Related papers: Grouped Variable Selection with Discrete Optimizat…

This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but…

In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…

In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…

We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…

The sparse portfolio selection problem is one of the most famous and frequently-studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal…

Logistic regression is a widely used statistical model to describe the relationship between a binary response variable and predictor variables in data sets. It is often used in machine learning to identify important predictor variables.…

This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes…

We study the problem of inferring sparse time-varying Markov random fields (MRFs) with different discrete and temporal regularizations on the parameters. Due to the intractability of discrete regularization, most approaches for solving this…

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

The explosion of large-scale data in fields such as finance, e-commerce, and social media has outstripped the processing capabilities of single-machine systems, driving the need for distributed statistical inference methods. Traditional…

Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…

This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…

Subgroup-discovery methods allow users to obtain simple descriptions of interesting regions in a dataset. Using constraints in subgroup discovery can enhance interpretability even further. In this article, we focus on two types of…

We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is…

In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…

Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group…

Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic…