Related papers: Sparse approximation of individual functions
Sparse representation has been applied successfully in abnormal event detection, in which the baseline is to learn a dictionary accompanied by sparse codes. While much emphasis is put on discriminative dictionary construction, there are no…
Some consequences of the Restricted Isometry Property (RIP) of matrices have been applied to develop a greedy algorithm called "ROMP" (Regularized Orthogonal Matching Pursuit) to recover sparse signals and to approximate non-sparse ones.…
This paper focuses on the development of novel greedy techniques for distributed learning under sparsity constraints. Greedy techniques have widely been used in centralized systems due to their low computational requirements and at the same…
We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent LP rounding algorithms and a hybrid algorithm…
Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsity generalization of the dense tensor BR1Approx, and is a higher-order extension of the sparse matrix BR1Approx, is one of the most important problems in sparse tensor…
Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this…
We show that sparsity constrained optimization problems over low dimensional spaces tend to have a small duality gap. We use the Shapley-Folkman theorem to derive both data-driven bounds on the duality gap, and an efficient primalization…
Differentially Private algorithms often need to select the best amongst many candidate options. Classical works on this selection problem require that the candidates' goodness, measured as a real-valued score function, does not change by…
In sparse linear regression, the SLOPE estimator generalizes LASSO by penalizing different coordinates of the estimate according to their magnitudes. In this paper, we present a precise performance characterization of SLOPE in the…
Non-negative signals form an important class of sparse signals. Many algorithms have already beenproposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. The…
An important research thread in algorithmic game theory studies the design of efficient truthful mechanisms that approximate the optimal social welfare. A fundamental question is whether an \alpha-approximation algorithm translates into an…
We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some linear methods of this approximation for univariate functions in the class induced by the convolution…
We develop a gradient-like algorithm to minimize a sum of peer objective functions based on coordination through a peer interconnection network. The coordination admits two stages: the first is to constitute a gradient, possibly with…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
Proximal gradient methods have been found to be highly effective for solving minimization problems with non-negative constraints or L1-regularization. Under suitable nondegeneracy conditions, it is known that these algorithms identify the…
In this paper, we study the problem of maximizing $k$-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a $\frac{1}{2}(1-e^{-2})\approx 0.432$ greedy approximation algorithm. For the…
We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides…
In this paper we introduce several extremal sequences of points on locally compact metric spaces and study their asymptotic properties. These sequences are defined through a greedy algorithm by minimizing a certain energy functional whose…
Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…
The maximization of submodular functions is an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of the optimal. When this algorithm…