The 8th Statistical Machine Learning Seminar (2012.7.12)

Date: July 12 (Thu) 13:30-17:45
Place: Seminar room 5

* Arthur Gretton (Gatsby Computational Neuroscience Unit, University College
London, UK)
Consistent Nonparametric Tests of Independence: L1, Log-Likelihood and Kernel

Three simple and explicit procedures for testing the independence of two
multi-dimensional random variables are described. Two of the associated test
statistics (L1, log-likelihood) are defined when the empirical distribution
of the variables is restricted to finite partitions. A third test statistic
is defined as a kernel-based independence measure. Two kinds of tests are
Distribution-free strong consistent tests are derived on the basis of large
deviation bounds on the test statistics: these tests make almost surely no
Type I or Type II error after a random sample size.
Asymptotically alpha-level tests are obtained from the limiting distribution
of the test statistics. For the latter tests, the Type I error converges to
a fixed non-zero value alpha, and the Type II error drops to zero, for
increasing sample size. All tests reject the null hypothesis of independence
if the test statistics become large. The performance of the tests is
evaluated experimentally on benchmark data.

* Subhajit Dutta (Indian Statistical Institute, India)
Title :
Classification using Localized Spatial Depth with Multiple Localization

Abstract :
In the recent past, data depth has been considered by several authors as an
effective methodology for supervised and unsupervised classification
problems. However, most of the depth based classifiers studied in the
literature require the population distributions to be elliptic and unimodal
differing only in their locations in order to have satisfactory performance.
Another limitation of such classifiers is that they usually require equal
prior probabilities for the populations. Further, for many choices of the
well-known depth function, practical implementation of depth based
classifiers becomes computationally prohibitive even for moderately large
dimensional data. In this talk, we propose a new classifier based on spatial
depth, which can be used for high-dimensional. The main idea behind the
construction of the proposed classifier is based on fitting generalized
additive models to the posterior probabilities corresponding to different
classes. In order to cope with possible multimodal and/or non-elliptic
nature of the population distributions, we develop a localized version of
spatial depth and use that with varying degrees of localization to build the
classifier. Our classifier is formed by aggregation of several classifiers
each of which is based on spatial depth with a fixed level of localization.
This new classifier can be conveniently used for high-dimensional data, and
its possess good discriminatory power for such data. Using some real
benchmark data sets, the proposed classifier is shown to have competitive
performance when compared with well-known and widely used classifiers like
those based on nearest-neighbors, kernel density estimates, support vector
machines, classification trees, artificial neural nets, etc.
(This is a joint work with Prof. P. Chaudhuri and Dr. A. K. Ghosh)

* Su-Yun Huang (Institute of Statistical Science, Academia Sinica, Taiwan)
Multilinear Principal Component Analysis -Asymptotic Theory

Principal component analysis is commonly used for dimension reduction in
analyzing high dimensional data. Multilinear principal component analysis
aims to serve a similar function for analyzing tensor structure data, and
has empirically been shown effective in reducing dimensionality. In this
paper, we investigate its statistical properties and demonstrate its
advantages. Conventional principal component analysis, which vectorizes the
tensor data, may lead to inefficient and unstable prediction due to the
often extremely large dimensionality involved. Multilinear principal
component analysis, in trying to preserve the data structure, searches for
low-dimensional projections and, thereby, decreases dimensionality more
Asymptotic theory of order-two multilinear principal component analysis,
including asymptotic efficiency and distributions of principal components,
associated projections, and the explained variance, is developed. A test of
dimensionality is also proposed.
Finally, multilinear principal component analysis is shown to improve
conventional principal component analysis in analyzing the Olivetti faces
data set, which is achieved by extracting a more modularly-oriented basis in
reconstructing test faces.
(joint with Hung Hung, Pei-Shien Wu and I-Ping Tu)

* Hung Hung (Institute of Epidemiology and Preventive Medicine, National
Taiwan University, Taiwan)

Matrix Variate Logistic Regression Model with Application to EEG Data

Logistic regression has been widely applied in the field of biomedical
research for a long time. In some applications, covariates of interest have
a natural structure, such as being a matrix, at the time of collection. The
rows and columns of the covariate matrix then have certain physical
meanings, and they must contain useful information regarding the response.
If we simply stack the covariate matrix as a vector and fit a conventional
logistic regression model, relevant information can be lost, and the problem
of inefficiency will arise. Motivated from these reasons, we propose in this
paper the matrix variate logistic (MV-logistic) regression model. Advantages
of MV-logistic regression model include the preservation of the inherent
matrix structure of covariates and the parsimony of parameters needed. In
the EEG Database Data Set, we successfully extract the structural effects of
covariate matrix, and a high classification accuracy is achieved. (Joint
with Chen-Chien Wang) MV-logistic regression belongs to the class of tensor
regression, which now attracts the attention of statisticians. In this talk,
I will also introduce some our recent developments of tensor regression, and
will focus on its application to the detection of gene-gene interactions.