Name
Abstract | ||
|---|---|---|
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. |
Year | Venue | Field |
|---|---|---|
2017 | ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 30 (NIPS 2017) | Applied mathematics,Mathematical optimization,Additive function,Exponential function,Location-scale family,Parametric family,Exponential family,Natural exponential family,Expectation propagation,Mathematics,Bayes' theorem |
DocType | Volume | ISSN |
Conference | 30 | 1049-5258 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Futami, Futoshi | 1 | 0 | 2.03 |
| Issei Sato | 2 | 331 | 41.59 |
| Masashi Sugiyama | 3 | 3353 | 264.24 |