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Optimization of MCMC sampling algorithm for the calculation of PAC-Bayes bound

Authors: null Li Tang; null Zheng Zhao; null Xiu-Jun Gong; null Hua-Peng Zeng;

Optimization of MCMC sampling algorithm for the calculation of PAC-Bayes bound

Abstract

PAC-Bayes bound provides a formal framework for deducing the tightest risk bounds of the classifiers. After formulating the concept space as a Reproducing Kernel Hilbert Space (RKHS), the Markov Chain Monte Carlo (MCMC) sampling algorithm for simulating posterior distributions of the concept space can realize the calculation of PAC-Bayes bound. A major issue is the computational complexity in geometric growth when the dimension of concept space increases. In this paper, we store a portion of the sampling data and calculate its variance, after which the variance minimization method is proposed to investigate the support vectors. Finally, we optimize the support vectors coupled with their weight vectors, and compare the PAC-Bayes bounds. The experimental results of our artificial data sets in low-dimensional spaces show that the optimization is reasonable and effective in practice.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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