Related papers: Tight bounds for maximum $\ell_1$-margin classifie…
We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the…
This paper studies the problem of differentially private empirical risk minimization (DP-ERM) for binary linear classification. We obtain an efficient $(\varepsilon,\delta)$-DP algorithm with an empirical zero-one risk bound of…
The convergence rates results in $\ell^1$-regularization when the sparsity assumption is narrowly missed, presented by Burger et al. (2013 Inverse Problems 29 025013), are based on a crucial condition which requires that all basis elements…
We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically…
We present preconditioned stochastic gradient descent (SGD) algorithms for the $\ell_1$ minimization problem $\min_{x}\|A x - b\|_1$ in the overdetermined case, where there are far more constraints than variables. Specifically, we have $A…
Learning with label dependent label noise has been extensively explored in both theory and practice; however, dealing with instance (i.e., feature) and label dependent label noise continues to be a challenging task. The difficulty arises…
Recently, several studies (Zhou et al., 2021a; Zhang et al., 2021b; Kim et al., 2021; Zhou and Gu, 2022) have provided variance-dependent regret bounds for linear contextual bandits, which interpolates the regret for the worst-case regime…
We propose $\ell_1$ norm regularized quadratic surface support vector machine models for binary classification in supervised learning. We establish their desired theoretical properties, including the existence and uniqueness of the optimal…
The population recovery problem is a basic problem in noisy unsupervised learning that has attracted significant research attention in recent years [WY12,DRWY12, MS13, BIMP13, LZ15,DST16]. A number of different variants of this problem have…
Max-margin learning is a powerful approach to building classifiers and structured output predictors. Recent work on max-margin supervised topic models has successfully integrated it with Bayesian topic models to discover discriminative…
In this paper, we prove convergence rates for time discretisation schemes for semi-linear stochastic evolution equations with additive or multiplicative Gaussian noise, where the leading operator $A$ is the generator of a strongly…
In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees…
We study the problem of learning classification functions from noiseless training samples, under the assumption that the decision boundary is of a certain regularity. We establish universal lower bounds for this estimation problem, for…
The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, $\ell_2$ penalties are compared to so-called sparsity promoting $\ell_1$ and $\ell_0$ penalties, and a…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
Motivated by problems in optimization we study the sparsity of the solutions to systems of linear Diophantine equations and linear integer programs, i.e., the number of non-zero entries of a solution, which is often referred to as the…
This paper establishes the first almost sure convergence rate and the first maximal concentration bound with exponential tails for general contractive stochastic approximation algorithms with Markovian noise. As a corollary, we also obtain…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
Sparse clustering, which aims to find a proper partition of an extremely high-dimensional data set with redundant noise features, has been attracted more and more interests in recent years. The existing studies commonly solve the problem in…
We determine a fundamental upper bound on the performance of any adaptive protocol for discrimination or estimation of a channel which has an unknown parameter encoded in the state of its environment. Since our approach relies on the…