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Reducing the amount of human supervision is a key problem in machine learning and a natural approach is that of exploiting the relations (structure) among different tasks. This is the idea at the core of multi-task learning. In this context…

This paper develops a convex approach for sparse one-dimensional deconvolution that improves upon L1-norm regularization, the standard convex approach. We propose a sparsity-inducing non-separable non-convex bivariate penalty function for…

In the paper, we develop a composite version of Mirror Prox algorithm for solving convex-concave saddle point problems and monotone variational inequalities of special structure, allowing to cover saddle point/variational analogies of what…

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…

Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…

In many practical applications of constrained optimization, scale and solving time limits make traditional optimization solvers prohibitively slow. Thus, the research question of how to design optimization proxies -- machine learning models…

Sparse reconstruction approaches using the re-weighted l1-penalty have been shown, both empirically and theoretically, to provide a significant improvement in recovering sparse signals in comparison to the l1-relaxation. However, numerical…

We present an exploration of the rich theoretical connections between several classes of regularized models, network flows, and recent results in submodular function theory. This work unifies key aspects of these problems under a common…

This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

This paper presents a novel learning-based approach to construct a surrogate problem that approximates a given parametric nonconvex optimization problem. The surrogate function is designed to be the minimum of a finite set of functions,…

Nowadays, analysing data from different classes or over a temporal grid has attracted a great deal of interest. As a result, various multiple graphical models for learning a collection of graphical models simultaneously have been derived by…

Compared with digital methods, sparse recovery based on spiking neural networks has great advantages like high computational efficiency and low power-consumption. However, current spiking algorithms cannot guarantee more accurate estimates…

Augmenting a smooth cost function with an $\ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods.…

Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…

Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…

Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…

Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…