Learning Inclusion-Optimal Chordal Graphs
نویسندگان
چکیده
Chordal graphs can be used to encode dependency models that are representable by both directed acyclic and undirected graphs. This paper discusses a very simple and efficient algorithm to learn the chordal structure of a probabilistic model from data. The algorithm is a greedy hillclimbing search algorithm that uses the inclusion boundary neighborhood over chordal graphs. In the limit of a large sample size and under appropriate hypotheses on the scoring criterion, we prove that the algorithm will find a structure that is inclusion-optimal when the dependency model of the data-generating distribution can be represented exactly by an undirected graph. The algorithm is evaluated on simulated datasets.
منابع مشابه
Complement of Special Chordal Graphs and Vertex Decomposability
In this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay.
متن کاملAlgorithms for Learning Decomposable Models and Chordal Graphs
Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two character izations of decomposable models in terms of independence relationships, we develop an exact algorithm for recovering the chordal graphical representation of any given decom posable model. We also propose an algorithm for le...
متن کاملLearning Causal Graphs with Small Interventions
We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearl’s Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of experiments to discover the causal directions of all the edges in a causal graph. Previous work has focused on the use of separating systems for complete graphs for t...
متن کاملUnified All-pairs Shortest Path Algorithms in the Chordal Hierarchy
The objective of this paper is to advance the view that solving the all-pairs shortest path (APSP) problem for a chordal graph G is a two-step process: the first step is determining vertex pairs at distance two (i.c., computing C’) and the second step is finding the vcrtcx pairs at distance three or more. The main technical result here is that the APSP problem for a chordal graph can be solved ...
متن کاملChordal Graphs and Their Clique Graphs
In the rst part of this paper, a new structure for chordal graph is introduced, namely the clique graph. This structure is shown to be optimal with regard to the set of clique trees. The greedy aspect of the recognition algorithms of chordal graphs is studied. A new greedy algorithm that generalizes both Maximal cardinality Search (MCS) and Lexicographic Breadth rst search is presented. The tra...
متن کامل