Article

Generalization bounds of ERM algorithm with Markov chain samples

Acta Mathematicae Applicatae Sinica (impact factor: 0.29). 05/2012; DOI:10.1007/s10255-011-0096-4 pp.1-16

ABSTRACT One of the main goals of machine learning is to study the generalization performance of learning algorithms. The previous
main results describing the generalization ability of learning algorithms are usually based on independent and identically
distributed (i.i.d.) samples. However, independence is a very restrictive concept for both theory and real-world applications.
In this paper we go far beyond this classical framework by establishing the bounds on the rate of relative uniform convergence
for the Empirical Risk Minimization (ERM) algorithm with uniformly ergodic Markov chain samples. We not only obtain generalization
bounds of ERM algorithm, but also show that the ERM algorithm with uniformly ergodic Markov chain samples is consistent. The
established theory underlies application of ERM type of learning algorithms.

Keywordsgeneralization bounds–ERM algorithm–relative uniform convergence–uniformly ergodic Markov chain–learning theory

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Keywords

algorithms
 
bounds
 
classical framework
 
Empirical Risk Minimization
 
ERM
 
ERM algorithm
 
ERM type
 
generalization ability
 
generalization performance
 
identically
 
Keywordsgeneralization bounds–ERM algorithm–relative uniform convergence–uniformly ergodic Markov chain–learning theory
 
real-world applications
 
relative uniform convergence
 
theory underlies application
 
uniformly ergodic Markov chain samples
 

Bin Zou