Learning recursive probability trees from probabilistic potentials

Abstract

A Recursive Probability Tree (RPT) is a data structure for representing the potentials involved in Probabilistic Graphical Models (PGMs). This structure is developed with the aim of capturing some types of independencies that cannot be represented with previous structures. This capability leads to improvements in memory space and computation time during inference. This paper describes a learning algorithm for building RPTs from probability distributions. The experimental analysis shows the proper behavior of the algorithm: it produces RPTs encoding good approximations of the original probability distributions.

An Extended Approach to Learning Recursive Probability Trees from Data

“…The previous algorithm, developed by Cano et al., consists of building an RPT from another probabilistic potential (a CPT or a PT, for instance). The problem of finding a minimal RPT is NP‐hard .…”

“…The previous algorithm, developed by Cano et al., consists of building an RPT from another probabilistic potential (a CPT or a PT, for instance). The problem of finding a minimal RPT is NP‐hard . Hence, this methodology focuses on obtaining an RPT in a greedy way, following a heuristic designed for selecting Split nodes that are likely to reduce the dependencies among the remaining variables.…”

“…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 …”

“…This work can be seen as a follow up of the first approach at learning RPT structures from a database, 4 extending an existing methodology based on detecting patterns within potentials. 5 The rest of the paper is organized as follows. Section 2 defines RPTs and describes their features; Section 3 offers a review of the previous work on the topic; Section 4 describes our approach for learning an RPT from a database and gives some examples of the workflow of the algorithm; Section 5 shows the experimental evaluation performed for testing the performance of the algorithm; and finally Section 6 presents the main conclusions of this work.…”

New strategies for finding multiplicative decompositions of probability trees

“…The methods studied in this paper can be embedded in a more general data structure for representing probabilistic potentials, called recursive probability trees [2]: a factorised representation of a probability tree is suitable to be stored inside a recursive tree as a list node [3].…”