Cora B. Pérez-Ariza

Recursive probability trees for Bayesian networks

This paper proposes a new data structure for representing potentials. Recursive probability trees are a generalization of probability trees. Both structures are able to represent context-specific independencies, but the new one is also able to hold a potential in a factorized way. This new structure can represent some kinds of potentials in a more efficient way than probability trees, and it can be the case that only recursive trees are able to represent certain factorizations. Basic operations for inference in Bayesian networks can be directly performed upon recursive probability trees.

Learning recursive probability trees from probabilistic potentials

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.

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

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.

Fast factorisation of probabilistic potentials and its application to approximate inference in Bayesian networks

Andr´es Cano, Manuel Gomez-Olmedo, Cora B. P´erez-ArizaDept. of Computer Science and Artificial Intelligence, University of Granada, C/ DanielSaucedo Aranda s/n, 18071 Granada, Spain{acu,mgomez,cora}@decsai.ugr.esAntonio Salmero´nDept. Statistics and Applied Mathematics, University of Almer´ia, La Can˜ada de San Urbanos/n, 04120 Almer´ia, Spainantonio.salmeron@ual.esReceived (received date)Revised (revised date)We present an efficient procedure for factorising probabilistic potentials represented asprobability trees. This new procedure is able to detect some regularities that cannot becaptured by existing methods. In cases where an exact decomposition is not achievable,we propose a heuristic way to carry out approximate factorisations guided by a parametercalled factorisation degree, which is fast to compute. We show how this parameter can beused to control the tradeoff between complexity and accuracy in approximate inferencealgorithms for Bayesian networks.Keywords: Bayesian networks; Probability trees; Factorisation; Probabilistic inference

Causal discovery of dynamic bayesian networks

While a great variety of algorithms have been developed and applied to learning static Bayesian networks, the learning of dynamic networks has been relatively neglected. The causal discovery program CaMML has been enhanced with a highly flexible set of methods for taking advantage of prior expert knowledge in the learning process. Here we describe how these representations of prior knowledge can be used instead to turn CaMML into a promising tool for learning dynamic Bayesian networks.

Extended Probability Trees for Probabilistic Graphical Models

This paper proposes a flexible framework to work with probabilistic potentials in Probabilistic Graphical Models. The so-called Extended Probability Trees allow the representation of multiplicative and additive factorisations within the structure, along with context-specific independencies, with the aim of providing a way of representing and managing complex distributions. This work gives the details of the structure and develops the basic operations on potentials necessary to perform inference. The three basic operations, namely restriction, combination and marginalisation, are defined so they can take advantage of the defined factorisations within the structure, following a lazy methodology.

Learning Recursive Probability Trees from Data

Recursive Probability Trees offer a flexible framework for representing the probabilistic information in Probabilistic Graphical Models. This structure is able to provide a detailed representation of the distribution it encodes, by specifying most of the types of independencies that can be found in a probability distribution. Learning this structure involves the search for context-specific independencies along with factorisations within the available data. In this paper we develop the first approach at learning Recursive Probability Trees from data by extending an existent greedy methodology for retrieving small Recursive Probability Trees from probabilistic potentials. We test the performance of the algorithm by learning from different databases, both real and handcrafted, and we compare the performance for different databases sizes.

Fast Factorization of Probability Trees and Its Application to Recursive Trees Learning

We present a fast potential decomposition algorithm that seeks for proportionality in a probability tree. We give a measure that determines the accuracy of a decomposition in case that exact factorization is not possible. This measure can be used to decide the variable with respect to which a tree should be factorized in order to obtain the most accurate decomposed model.

An Extended Approach to Learning Recursive Probability Trees from Data

Rlatecursive probability trees (RPTs) offer a flexible framework for representing the probabilistic information in probabilistic graphical models. This structure is able to provide a compact representation of the distribution it encodes by specifying most of the types of independencies that can be found in a probability distribution. The real benefit of this representation heavily depends on the ability of learning such independencies from data. In this paper, we expand our approach at learning RPTs from data by extending an existing greedy methodology for retrieving small RPTs from probabilistic potentials. We test the performance of the algorithm by learning from different databases, both real and handcrafted, and we compare the performance for different databases sizes.