Probability matrices, non-negative rank, and parameterization of mixture models

Enrico Carlini; Fabio Rapallo

doi:10.1016/j.laa.2010.03.010

Probability matrices, non-negative rank, and parameterization of mixture models

Enrico Carlini
, Fabio Rapallo

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we parameterize non-negative matrices of sum one and rank at most two using the least possible number of parameters. We also show how this parameterization relates to a class of statistical models, known in Probability and Statistics as mixture models for contingency tables. In particular, we show how to use this parameterization to make some optimization problems computationally easier.

Original language	English
Pages (from-to)	424-432
Number of pages	9
Journal	Linear Algebra and Its Applications
Volume	433
Issue number	2
DOIs	https://doi.org/10.1016/j.laa.2010.03.010
Publication status	Published - 1 Aug 2010
Externally published	Yes

Keywords

Contingency tables
Optimization on algebraic varieties
Parameter redundancy

Access to Document

10.1016/j.laa.2010.03.010

Cite this

@article{ffbec013fe7a4a5cb98eb061b60f2beb,

title = "Probability matrices, non-negative rank, and parameterization of mixture models",

abstract = "In this paper, we parameterize non-negative matrices of sum one and rank at most two using the least possible number of parameters. We also show how this parameterization relates to a class of statistical models, known in Probability and Statistics as mixture models for contingency tables. In particular, we show how to use this parameterization to make some optimization problems computationally easier.",

keywords = "Contingency tables, Optimization on algebraic varieties, Parameter redundancy",

author = "Enrico Carlini and Fabio Rapallo",

year = "2010",

month = aug,

day = "1",

doi = "10.1016/j.laa.2010.03.010",

language = "English",

volume = "433",

pages = "424--432",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "2",

}

TY - JOUR

T1 - Probability matrices, non-negative rank, and parameterization of mixture models

AU - Carlini, Enrico

AU - Rapallo, Fabio

PY - 2010/8/1

Y1 - 2010/8/1

N2 - In this paper, we parameterize non-negative matrices of sum one and rank at most two using the least possible number of parameters. We also show how this parameterization relates to a class of statistical models, known in Probability and Statistics as mixture models for contingency tables. In particular, we show how to use this parameterization to make some optimization problems computationally easier.

AB - In this paper, we parameterize non-negative matrices of sum one and rank at most two using the least possible number of parameters. We also show how this parameterization relates to a class of statistical models, known in Probability and Statistics as mixture models for contingency tables. In particular, we show how to use this parameterization to make some optimization problems computationally easier.

KW - Contingency tables

KW - Optimization on algebraic varieties

KW - Parameter redundancy

UR - https://www.scopus.com/pages/publications/77953135649

U2 - 10.1016/j.laa.2010.03.010

DO - 10.1016/j.laa.2010.03.010

M3 - Article

SN - 0024-3795

VL - 433

SP - 424

EP - 432

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 2

ER -

Probability matrices, non-negative rank, and parameterization of mixture models

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this