Learning the Information Divergence

IEEE Transactions on Pattern Analysis and Machine Intelligence
Onur DikmenErkki Oja

Abstract

Information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems. Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor Embedding, topic models, and Bayesian network optimization. The success of such a learning task depends heavily on a suitable divergence. A large variety of divergences have been suggested and analyzed, but very few results are available for an objective choice of the optimal divergence for a given task. Here we present a framework that facilitates automatic selection of the best divergence among a given family, based on standard maximum likelihood estimation. We first propose an approximated Tweedie distribution for the β-divergence family. Selecting the best β then becomes a machine learning problem solved by maximum likelihood. Next, we reformulate α-divergence in terms of β-divergence, which enables automatic selection of α by maximum likelihood with reuse of the learning principle for β-divergence. Furthermore, we show the connections between γ- and β-divergences as well as Renyi- and α-divergences, such that our automatic selection framework is extended to non-separable divergences. Experiments ...Continue Reading

References

Aug 16, 2002·Neural Computation·Minami Mihoko, Shinto Eguchi
Jul 14, 2005·Acta Oto-laryngologica·Lela MigirovJona Kronenberg
Feb 15, 2007·Neural Computation·Raul Kompass
Sep 13, 2008·Neural Computation·Cédric FévotteJean-Louis Durrieu
Mar 31, 2010·IEEE Transactions on Neural Networks·Zhirong Yang, Erkki Oja
Oct 20, 2011·IEEE Transactions on Neural Networks·Zhirong Yang, Erkki Oja

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