Conference proceeding
On the mixing time of Markov Chain Monte Carlo for integer least-square problems
2012 IEEE 51st IEEE Conference on Decision and Control (CDC), pp.2545-2550
12/2012
DOI: 10.1109/CDC.2012.6425890
Abstract
In this paper, we study the mixing time of Markov Chain Monte Carlo (MCMC) for integer least-square (LS) optimization problems. It is found that the mixing time of MCMC for integer LS problems depends on the structure of the underlying lattice. More specifically, the mixing time of MCMC is closely related to whether there is a local minimum in the lattice structure. For some lattices, the mixing time of the Markov chain is independent of the signal-to-noise ratio (SNR) and grows polynomially in the problem dimension; while for some lattices, the mixing time grows unboundedly as SNR grows. Both theoretical and empirical results suggest that to ensure fast mixing, the temperature for MCMC should often grow positively as the SNR increases. We also derive the probability that there exist local minima in an integer least-square problem, which can be as high as equation.
Details
- Title: Subtitle
- On the mixing time of Markov Chain Monte Carlo for integer least-square problems
- Creators
- Weiyu Xu - University of IowaGeorgios Alexandros Dimakis - University of Southern CaliforniaBabak Hassibi - California Institute of Technology
- Resource Type
- Conference proceeding
- Publication Details
- 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), pp.2545-2550
- DOI
- 10.1109/CDC.2012.6425890
- ISSN
- 0191-2216
- Publisher
- IEEE
- Language
- English
- Date published
- 12/2012
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984197175302771
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