Related papers: Rescaled Pure Greedy Algorithm for Hilbert and Ban…
In this paper, we propose a new greedy algorithm for sparse approximation, called SLS for Single L_1 Selection. SLS essentially consists of a greedy forward strategy, where the selection rule of a new component at each iteration is based on…
Sparse regression and variable selection for large-scale data have been rapidly developed in the past decades. This work focuses on sparse ridge regression, which enforces the sparsity by use of the L0 norm. We first prove that the…
In this paper we analyze approximation and recovery properties with respect to systems satisfying universal sampling discretization property and a special incoherence property. We apply a powerful nonlinear approximation method -- the Weak…
The problem of selecting a small-size representative summary of a large dataset is a cornerstone of machine learning, optimization and data science. Motivated by applications to recommendation systems and other scenarios with query-limited…
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…
$ \newcommand{\kalg}{{k_{\mathrm{alg}}}} \newcommand{\kopt}{{k_{\mathrm{opt}}}} \newcommand{\algset}{{T}} \renewcommand{\Re}{\mathbb{R}} \newcommand{\eps}{\varepsilon} \newcommand{\pth}[2][\!]{#1\left({#2}\right)} \newcommand{\npoints}{n}…
Motivated by an application in kidney exchange, we study the following query-commit problem: we are given the set of vertices of a non-bipartite graph G. The set of edges in this graph are not known ahead of time. We can query any pair of…
Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except for special cases, previous work has…
The aim of this paper is to show that almost greedy bases induce tighter embeddings in superreflexive Banach spaces than in general Banach spaces. More specifically, we show that an almost greedy basis in a superreflexive Banach space…
This paper concerns a fundamental class of convex matrix optimization problems. It presents the first algorithm that uses optimal storage and provably computes a low-rank approximation of a solution. In particular, when all solutions have…
We address the problems of minimizing and of maximizing the spectral radius overa compact family of non-negative matrices. Those problems being hard in generalcan be efficiently solved for some special families. We consider the so-called…
For two countable ordinals $\alpha$ and $\beta$, a basis of a Banach space $X$ is said to be $(\alpha, \beta)$-quasi-greedy if it is 1) quasi-greedy, 2) $\mathcal{S}_\alpha$-unconditional but not $\mathcal{S}_{\alpha+1}$-unconditional, and…
In this paper, a new optimization framework is defined that includes the optimization framework recently proposed in [1]-[2] as a special case. The convex optimization in [1]-[2] includes centralized optimization and distributed…
Using a technique of adjoining an order unit to a normed linear space, we have characterized strictly convex spaces among normed linear spaces and Hilbert spaces among strictly convex Banach spaces respectively. This leads to a…
The anchor words algorithm performs provably efficient topic model inference by finding an approximate convex hull in a high-dimensional word co-occurrence space. However, the existing greedy algorithm often selects poor anchor words,…
In the design of greedy algorithms for the maximum cardinality matching problem the utilization of degree information when selecting the next edge is a well established and successful approach. We define the class of "degree sensitive"…
Inverse imaging problems rely on limited and indirect measurements, making reconstruction highly dependent on both regularization and sample locations. We introduce a novel greedy framework for the optimal selection of indirect measurements…
This paper presents an algorithm tailored for the efficient recovery of sparse probability measures incorporating $\ell_0$-sparse regularization within the probability simplex constraint. Employing the Bregman proximal gradient method, our…
Many image processing applications benefited remarkably from the theory of sparsity. One model of sparsity is the cosparse analysis one. It was shown that using l_1-minimization one might stably recover a cosparse signal from a small set of…
When solving PDEs, classical numerical solvers are often computationally expensive, while machine learning methods can suffer from spectral bias, failing to capture high-frequency components. Designing an optimal hybrid iterative…