Putting MRFs on a Tensor Train

Alexander Novikov, Anton Rodomanov, Anton Osokin, Dmitry Vetrov
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):811-819, 2014.

Abstract

In the paper we present a new framework for dealing with probabilistic graphical models. Our approach relies on the recently proposed Tensor Train format (TT-format) of a tensor that while being compact allows for efficient application of linear algebra operations. We present a way to convert the energy of a Markov random field to the TT-format and show how one can exploit the properties of the TT-format to attack the tasks of the partition function estimation and the MAP-inference. We provide theoretical guarantees on the accuracy of the proposed algorithm for estimating the partition function and compare our methods against several state-of-the-art algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-novikov14, title = {Putting MRFs on a Tensor Train}, author = {Novikov, Alexander and Rodomanov, Anton and Osokin, Anton and Vetrov, Dmitry}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {811--819}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/novikov14.pdf}, url = {https://proceedings.mlr.press/v32/novikov14.html}, abstract = {In the paper we present a new framework for dealing with probabilistic graphical models. Our approach relies on the recently proposed Tensor Train format (TT-format) of a tensor that while being compact allows for efficient application of linear algebra operations. We present a way to convert the energy of a Markov random field to the TT-format and show how one can exploit the properties of the TT-format to attack the tasks of the partition function estimation and the MAP-inference. We provide theoretical guarantees on the accuracy of the proposed algorithm for estimating the partition function and compare our methods against several state-of-the-art algorithms.} }
Endnote
%0 Conference Paper %T Putting MRFs on a Tensor Train %A Alexander Novikov %A Anton Rodomanov %A Anton Osokin %A Dmitry Vetrov %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-novikov14 %I PMLR %P 811--819 %U https://proceedings.mlr.press/v32/novikov14.html %V 32 %N 2 %X In the paper we present a new framework for dealing with probabilistic graphical models. Our approach relies on the recently proposed Tensor Train format (TT-format) of a tensor that while being compact allows for efficient application of linear algebra operations. We present a way to convert the energy of a Markov random field to the TT-format and show how one can exploit the properties of the TT-format to attack the tasks of the partition function estimation and the MAP-inference. We provide theoretical guarantees on the accuracy of the proposed algorithm for estimating the partition function and compare our methods against several state-of-the-art algorithms.
RIS
TY - CPAPER TI - Putting MRFs on a Tensor Train AU - Alexander Novikov AU - Anton Rodomanov AU - Anton Osokin AU - Dmitry Vetrov BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-novikov14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 811 EP - 819 L1 - http://proceedings.mlr.press/v32/novikov14.pdf UR - https://proceedings.mlr.press/v32/novikov14.html AB - In the paper we present a new framework for dealing with probabilistic graphical models. Our approach relies on the recently proposed Tensor Train format (TT-format) of a tensor that while being compact allows for efficient application of linear algebra operations. We present a way to convert the energy of a Markov random field to the TT-format and show how one can exploit the properties of the TT-format to attack the tasks of the partition function estimation and the MAP-inference. We provide theoretical guarantees on the accuracy of the proposed algorithm for estimating the partition function and compare our methods against several state-of-the-art algorithms. ER -
APA
Novikov, A., Rodomanov, A., Osokin, A. & Vetrov, D.. (2014). Putting MRFs on a Tensor Train. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):811-819 Available from https://proceedings.mlr.press/v32/novikov14.html.

Related Material