相关论文: Convex body domination for a class of multi-scale …

The purpose of this paper is to investigate the stationary dense operators and their connection to distribution semigroups and abstract Cauchy problem in sequentially complete spaces.

While modern large-scale datasets often consist of heterogeneous subpopulations -- for example, multiple demographic groups or multiple text corpora -- the standard practice of minimizing average loss fails to guarantee uniformly low losses…

We initiate the study of matrix convexity for operator spaces. We define the notion of compact rectangular matrix convex set, and prove the natural analogs of the Krein-Milman and the bipolar theorems in this context. We deduce a canonical…

This paper is devoted to the study of the problem of prevalence in the class of quadratic stochastic operators acting on the L1 space for the uniform topology. We obtain that the set of norm quasi-mixing quadratic stochastic operators is a…

We develop techniques to construct a series of sparse polyhedral approximations of the semidefinite cone. Motivated by the semidefinite (SD) bases proposed by Tanaka and Yoshise (2018), we propose a simple expansion of SD bases so as to…

This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…

In recent years, it has been well understood that a Calder\'on-Zygmund operator $T$ is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar pointwise…

This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…

The extended-domain method is a strategy for applying spectral methods to complex geometries. Its stability is complicated by the ill-conditioning of the Fourier extension frame. This paper provides a rigorous analysis of the method's…

A set-system $S\subseteq \{0,1\}^n$ is cube-ideal if its convex hull can be described by capacity and generalized set covering inequalities. In this paper, we use combinatorics, convex geometry, and polyhedral theory to give exponential…

In this letter we propose a method for sparse allocation of resources to control spreading processes -- such as epidemics and wildfires -- using convex optimization, in particular exponential cone programming. Sparsity of allocation has…

In this work, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the…

In the first part of the paper, we consider a discrete-time stochastic control system. We show that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of the system as well as the…

Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…

Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple…

We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. This operator is perturbed by a first order differential operator, the coefficients of which depend arbitrarily on a…

We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using…

We study the problem of half-domination sets of vertices in vertex transitive infinite graphs generated by regular or semi-regular tessellations of the plane. In some cases, the results obtained are sharp and in the rest, we show upper…

We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear…