Bayes PCA Revisited

Jon Sporring

Bayes PCA Revisited

Jon Sporring

Abstract

Principle Component Analysis is a simple tool to obtain linear models for

stochastic data and is used both for a data reduction or equivalently noise elim-

ination and for data analysis. Principle Component Analysis ts a multivariate

Gaussian distribution to the data, and the typical method is by using the log-

likelihood estimator. However for small sets of high dimensional data, the log-

likelihood estimator is often far from convergence, and therefore reliable models

must be obtained by use of prior information. In this paper, we will examine

an earlier work on reconstructing missing data using statistical knowledge and

regularization, we will show the circumstances for which this is equivalent to

a Bayes estimation, we will give an expository presentation of Bayes Principle

Component Analysis for a range of exponential type priors, and we will develop

algorithms for their estimate.

Original language	English

Place of Publication	Department of Computer Science
Publisher	Museum Tusculanum
Number of pages	12
Publication status	Published - 2008

Series	Department of Computer Science. University of Copenhagen. Technical Report
Number	08-09
ISSN	0107-8283

Access to Document

http://www.diku.dk/publikationer/tekniske.rapporter/rapporter/08-09.pdf

Cite this

@book{3bb87cf06a0511dd8d9f000ea68e967b,

title = "Bayes PCA Revisited",

abstract = "Principle Component Analysis is a simple tool to obtain linear models forstochastic data and is used both for a data reduction or equivalently noise elim-ination and for data analysis. Principle Component Analysis ts a multivariateGaussian distribution to the data, and the typical method is by using the log-likelihood estimator. However for small sets of high dimensional data, the log-likelihood estimator is often far from convergence, and therefore reliable modelsmust be obtained by use of prior information. In this paper, we will examinean earlier work on reconstructing missing data using statistical knowledge andregularization, we will show the circumstances for which this is equivalent toa Bayes estimation, we will give an expository presentation of Bayes PrincipleComponent Analysis for a range of exponential type priors, and we will developalgorithms for their estimate.",

author = "Jon Sporring",

year = "2008",

language = "English",

series = "Department of Computer Science. University of Copenhagen. Technical Report",

number = "08-09",

publisher = "Museum Tusculanum",

}

TY - RPRT

T1 - Bayes PCA Revisited

AU - Sporring, Jon

PY - 2008

Y1 - 2008

N2 - Principle Component Analysis is a simple tool to obtain linear models forstochastic data and is used both for a data reduction or equivalently noise elim-ination and for data analysis. Principle Component Analysis ts a multivariateGaussian distribution to the data, and the typical method is by using the log-likelihood estimator. However for small sets of high dimensional data, the log-likelihood estimator is often far from convergence, and therefore reliable modelsmust be obtained by use of prior information. In this paper, we will examinean earlier work on reconstructing missing data using statistical knowledge andregularization, we will show the circumstances for which this is equivalent toa Bayes estimation, we will give an expository presentation of Bayes PrincipleComponent Analysis for a range of exponential type priors, and we will developalgorithms for their estimate.

AB - Principle Component Analysis is a simple tool to obtain linear models forstochastic data and is used both for a data reduction or equivalently noise elim-ination and for data analysis. Principle Component Analysis ts a multivariateGaussian distribution to the data, and the typical method is by using the log-likelihood estimator. However for small sets of high dimensional data, the log-likelihood estimator is often far from convergence, and therefore reliable modelsmust be obtained by use of prior information. In this paper, we will examinean earlier work on reconstructing missing data using statistical knowledge andregularization, we will show the circumstances for which this is equivalent toa Bayes estimation, we will give an expository presentation of Bayes PrincipleComponent Analysis for a range of exponential type priors, and we will developalgorithms for their estimate.

M3 - Report

T3 - Department of Computer Science. University of Copenhagen. Technical Report

BT - Bayes PCA Revisited

PB - Museum Tusculanum

CY - Department of Computer Science

ER -

Bayes PCA Revisited

Abstract

Access to Document

Fingerprint

Cite this