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Accelerated Information Gradient Flow
- Source :
- Journal of Scientific Computing. 90
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- We present a framework for Nesterov's accelerated gradient flows in probability space to design efficient mean-field Markov chain Monte Carlo (MCMC) algorithms for Bayesian inverse problems. Here four examples of information metrics are considered, including Fisher-Rao metric, Wasserstein-2 metric, Kalman-Wasserstein metric and Stein metric. For both Fisher-Rao and Wasserstein-2 metrics, we prove convergence properties of accelerated gradient flows. In implementations, we propose a sampling-efficient discrete-time algorithm for Wasserstein-2, Kalman-Wasserstein and Stein accelerated gradient flows with a restart technique. We also formulate a kernel bandwidth selection method, which learns the gradient of logarithm of density from Brownian-motion samples. Numerical experiments, including Bayesian logistic regression and Bayesian neural network, show the strength of the proposed methods compared with state-of-the-art algorithms.
- Subjects :
- FOS: Computer and information sciences
Logarithm
Computer Science - Information Theory
Bayesian probability
Machine Learning (stat.ML)
Statistics::Other Statistics
Kernel Bandwidth
Statistics - Computation
Theoretical Computer Science
symbols.namesake
Statistics - Machine Learning
Convergence (routing)
FOS: Mathematics
Mathematics - Optimization and Control
Computation (stat.CO)
Mathematics
Numerical Analysis
Information Theory (cs.IT)
Applied Mathematics
General Engineering
Markov chain Monte Carlo
Inverse problem
Statistics::Computation
Computational Mathematics
Computational Theory and Mathematics
Optimization and Control (math.OC)
Metric (mathematics)
symbols
Balanced flow
Algorithm
Software
Subjects
Details
- ISSN :
- 15737691 and 08857474
- Volume :
- 90
- Database :
- OpenAIRE
- Journal :
- Journal of Scientific Computing
- Accession number :
- edsair.doi.dedup.....d382de8b3b06dee66fff8b33219541af