Related papers: Sparse Semidefinite Programs with Guaranteed Near-…
Many clustering problems enjoy solutions by semidefinite programming. Theoretical results in this vein frequently consider data with a planted clustering and a notion of signal strength such that the semidefinite program exactly recovers…
We describe a method for fast approximation of sparse coding. The input space is subdivided by a binary decision tree, and we simultaneously learn a dictionary and assignment of allowed dictionary elements for each leaf of the tree. We…
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…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
We show that under mild assumptions for a problem whose solutions admit a dynamic programming-like recurrence relation, we can still find a solution under additional packing constraints, which need to be satisfied approximately. The number…
The complexity of problems involving global constraints is usually much more difficult to understand than the complexity of problems only involving local constraints. A natural form of global constraints are connectivity constraints. We…
Given a graph, the sparsest cut problem asks for a subset of vertices whose edge expansion (the normalized cut given by the subset) is minimized. In this paper, we study a generalization of this problem seeking for $ k $ disjoint subsets of…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
The TREE method has been widely used for long-range interaction {\it N}-body problems. We have developed a parallel TREE code for two-component classical plasmas with open boundary conditions and highly non-uniform charge distributions. The…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of 2 sub-gaussian distributions in $\R^p$. We consider semidefinite programming relaxations of an integer quadratic program that is…
The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…
The independence number of a tree decomposition is the size of a largest independent set contained in a single bag. The tree-independence number of a graph $G$ is the minimum independence number of a tree decomposition of $G$. As shown…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…
The verification of multithreaded software is still a challenge. This comes mainly from the fact that the number of thread interleavings grows exponentially in the number of threads. The idea that thread interleavings can be studied with a…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…
We study finite-sum nonlinear programs with localized variable coupling encoded by a (hyper)graph. We introduce a graph-compliant decomposition framework that brings message passing into continuous optimization in a rigorous, implementable,…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…