Fecha: 24/09/2012
Hora: 12 horas
Speaker: Shinichi Nakajima, Optical Research Laboratory, Nikon Corporation
Shinichi Nakajima was born in Kobe, Japan in 1971.
After receiving the master degree on physics in 1995 from Kobe university, he joined with Nikon Corporation, and started working on developing algorithms for IC equipment tools (stepper/scanner).
Through his work that required knowledge of statistics, he got interested in machine learning and started research at Tokyo Institute of Technology.
After receiving the doctoral degree on computer science in 2006 from Tokyo Institute of Technology, he moved to Optical Research Laboratory, Nikon Corporation.
Since then, his work is research on machine learning and its application to all the Nikon products, including computer vision for digital camera and microscope, data mining for manufacturing, and automatic control for IC equipment tools.
In 2008, he worked as a visiting researcher at intelligent data analysis group in Technical University of Berlin.
He has been working on machine learning, computer vision, and data mining.
But recently, he is very much interested in computational photography.
Title: Perfect Dimensionality Recovery Condition of Variational Bayesian PCA
This talk is on a theoretical analysis of variational Bayesian (VB) PCA when the observed matrix has no missing entry.
Our previous work showed that the global solution of VB-PCA can be obtained by solving a quartic equation, when the noise variance is given.
In this work, we analyzed the behavior of the noise variance estimator when it is estimated from observation.
As a main result, we obtained a sufficient condition for perfect recovery of the true PCA
dimensionality in the large-scale limit (when the size of the observed matrix goes to infinity with its column-row ratio fixed).
We also discuss the exact sparsity of VB-PCA solution, which is induced by the independence assumption for the VB approximation.
References:
C. M. Bishop, Variational Principal Components. ICANN1999.
http://research.microsoft.com/en-us/um/people/cmbishop/downloads/Bishop-VPCA-ICANN-99.pdf
S. Nakajima, M. Sugiyama, D. Babacan, Global Solution of Fully-Observed Variational Bayesian
Matrix Factorization is Column-Wise Independent, NIPS2011.
http://sites.google.com/site/shinnkj23/home/manuscript_nips2011.pdf