Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/99342
Title: Generalization bounds of ERM-based learning processes for continuous-time Markov chains
Authors: Zhang, Chao
Tao, Dacheng
Keywords: DRNTU::Engineering::Computer science and engineering
Issue Date: 2012
Source: Zhang, C., & Tao, D. (2012). Generalization bounds of ERM-based learning processes for continuous-time Markov chains. IEEE transactions on neural networks and learning systems, 23(12), 1872-1883.
Series/Report no.: IEEE transactions on neural networks and learning systems
Abstract: Many existing results on statistical learning theory are based on the assumption that samples are independently and identically distributed (i.i.d.). However, the assumption of i.i.d. samples is not suitable for practical application to problems in which samples are time dependent. In this paper, we are mainly concerned with the empirical risk minimization (ERM) based learning process for time-dependent samples drawn from a continuous-time Markov chain. This learning process covers many kinds of practical applications, e.g., the prediction for a time series and the estimation of channel state information. Thus, it is significant to study its theoretical properties including the generalization bound, the asymptotic convergence, and the rate of convergence. It is noteworthy that, since samples are time dependent in this learning process, the concerns of this paper cannot (at least straightforwardly) be addressed by existing methods developed under the sample i.i.d. assumption. We first develop a deviation inequality for a sequence of time-dependent samples drawn from a continuous-time Markov chain and present a symmetrization inequality for such a sequence. By using the resultant deviation inequality and symmetrization inequality, we then obtain the generalization bounds of the ERM-based learning process for time-dependent samples drawn from a continuous-time Markov chain. Finally, based on the resultant generalization bounds, we analyze the asymptotic convergence and the rate of convergence of the learning process.
URI: https://hdl.handle.net/10356/99342
http://hdl.handle.net/10220/13531
ISSN: 2162-237X
DOI: http://dx.doi.org/10.1109/TNNLS.2012.2217987
Rights: © 2012 IEEE
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SCSE Journal Articles

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