Related papers: Expressing Sparse Matrix Computations for Producti…
Analyzing array-based computations to determine data dependences is useful for many applications including automatic parallelization, race detection, computation and communication overlap, verification, and shape analysis. For sparse matrix…
Hierarchical matrices are space and time efficient representations of dense matrices that exploit the low rank structure of matrix blocks at different levels of granularity. The hierarchically low rank block partitioning produces…
A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…
Architectures with multiple classes of memory media are becoming a common part of mainstream supercomputer deployments. So called multi-level memories offer differing characteristics for each memory component including variation in…
Sparse matrix-dense matrix multiplication (SpMM) is a critical kernel in scientific computing, graph analytics, and machine learning, whose performance is often constrained by memory bandwidth. In this work, we investigate the applicability…
How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental…
In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…
Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…
Field Programmable Gate Arrays generate algorithmic specific architectures that improve the code's FLOP per watt ratio. Such devices are re-gaining interest due to the rise of new tools that facilitate their programming, such as OmpSs. The…
This is the second of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The first paper presented the original algorithm, its…
In this paper, we show a way to exploit sparsity in the problem data in a primal-dual potential reduction method for solving a class of semidefinite programs. When the problem data is sparse, the dual variable is also sparse, but the primal…
We develop the theory and practical implementation of p-adic sparse coding of data. Rather than the standard, sparsifying criterion that uses the $L_0$ pseudo-norm, we use the p-adic norm. We require that the hierarchy or tree be…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
Straggler nodes are well-known bottlenecks of distributed matrix computations which induce reductions in computation/communication speeds. A common strategy for mitigating such stragglers is to incorporate Reed-Solomon based MDS (maximum…
Computing the product of two sparse matrices (SpGEMM) is a fundamental operation in various combinatorial and graph algorithms as well as various bioinformatics and data analytics applications for computing inner-product similarities. For…
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…
Sparse matrix representations are ubiquitous in computational science and machine learning, leading to significant reductions in compute time, in comparison to dense representation, for problems that have local connectivity. The adoption of…
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…
Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…
Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…