THIS GRANT IS A CONTINUATION OF N000141410369 EXPLOITING LOW-DIMENSIONAL STRUCTURE FOR ACCELERATED COMPUTATIONS
Abstract
The proposed research will investigate dictionary learning in the context of a new class of local-global shrinkage priors. Compressibility (not sparsity) of the dictionary coefficients is imposed based on heavy-tailed distributions, like the Levy process. One of the significant challenges of this approach is that it scales poorly as the quantity of data expands. This has motivated stochastic-gradient-descent methods, which correspond to random data sampling. In the proposed research we will consider general projections of the original data (delta-function projections correspond to sampling), to reduce it to a lower-dimensional space. In the proposed research we will examine use of the low-dimensional representations for such large-scale matrix computations. For example, portions of the matrix may have components that reside in a low-dimensional subspace. One need not compute the entire matrix to learn this subspace, thereby offering the potential to significantly reduce the total computation. The low-dimensional representations are advantageous for the efficient computation of matrix inverses and products. We will examine this challenge in the second year of the proposed program, in the context of one- and two-dimensional scalar wave equations and numerical methods (e.g., the method of moments and the fast multi-pole method).
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141612366
Entities
People
- Lawrence Carin
Organizations
- Duke University
- Office of Naval Research
- United States Navy