Related papers: Faster Inversion and Other Black Box Matrix Comput…
We develop a fixed-point iterative algorithm that computes the matrix projection with respect to the Bures distance on the set of positive definite matrices that are invariant under some symmetry. We prove that the fixed-point iteration…
We propose different implementations of the sparse matrix--dense vector multiplication (\spmv{}) for finite fields and rings $\Zb/m\Zb$. We take advantage of graphic card processors (GPU) and multi-core architectures. Our aim is to improve…
Conventional deep convolutional neural networks (CNNs) apply convolution operators uniformly in space across all feature maps for hundreds of layers - this incurs a high computational cost for real-time applications. For many problems such…
Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual…
In this paper we show how to recover a spectral approximations to broad classes of structured matrices using only a polylogarithmic number of adaptive linear measurements to either the matrix or its inverse. Leveraging this result we obtain…
Gradient descent optimizations and backpropagation are the most common methods for training neural networks, but they are computationally expensive for real time applications, need high memory resources, and are difficult to converge for…
In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main…
We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of…
We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
Single-objective black box optimization (also known as zeroth-order optimization) is the process of minimizing a scalar objective $f(x)$, given evaluations at adaptively chosen inputs $x$. In this paper, we consider multi-objective…
We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be…
A fast direct inversion scheme for the large sparse systems of linear equations resulting from the discretization of elliptic partial differential equations in two dimensions is given. The scheme is described for the particular case of a…
Traditional algorithms for stochastic optimization require projecting the solution at each iteration into a given domain to ensure its feasibility. When facing complex domains, such as positive semi-definite cones, the projection operation…
This paper addresses spatial programming of sparse matrix computations for productive performance. The challenge is how to express an irregular computation and its optimizations in a regular way. A sparse matrix has (non-zero) values and a…
Optimization algorithms such as projected Newton's method, FISTA, mirror descent, and its variants enjoy near-optimal regret bounds and convergence rates, but suffer from a computational bottleneck of computing ``projections'' in…
We propose an algorithm for rotational sparse coding along with an efficient implementation using steerability. Sparse coding (also called dictionary learning) is an important technique in image processing, useful in inverse problems,…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…