Expectation Propagation for t-Exponential Family (t指数型分布族に対する期待値伝播法）

• Item type: SIG Technical Reports(1)
• 公開日: 2017-06-16
• タイトル: Expectation Propagation for t-Exponential Family (t指数型分布族に対する期待値伝播法）
• タイトル / 言語: en
• タイトル: Expectation Propagation for t-Exponential Family
• 言語: eng
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_18gh
• 資源タイプ: technical report
• 著者所属: The University of Tokyo／RIKEN
• 著者所属: The University of Tokyo／RIKEN
• 著者所属: RIKEN／The University of Tokyo
• 著者所属(英): en
• 著者所属(英): The University of Tokyo / RIKEN
• 著者所属(英): en
• 著者所属(英): The University of Tokyo / RIKEN
• 著者所属(英): en
• 著者所属(英): RIKEN / The University of Tokyo
• 著者名: Futoshi, Futami; Issei, Sato; Masashi, Sugiyama
• 著者名(英): Futoshi, Futami; Issei, Sato; Masashi, Sugiyama
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: 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, we cannot derive an efficient learning algorithm for the t-exponential family such as expectation propagation (EP). 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.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: 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, we cannot derive an efficient learning algorithm for the t-exponential family such as expectation propagation (EP). 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.
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AA12055912
• 書誌情報: 研究報告バイオ情報学（BIO）; 巻 2017-BIO-50, 号 45, p. 1-6, 発行日 2017-06-16
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 2188-8590
• Notice: SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc.
• 出版者 / 言語: ja
• 出版者: 情報処理学会