Related papers: Bregman Distance to L1 Regularized Logistic Regres…
Distance metric learning (DML), which learns a distance metric from labeled "similar" and "dissimilar" data pairs, is widely utilized. Recently, several works investigate orthogonality-promoting regularization (OPR), which encourages the…
Prediction error is critical to assessing the performance of statistical methods and selecting statistical models. We propose the cross-validation and approximated cross-validation methods for estimating prediction error under a broad…
$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects…
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…
Learning-to-optimize is an emerging framework that seeks to speed up the solution of certain optimization problems by leveraging training data. Learned optimization solvers have been shown to outperform classical optimization algorithms in…
The MM principle is a device for creating optimization algorithms satisfying the ascent or descent property. The current survey emphasizes the role of the MM principle in nonlinear programming. For smooth functions, one can construct an…
Modern machine learning models are often trained in a setting where the number of parameters exceeds the number of training samples. To understand the implicit bias of gradient descent in such overparameterized models, prior work has…
Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…
Parameter estimation in logistic regression is a well-studied problem with the Newton-Raphson method being one of the most prominent optimization techniques used in practice. A number of monotone optimization methods including…
We apply the network Lasso to solve binary classification and clustering problems for network-structured data. To this end, we generalize ordinary logistic regression to non-Euclidean data with an intrinsic network structure. The resulting…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
We propose a novel Bregman descent algorithm for minimizing a convex function that is expressed as the sum of a differentiable part (defined over an open set) and a possibly nonsmooth term. The approach, referred to as the Variable Bregman…
Molecular profiling data (e.g., gene expression) has been used for clinical risk prediction and biomarker discovery. However, it is necessary to integrate other prior knowledge like biological pathways or gene interaction networks to…
Generalized linear regressions, such as logistic regressions or Poisson regressions, are long-studied regression analysis approaches, and their applications are widely employed in various classification problems. Our study considers a…
Application of the minimum distance method to the linear regression model for estimating regression parameters is a difficult and time-consuming process due to the complexity of its distance function, and hence, it is computationally…
We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in…
The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…
Multivariate classification methods using explanatory and predictive models are necessary for characterizing subgroups of patients according to their risk profiles. Popular methods include logistic regression and classification trees with…
Convex optimization models find interesting applications, especially in signal/image processing and compressive sensing. We study some augmented convex models, which are perturbed by strongly convex functions, and propose a dual gradient…