Inference in Bayesian Networks with Recursive Probability Trees: Data Structure Definition and Operations

Abstract

Recursive probability trees (RPTs) are a data structure for representing several types of potentials involved in probabilistic graphical models. The RPT structure improves the modeling capabilities of previous structures (like probability trees or conditional probability tables). These capabilities can be exploited to gain savings in memory space and/or computation time during inference. This paper describes the modeling capabilities of RPTs as well as how the basic operations required for making inference on Bayesian networks operate on them. The performance of the inference process with RPTs is examined with some experiments using the variable elimination algorithm.

An Extended Approach to Learning Recursive Probability Trees from Data

“…RPTs are a generalization of PTs. RPTs were developed with the aim of enhancing PTs' flexibility and so they are able to represent different kinds of patterns that so far were out of the scope of PTs.…”

“…r Restriction of a potential φ to a configuration x of its variables, written as φ R(x) , r Combination of potentials, denoted as φ 1 · φ 2 , and r Marginalization of φ over the variables in X, written as φ ↓X, can be adapted to be supported by RPTs. 2 The operations are designed to deal with the multiplicative factorizations introduced within the RPTs by the List nodes. The definition of the operations aims at postponing the actual computation of any product of numbers, in this sense, RPTs are compatible with inference schemes based on lazy propagation.…”

“…Recursive probability trees (RPTs) were designed as an alternative to traditional data structures for representing probabilistic potentials, such as conditional probability tables (CPTs) or probability trees (PTs). This work can be seen as a follow up of the first approach at learning RPT structures from a database, extending an existing methodology based on detecting patterns within potentials …”