Embedding Maximum Entropy Models in Algebraic Varieties by Grobner Bases Methods

被引：2

作者：

Dukkipati, Ambedkar ^{[1
]}

机构：

[1] Indian Inst Sci, Dept Comp Sci & Automat, Bangalore 560012, Karnataka, India

来源：

2009 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1- 4 | 2009年

关键词：

D O I：

10.1109/ISIT.2009.5205528

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

The main aim of this paper is to present some notions on how results from commutative algebra and algebraic geometry could be used in representation and computation of maximum entropy (ME) models in the cases, where an integer valued sufficient statistic exists. We give an implicit description of ME-models by embedding them in algebraic varieties for which we use Grobner bases methods. We prove that in the case of ME, both the model and the data can be represented by algebraic varieties.

引用

页码：1904 / +

页数：2

共 12 条

[1]

[Anonymous], 1994, GRADUATE STUDIES MAT

[2]

Cox D., 1991, Ideals, Varieties, and Algorithms

[3] A GEOMETRIC INTERPRETATION OF DARROCH AND RATCLIFF GENERALIZED ITERATIVE SCALING [J].

CSISZAR, I .

ANNALS OF STATISTICS, 1989, 17 (03) :1409-1413

[4]

Csiszar I., 2004, FDN TRENDS COMMUNICA, V1

[5] GENERALIZED ITERATIVE SCALING FOR LOG-LINEAR MODELS [J].

DARROCH, JN ;

RATCLIFF, D .

ANNALS OF MATHEMATICAL STATISTICS, 1972, 43 (05) :1470-&

[6]

DIACONIS P, 1988, I MATH STAT MONOGRAP, V11

[7] INFORMATION THEORY AND STATISTICAL MECHANICS [J].

JAYNES, ET .

PHYSICAL REVIEW, 1957, 106 (04) :620-630

[8] PRIOR PROBABILITIES [J].

JAYNES, ET .

IEEE TRANSACTIONS ON SYSTEMS SCIENCE AND CYBERNETICS, 1968, SSC4 (03) :227-&

[9]

Kullback S., 1959, Information theory and statistics

[10]

Pachter L., 2005, ALGEBRAIC STAT COMPU

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