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Maximum likelihood estimation of regularisation parameters in high-dimensional inverse problems: an empirical Bayesian approach. Part II: Theoretical Analysis
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove the convergence of a more general stochastic approximation scheme that includes the three algorithms of [49] as special cases. This includes asymptotic and non-asymptotic convergence results with natural and easily verifiable conditions, as well as explicit bounds on the convergence rates. Importantly, the theory is also general in that it can be applied to other intractable optimisation problems. A main novelty of the work is that the stochastic gradient estimates of our scheme are constructed from inexact proximal Markov chain Monte Carlo samplers. This allows the use of samplers that scale efficiently to large problems and for which we have precise theoretical guarantees.<br />Comment: SIIMS 2020 - 30 pages
- Subjects :
- FOS: Computer and information sciences
Applied Mathematics
General Mathematics
Maximum likelihood
Bayesian probability
Probability (math.PR)
Image processing
Mathematics - Statistics Theory
02 engineering and technology
Statistics Theory (math.ST)
Inverse problem
Stochastic approximation
Regularization (mathematics)
Statistics - Computation
[STAT] Statistics [stat]
[STAT]Statistics [stat]
0202 electrical engineering, electronic engineering, information engineering
Statistical inference
FOS: Mathematics
Applied mathematics
020201 artificial intelligence & image processing
Stochastic optimization
Mathematics - Probability
Computation (stat.CO)
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....d2e0bb253f22d9f03db12261700aaea8
- Full Text :
- https://doi.org/10.48550/arxiv.2008.05793