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An Eigenvector Variability Plot
Prof. I-Ping Tu ( Institute of Statistical Science , Academia Sinica )

2008 - 04 - 29 (Tue.)
13:30 - 15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Principal components analysis is perhaps the most widely used method for ex-ploring multivariate data. In this talk, we present a variability plot composed of measures on the stability of each eigenvectors over samples as a data exploration tool. We also show that this variability measure gives a good measure on the intersample variability of eigenvectors through asymptotic analysis. For distinct eigenvalues, the asymptotic behavior for this variability measure is comparable to the size of the asymptotic covariance of the eigenvector in Anderson (1963). A simulation for functional data analysis with dimension p greater than sample size n is provided. The proposed variability plot is successful to distinguish the signal components, noise components and 0 eigenvalue components. Applying this method on a gene expression data set for a gastric cancer study, many hills on the proposed variability plot are observed. When the intersample variability of eigenvectors is considered, the cuto point on informative eigenvectors should not be on the top of the hill as suggested by the proposed variability plot.

Time:November 20, 2007 - July 31, 2009
Room:
Organizer:Hung Chen ( Department of Mathematics, National Taiwan University )

Available Talk List

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2007-12-04 (Tue.)		Model Selection via the Group Lasso
2008-01-08 (Tue.)		Nonparametric Estimation For Time-Dependent AUC
2008-01-15 (Tue.)		Identify Design Conditions to Achieve the Optimal Rate of Convergence in a Bivariate Additive Model
2008-02-19 (Tue.)		Optimal Composite Markers for Time-Dependent ROC
2008-03-04 (Tue.)		Adjusted Empirical Likelihood and its Properties
2008-03-18 (Tue.)		Model Checking for ROC Regression Analysis
2008-03-21 (Fri.)		Pseudo-Partial Likelihood for Proportional Hazards Models with Biased-Sampling Data
2008-03-21 (Fri.)		Pseudo-Partial Likelihood Estimators for Cox Regression Model With Missing Covariates
2008-04-15 (Tue.)		Nonparametric Estimation of the Joint Distribution of Survival Time and Mark variables
2008-04-15 (Tue.)		Joint analysis of longitudinal data with informative right censoring
2008-04-29 (Tue.)		An Eigenvector Variability Plot
2008-05-27 (Tue.)		selected review on unified framework of discriminant analysis
2008-06-03 (Tue.)		Differential Expression of Microarray Time Course Data
2008-06-10 (Tue.)		A general logistic type discriminant analysis with U-divergence for contaminated data
2008-06-17 (Tue.)		Binary Time Series Modeling with Application to Adhesion Frequency Experiments
2008-07-15 (Tue.)		Nonparametric Estimation Methods for the Optimal Composite Markers with Censored Survival Data
2008-07-29 (Tue.)		An explanation of "Kernel trick" and the construction of kernels for discrete structures
2008-08-12 (Tue.)		Review of the paper “Analysis of interval-censored longitudinal data with application to onco-haematology”
2008-08-26 (Tue.)		Potential sampling bias of regression models and evolving population models
2008-09-09 (Tue.)		An overview of "Functional Convex Averaging and Synchronization for Time-Warped Random Curve" by Liu and Muller (2004)
2008-09-19 (Fri.)		Model Selection in Regression Analysis: Classical Development
2008-09-26 (Fri.)		Data-driven Selection of Penalty in Lasso
2008-10-03 (Fri.)		Online Learning with Matrix Exponentiated Gradient Updates
2008-10-24 (Fri.)		RELATIONSHIP BETWEEN THE COX, LEHMANN, WEIBULL AND ACCELERATED LIFETIME MODELS
2008-10-31 (Fri.)		Estimation Of Integrated Covolatility For Non-synchronous Assets In The Presence Of Microstructure Noise
2008-11-07 (Fri.)		Testing conditional independence using maximal nonlinear
2008-11-21 (Fri.)		Review of Local Polynomial Kernel Regression for Generalized Linear Models and Quasi-Likelihood Functions (Fan, J.,Heckman, N. E., and Wand, M. P. (1995))
2008-12-05 (Fri.)		General Adaptive Sparse Principal Component Analysis
2008-12-17 (Wed.)		Supreme Court Judges: Blue or Red?
2008-12-26 (Fri.)		Review of paper “Semiparametric Estimation of Index Coefficients" by Powell J. L., Stock, J. H., and Stoker, T. M.
2009-01-07 (Wed.)		Prediction and Diagnosis of Disease Outcome with Microarray Data and a Classification Method Based on a New Information Measure
2009-02-20 (Fri.)		Review of the paper ``Evaluating Prediction Rules for t-Year
2009-03-06 (Fri.)		Review on the Estimation of Prediction Error in terms of Covariance Penalty
2009-03-11 (Wed.)		Linear Regression Analysis Extension and Application in Financial Market
2009-03-20 (Fri.)		Review on The paper ``Current methods for recurrent events data with dependent termination” (Sinha et al., 2008, JASA, 866-878)"
2009-04-10 (Fri.)		Review on the paper ``Partly conditional survival models for longitudinal data” (Zheng and Heagerty (2005)"
2009-04-13 (Mon.)		Bayesian subset selections in multiple regression models
2009-04-24 (Fri.)		Review on the paper ``Scan statistics with weighted observations”(Chan, H. and Zhang, N. (2007), JASA, 595-602)
2009-04-29 (Wed.)		Analysis of Nonstationary Time Series
2009-05-08 (Fri.)		Improving on t-tests or F-tests for a large number of hypothesis with application to Microarray data analysis
2009-05-22 (Fri.)		Analysis of Nonstationary Time Series
2009-05-27 (Wed.)		Functional Data Analysis: Some Recent Advancement
2009-06-10 (Wed.)		Recursive Structure in Default Probabilities
2009-06-12 (Fri.)		Discussion of the paper “Efficient Estimation In Conditional Single- Index Regression" by Delecroix, Hardle, and Hristache
2009-09-25 (Fri.)		New Testing Procedure for Receiver Operating Characteristic Curves