Related papers: Convex Regularization for High-Dimensional Multi-R…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…

In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…

We derive bounds relating Renegar's condition number to quantities that govern the statistical performance of convex regularization in settings that include the $\ell_1$-analysis setting. Using results from conic integral geometry, we show…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

Tensor-based methods have recently emerged as a more natural and effective formulation to address many problems in hyperspectral imaging. In hyperspectral unmixing (HU), low-rank constraints on the abundance maps have been shown to act as a…

In this paper, we analyse the recovery properties of nonconvex regularized $M$-estimators, under the assumption that the true parameter is of soft sparsity. In the statistical aspect, we establish the recovery bound for any stationary point…

In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…

Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…

The reduced-rank vector autoregressive (VAR) model can be interpreted as a supervised factor model, where two factor modelings are simultaneously applied to response and predictor spaces. This article introduces a new model, called vector…

In this paper we consider a general problem set-up for a wide class of convex and robust distributed optimization problems in peer-to-peer networks. In this set-up convex constraint sets are distributed to the network processors who have to…

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…

This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…

Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…

We study nonconvex distributed optimization in multi-agent networks with time-varying (nonsymmetric) connectivity. We introduce the first algorithmic framework for the distributed minimization of the sum of a smooth (possibly nonconvex and…

Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few…

We consider the problem of recovering a target matrix that is a superposition of low-rank and sparse components, from a small set of linear measurements. This problem arises in compressed sensing of structured high-dimensional signals such…

The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining…

This paper introduces a general framework for solving constrained convex quaternion optimization problems in the quaternion domain. To soundly derive these new results, the proposed approach leverages the recently developed generalized…

We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…