Non-Asymptotic Analysis of Relational Learning with One Network

Peng He, Changshui Zhang
Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, PMLR 33:320-327, 2014.

Abstract

This theoretical paper is concerned with a rigorous non-asymptotic analysis of relational learning applied to a single network. Under suitable and intuitive conditions on features and clique dependencies over the network, we present the first probably approximately correct (PAC) bound for maximum likelihood estimation (MLE). To our best knowledge, this is the first sample complexity result of this problem. We propose a novel combinational approach to analyze complex dependencies of relational data, which is crucial to our non-asymptotic analysis. The consistency of MLE under our conditions is also proved as the consequence of our sample complexity bound. Finally, our combinational method for analyzing dependent data can be easily generalized to treat other generalized maximum likelihood estimators for relational learning.

Cite this Paper


BibTeX
@InProceedings{pmlr-v33-he14a, title = {{Non-Asymptotic Analysis of Relational Learning with One Network}}, author = {Peng He and Changshui Zhang}, booktitle = {Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics}, pages = {320--327}, year = {2014}, editor = {Samuel Kaski and Jukka Corander}, volume = {33}, series = {Proceedings of Machine Learning Research}, address = {Reykjavik, Iceland}, month = {22--25 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v33/he14a.pdf}, url = {http://proceedings.mlr.press/v33/he14a.html}, abstract = {This theoretical paper is concerned with a rigorous non-asymptotic analysis of relational learning applied to a single network. Under suitable and intuitive conditions on features and clique dependencies over the network, we present the first probably approximately correct (PAC) bound for maximum likelihood estimation (MLE). To our best knowledge, this is the first sample complexity result of this problem. We propose a novel combinational approach to analyze complex dependencies of relational data, which is crucial to our non-asymptotic analysis. The consistency of MLE under our conditions is also proved as the consequence of our sample complexity bound. Finally, our combinational method for analyzing dependent data can be easily generalized to treat other generalized maximum likelihood estimators for relational learning.} }
Endnote
%0 Conference Paper %T Non-Asymptotic Analysis of Relational Learning with One Network %A Peng He %A Changshui Zhang %B Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2014 %E Samuel Kaski %E Jukka Corander %F pmlr-v33-he14a %I PMLR %P 320--327 %U http://proceedings.mlr.press/v33/he14a.html %V 33 %X This theoretical paper is concerned with a rigorous non-asymptotic analysis of relational learning applied to a single network. Under suitable and intuitive conditions on features and clique dependencies over the network, we present the first probably approximately correct (PAC) bound for maximum likelihood estimation (MLE). To our best knowledge, this is the first sample complexity result of this problem. We propose a novel combinational approach to analyze complex dependencies of relational data, which is crucial to our non-asymptotic analysis. The consistency of MLE under our conditions is also proved as the consequence of our sample complexity bound. Finally, our combinational method for analyzing dependent data can be easily generalized to treat other generalized maximum likelihood estimators for relational learning.
RIS
TY - CPAPER TI - Non-Asymptotic Analysis of Relational Learning with One Network AU - Peng He AU - Changshui Zhang BT - Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics DA - 2014/04/02 ED - Samuel Kaski ED - Jukka Corander ID - pmlr-v33-he14a PB - PMLR DP - Proceedings of Machine Learning Research VL - 33 SP - 320 EP - 327 L1 - http://proceedings.mlr.press/v33/he14a.pdf UR - http://proceedings.mlr.press/v33/he14a.html AB - This theoretical paper is concerned with a rigorous non-asymptotic analysis of relational learning applied to a single network. Under suitable and intuitive conditions on features and clique dependencies over the network, we present the first probably approximately correct (PAC) bound for maximum likelihood estimation (MLE). To our best knowledge, this is the first sample complexity result of this problem. We propose a novel combinational approach to analyze complex dependencies of relational data, which is crucial to our non-asymptotic analysis. The consistency of MLE under our conditions is also proved as the consequence of our sample complexity bound. Finally, our combinational method for analyzing dependent data can be easily generalized to treat other generalized maximum likelihood estimators for relational learning. ER -
APA
He, P. & Zhang, C.. (2014). Non-Asymptotic Analysis of Relational Learning with One Network. Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 33:320-327 Available from http://proceedings.mlr.press/v33/he14a.html.

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