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: | 10.1109/TNNLS.2012.2217987 | Schools: | School of Computer Engineering | Rights: | © 2012 IEEE | Fulltext Permission: | none | Fulltext Availability: | No Fulltext |
Appears in Collections: | SCSE Journal Articles |
SCOPUSTM
Citations
20
13
Updated on Mar 23, 2024
Web of ScienceTM
Citations
20
14
Updated on Oct 27, 2023
Page view(s) 50
543
Updated on Mar 27, 2024
Google ScholarTM
Check
Altmetric
Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.