastic optimization algorithms that proceed by sampling new data points and minimizing a recursive average of surrogate functions of an objective function. The surrogates are…