相关论文: Deterministic Bridge Regression for Compressive Cl…

This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an $\ell^1$…

The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…

This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular,…

An universal primal-dual approach of description equilibriums in large class of hierarchical congestion population games is proposed. At the very core of the approach is hierarchy of enclosed to each other transport networks. In different…

The bridge regression estimator generalizes both ridge regression and LASSO estimators. Since it minimizes the sum of squared residuals with a $L_{\gamma }$ penalty, this estimator is typically not robust against outliers in the data. There…

While knowledge representation and reasoning are considered the keys for human-level artificial intelligence, connectionist networks have been shown successful in a broad range of applications due to their capacity for robust learning and…

Finding methods for making generalizable predictions is a fundamental problem of machine learning. By looking into similarities between the prediction problem for unknown data and the lossless compression we have found an approach that…

We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…

We propose a novel method for compressed sensing recovery using untrained deep generative models. Our method is based on the recently proposed Deep Image Prior (DIP), wherein the convolutional weights of the network are optimized to match…

We formulate the problem of performing optimal data compression under the constraints that compressed data can be used for accurate classification in machine learning. We show that this translates to a problem of minimizing the mutual…

We derive asymptotic properties of penalized estimators for singular models for which identifiability may break and the true parameter values can lie on the boundary of the parameter space. Selection consistency of the estimators is also…

Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of…

A change of the prevalent supervised learning techniques is foreseeable in the near future: from the complex, computational expensive algorithms to more flexible and elementary training ones. The strong revitalization of randomized…

Despite extensive research spanning several decades, class imbalance is still considered a profound difficulty for both machine learning and deep learning models. While data oversampling is the foremost technique to address this issue,…

This paper proposes a novel algorithm for signal classification problems. We consider a non-stationary random signal, where samples can be classified into several different classes, and samples in each class are identically independently…

We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…

This paper studies the problem of learning the large-scale Gaussian graphical models that are multivariate totally positive of order two ($\text{MTP}_2$). By introducing the concept of bridge, which commonly exists in large-scale sparse…

Recent work on Path-Dependent Partial Differential Equations (PPDEs) has shown that PPDE solutions can be approximated by a probabilistic representation, implemented in the literature by the estimation of conditional expectations using…

Diffusion bridge models in both continuous and discrete state spaces have recently become powerful tools in the field of generative modeling. In this work, we leverage the discrete state space formulation of bridge matching models to…

In distributed optimization, the communication of model updates can be a performance bottleneck. Consequently, gradient compression has been proposed as a means of increasing optimization throughput. In general, due to information loss,…