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Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\ell_0$ pseudo norm…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
The randomized version of the Kaczmarz method for the solution of linear systems is known to converge linearly in expectation. In this work we extend this result and show that the recently proposed Randomized Sparse Kaczmarz method for…
In this paper, we study the problem of sparse mixed linear regression on an unlabeled dataset that is generated from linear measurements from two different regression parameter vectors. Since the data is unlabeled, our task is not only to…
In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now those corresponding non-convex algorithms lack convergence guarantees from the initial…
We consider the nonconvex regularized method for low-rank matrix recovery. Under the assumption on the singular values of the parameter matrix, we provide the recovery bound for any stationary point of the nonconvex method by virtue of…
We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
In this paper we are concerned with fully automatic and locally adaptive estimation of functions in a "signal + noise"-model where the regression function may additionally be blurred by a linear operator, e.g. by a convolution. To this end,…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
Machine learning techniques always aim to reduce the generalized prediction error. In order to reduce it, ensemble methods present a good approach combining several models that results in a greater forecasting capacity. The Random Machines…
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…