Related papers: Bregman Distance to L1 Regularized Logistic Regres…
Feature selection is a standard approach to understanding and modeling high-dimensional classification data, but the corresponding statistical methods hinge on tuning parameters that are difficult to calibrate. In particular, existing…
Recently, a new distance has been introduced for the graphs of two point-to-set operators, one of which is maximally monotone. When both operators are the subdifferential of a proper lower semicontinuous convex function, this distance…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
This paper investigates a new approach to estimate the gradient of the conditional probability given the covariates in the binary classification framework. The proposed approach consists in fitting a localized nearest-neighbor logistic…
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 consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably…
We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…
The linearized Bregman iterations (LBreI) and its variants are powerful tools for finding sparse or low-rank solutions to underdetermined linear systems. In this study, we propose a cut-and-project perspective for the linearized Bregman…
Logistic regression is an important statistical tool for assessing the probability of an outcome based upon some predictive variables. Standard methods can only deal with precisely known data, however many datasets have uncertainties which…
We propose a novel parameter estimation procedure that works efficiently for conditional random fields (CRF). This algorithm is an extension to the maximum likelihood estimation (MLE), using loss functions defined by Bregman divergences…
Logistic regression model is widely used in many studies to investigate the relationship between a binary response variable Y and a set of potential predictors $X_1,\ldots, X_p$ (for example: $Y = 1$ if the outcome occurred and $Y = 0$…
Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
High-dimensional prediction is a challenging problem setting for traditional statistical models. Although regularization improves model performance in high dimensions, it does not sufficiently leverage knowledge on feature importances held…
The regression problem associated with finding a matrix approximation of the Koopman operator from data is considered. The regression problem is formulated as a convex optimization problem subject to linear matrix inequality (LMI)…
In this work we study the method of Bregman projections for deterministic and stochastic convex feasibility problems with three types of control sequences for the selection of sets during the algorithmic procedure: greedy, random, and…
We develop a Bregman proximal gradient method for structure learning on linear structural causal models. While the problem is non-convex, has high curvature and is in fact NP-hard, Bregman gradient methods allow us to neutralize at least…
$\ell_1$ regularization has been used for logistic regression to circumvent the overfitting and use the estimated sparse coefficient for feature selection. However, the challenge of such a regularization is that the $\ell_1$ norm is not…
Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework…
Classical linear metric learning methods have recently been extended along two distinct lines: deep metric learning methods for learning embeddings of the data using neural networks, and Bregman divergence learning approaches for extending…