Model Averaging and Dimension Selection for the Singular Value Decomposition

reportActive / Technical Report | Accession Number: ADA454966 | Open PDF

Abstract:

Many multivariate data analysis techniques for an m x n matrix Y are related to the model Y ME, where Y is an m x n matrix of full rank and M is an unobserved mean matrix of rank K mn. Typically the rank of M is estimated in a heuristic way and then the least-squares estimate of M is obtained via the singular value decomposition of Y, yielding an estimate that can have a very high variance. In this paper we suggest a model-based alternative to the above approach by providing prior distributions and posterior estimation for the rank of M and the components of its singular value decomposition.

Author(s):
Hoff, Peter D.
Author Organization(s):
WASHINGTON UNIV SEATTLE DEPT OF STATISTICS
Descriptive Note:
Technical rept. no. 494
Supplementary Note:
Supported in part by the National Science Foundation. DOI: 10.21236/ADA454966
Pagination:
0025

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release
Distribution Statement:
Approved For Public Release; Distribution Is Unlimited. This Document Is Not Available From Dtic In Microfiche.

RECORD

Collection: TR
Identifying Numbers
Contract/Grant Number(s):
N00014-02-1-1011, NSF-SES-0417559
Monitor Series:
ONR
 Subject Terms
Joint Capability Areas:
JCA_5_Command and Control; JCA_5.3_Planning; JCA_1_Force Support; JCA_1.2_Force Preparation; JCA_6_Net Centric; JCA_1.4_Force Support; JCA_6.1_Information Transport; JCA_6.4.1_Secure Information Exchange; JCA_1.4.2_Health Service Delivery; JCA_8_Building Partnerships
Modernization Areas:
AI and Machine Learning
Communities of Interest:
Air Platforms
Descriptor(s):
*MATHEMATICAL MODELS, *MULTIVARIATE ANALYSIS, MONTE CARLO METHOD, BAYES THEOREM, MARKOV PROCESSES, FACTOR ANALYSIS
Field(s)/Group(s):
Theoretical Mathematics, Statistics and Probability, Operations Research
Keyword(s):
CARLSON S HYPERGEOMETRIC FUNCTION, DIRECTIONAL DATA, MODEL SELECTION, STEIFEL MANIFOLD, RELATIONAL DATA, MODEL AVERAGING, SINGULAR VALUE DECOMPOSITION
Report Date:
2006 Jan 10
Creation Date:
2006 Oct 11