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Expectation Propagation for t-Exponential Family Using q-Algebra
Futoshi Futami · Issei Sato · Masashi Sugiyama

Mon Dec 04 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #194 #None

Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which contains Student-t distributions as family members and thus allows us to handle noisy data well. However, since the t-exponential family is defined by the deformed exponential, an efficient learning algorithm for the t-exponential family such as expectation propagation (EP) cannot be derived in the same way as the ordinary exponential family. In this paper, we borrow the mathematical tools of q-algebra from statistical physics and show that the pseudo additivity of distributions allows us to perform calculation of t-exponential family distributions through natural parameters. We then develop an expectation propagation (EP) algorithm for the t-exponential family, which provides a deterministic approximation to the posterior or predictive distribution with simple moment matching. We finally apply the proposed EP algorithm to the Bayes point machine and Student-t process classification, and demonstrate their performance numerically.

Author Information

Futoshi Futami (University of Tokyo/RIKEN)
Issei Sato (The University of Tokyo/RIKEN)
Masashi Sugiyama (RIKEN / University of Tokyo)

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