Faithfulness and learning hypergraphs from discrete distributions

被引：2

作者：

Klimova, Anna ^{[1
]}

Uhler, Caroline ^{[1
]}

Rudas, Tamas ^{[2
]}

机构：

[1] IST Austria, A-3400 Klosterneuburg, Austria

[2] Eotvos Lorand Univ, H-1117 Budapest, Hungary

来源：

COMPUTATIONAL STATISTICS & DATA ANALYSIS | 2015年 / 87卷

关键词：

Contingency tables; Directed acyclic graphs; Hierarchical log-linear models; Hypergraphs; (Strong-)faithfulness; MODELS;

D O I：

10.1016/j.csda.2015.01.017

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The concepts of faithfulness and strong-faithfulness are important for statistical learning of graphical models. Graphs are not sufficient for describing the association structure of a discrete distribution. Hypergraphs representing hierarchical log-linear models are considered instead, and the concept of parametric (strong-)faithfulness with respect to a hypergraph is introduced. The strength of association in a discrete distribution can be quantified with various measures, leading to different concepts of strong-faithfulness. It is proven that strong-faithfulness defined in terms of interaction parameters ensures the existence of uniformly consistent parameter estimators and enables building uniformly consistent procedures for a hypergraph search. Lower and upper bounds for the proportions of distributions that do not satisfy strong-faithfulness are computed for different parameterizations and measures of association. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：57 / 72

页数：16

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