Workshop on Independent Component Analysis
研究会「独立成分分析に関する理論と応用」

Date : March 20, 2006
Place: Institute of Statistical Mathematics, Kenshuu-room
統計数理研究所 研修室

10:00 - 10:45 ``Non-negative matrix factorization:divergences and distributions''
Mihoko Minami (Institute of Statistical Mathematics)

10:50 - 11:40 ``Discovery of non-gaussian linear causal models using independent component analysis''
Shouhei Shimizu (Osaka University)

11:40 - 13:30 lunch; information exchange

13:30 - 14:20 ``Change Detection with Identification: A Bayesian Algorithm for Sequential Analysis''
Jun Zhang (University of Michigan-Ann Arbor)
Abstract

14:30 - 15:20 ``Paradox on estimating functions - estimated importance sampling-''
Shinto Eguchi (Institute of Statistical Mathematics)
Abstract

15:30 - 16:20 「Non-negative matrix factorization (NMF)による音響信号スペクトルの分解と誤差分布の検討」＆「Sparse codingとwavelet展開を併用したMEG信号の解析」

Noboru Murata (Waseda University)

16:20 - 16:40 information exchange

================================================= Abstract
Change Detection with Identification: A Bayesian Algorithm for Sequential Analysis

Jun Zhang (University of Michigan-Ann Arbor, junz@umich.edu)

Following Wald's seminal SPRT model on two hypotheses, traditional sequential analysis has been centered on two directions: (i) the optimal change detection problem where change-point distribution is either unknown as in the CUSUM model (Page, 1954), or assumed to be under a particular form such as geometric distribution (Shiryayev, 1963); (ii) the multi-hypothesis extension using either the likelihood ratios (
Armitage, 1950) or posterior probability (Baum and Veeravalli, 1994) and an analysis of their asymptotic optimality (Dragalin et al., 1999, 2000). Here, we consider the problem of change detection along with identification in multi-hypotheses setting, assuming a known prior. A Bayesian sequential updating algorithm is proposed, along with the usual boundary-crossing stopping rule; the value of an absorbing boundary is shown to exactly equal the hit rate of a decision-maker conditioned on that response. Computer simulation reveals that the algorithm shares many similarities with human performance in stimulus detection/identification experiments.

=================================================
Paradox on estimating functions -estimated importance sampling-

Shinto Eguchi (Institute of Statistical Mathematics)

I overview the paradox argument in Henmi and Eguchi (Biometrika 91,2004). Consider a parametric family of sampling distributions, and propose a use of the sampling distribution estimated by maximum likelihood. The proposed method of importance sampling using the estimated sampling distribution is shown to improve the asymptotic variance of the ordinary method using the true sampling distribution. It is shown by a direct application of the paradox argument. We focus on a condition under which the estimated integration value obtained by the proposed method has asymptotic zero variance, and higher order asymptotics of the variance and bias are investigated.
=================================================