DeepAI AI Chat
Log In Sign Up

Covariance-Free Sparse Bayesian Learning

05/21/2021
by   Alexander Lin, et al.
0

Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem while also providing uncertainty quantification. However, the most popular inference algorithms for SBL become too expensive for high-dimensional problems due to the need to maintain a large covariance matrix. To resolve this issue, we introduce a new SBL inference algorithm that avoids explicit computation of the covariance matrix, thereby saving significant time and space. Instead of performing costly matrix inversions, our covariance-free method solves multiple linear systems to obtain provably unbiased estimates of the posterior statistics needed by SBL. These systems can be solved in parallel, enabling further acceleration of the algorithm via graphics processing units. In practice, our method can be up to thousands of times faster than existing baselines, reducing hours of computation time to seconds. We showcase how our new algorithm enables SBL to tractably tackle high-dimensional signal recovery problems, such as deconvolution of calcium imaging data and multi-contrast reconstruction of magnetic resonance images. Finally, we open-source a toolbox containing all of our implementations to drive future research in SBL.

READ FULL TEXT

page 1

page 11

02/25/2022

High-Dimensional Sparse Bayesian Learning without Covariance Matrices

Sparse Bayesian learning (SBL) is a powerful framework for tackling the ...
01/27/2022

Fast Moving Natural Evolution Strategy for High-Dimensional Problems

In this work, we propose a new variant of natural evolution strategies (...
11/24/2017

Sparse Inverse Covariance Estimation for Chordal Structures

In this paper, we consider the Graphical Lasso (GL), a popular optimizat...
10/06/2008

Large Scale Variational Inference and Experimental Design for Sparse Generalized Linear Models

Many problems of low-level computer vision and image processing, such as...
07/17/2021

Sparse Bayesian Learning with Diagonal Quasi-Newton Method For Large Scale Classification

Sparse Bayesian Learning (SBL) constructs an extremely sparse probabilis...
10/12/2019

Real-time outlier detection for large datasets by RT-DetMCD

Modern industrial machines can generate gigabytes of data in seconds, fr...