André E. dos Santos

On Darwinian Networks

We suggest Darwinian Networks (DNs) as a simplification of working with Bayesian networks (BNs). DNs adapt a handful of well‐known concepts in biology into a single framework that is surprisingly simple yet remarkably robust. With respect to modeling, on one hand, DNs not only represent BNs but also faithfully represent the testing of independencies in a more straightforward fashion. On the other hand, with respect to three exact inference algorithms in BNs, DNs simplify each of them while unifying all of them. DNs can determine good elimination orderings using the same platform as used for modeling and inference. Finally, we demonstrate how DNs can represent two additional frameworks. Practical benefits of DNs include faster algorithms for inference and modeling.

Efficient Examination of Soil Bacteria Using Probabilistic Graphical Models

This paper describes a novel approach to study bacterial relationships in soil datasets using probabilistic graphical models. We demonstrate how to access and reformat publicly available datasets in order to apply machine learning techniques. We first learn a Bayesian network in order to read independencies in linear time between bacterial community characteristics. These independencies are useful in understanding the semantic relationships between bacteria within communities. Next, we learn a Sum-Product network in order to perform inference in linear time. Here, inference can be conducted to answer traditional queries, involving posterior probabilities, or MPE queries, requesting the most likely values of the non-evidence variables given evidence. Our results extend the literature by showing that known relationships between soil bacteria holding in one or a few datasets in fact hold across at least 3500 diverse datasets. This study paves the way for future large-scale studies of agricultural, health, and environmental applications, for which data are publicly available.

On a simple method for testing independencies in Bayesian networks: Testing Independencies in Bayesian Networks

Testing independencies is a fundamental task in reasoning with Bayesian networks (BNs). In practice, d‐separation is often used for this task, since it has linear‐time complexity. However, many have had difficulties understanding d‐separation in BNs. An equivalent method that is easier to understand, called m‐separation, transforms the problem from directed separation in BNs into classical separation in undirected graphs. Two main steps of this transformation are pruning the BN and adding undirected edges.

An empirical study of Bayesian network inference with simple propagation

Abstract We propose Simple Propagation (SP) as a new join tree propagation algorithm for exact inference in discrete Bayesian networks. We establish the correctness of SP. The striking feature of SP is that its message construction exploits the factorization of potentials at a sending node, but without the overhead of building and examining graphs as done in Lazy Propagation (LP). Experimental results on optimal (or close to optimal) join trees built from numerous benchmark Bayesian networks show that SP is often faster than LP.

An empirical study of testing independencies in Bayesian networks using rp-separation

Abstract Directed separation (d-separation) played a fundamental role in the founding of Bayesian networks (BNs) and continues to be useful today in a wide range of applications. Given an independence to be tested, current implementations of d-separation explore the active part of a BN. On the other hand, an overlooked property of d-separation implies that d-separation need only consider the relevant part of a BN. We propose a new method for testing independencies in BNs, called relevant path separation (rp-separation), which explores the intersection between the active and relevant parts of a BN. Favourable experimental results are reported.

Resolving Inconsistencies of Scope Interpretations in Sum-Product Networks

Sum-product networks (SPNs) are a deep learning model that have shown impressive results in several artificial intelligence applications. Tractable inference in practice requires an SPN to be complete and either consistent or decomposable. These properties can be verified using the definition of scope. In fact, the notion of scope can be used to define SPNs when they are interpreted as hierarchically structured latent variables in mixture models.

On Converting Sum-Product Networks into Bayesian Networks

Sum-Product Networks (SPNs) are a probabilistic graphical model with deep learning applications. A key feature in an SPN is that inference is linear with respect to the size of the network under certain structural constraints. Initial studies of SPNs have investigated transforming SPNs into Bayesian Networks (BNs). Two such methods modify the SPN before conversion. One method modifies the SPN into a normal form. The resulting BN does not contain edges between latent variables. The other method considered here augments the SPN with twin nodes. Here, the constructed BN does contain edges between latent variables, thereby encoding a richer set of dependencies among them.

A Simple Method for Testing Independencies in Bayesian Networks

Testing independencies is a fundamental task in reasoning with Bayesian networks BNs. In practice, d-separation is often utilized for this task, since it has linear-time complexity. However, many have had difficulties in understanding d-separation in BNs. An equivalent method that is easier to understand, called m-separation, transforms the problem from directed separation in BNs into classical separation in undirected graphs. Two main steps of this transformation are pruning the BN and adding undirected edges. In this paper, we propose u-separation as an even simpler method for testing independencies in a BN. Our approach also converts the problem into classical separation in an undirected graph. However, our method is based upon the novel concepts of inaugural variables and rationalization. Thereby, the primary advantage of u-separation over m-separation is that m-separation can prune unnecessarily and add superfluous edges. Hence, u-separation is a simpler method in this respect.

On Tree Structures Used by Simple Propagation

Simple Propagation SP is a new junction tree-based algorithm for probabilistic inference in discrete Bayesian networks. It is similar to Lazy Propagation, but uses a simpler approach to exploit the factorization during message computation. The message construction is based on a one-in, one-out-principle meaning a potential has at least one non-evidence variable in the separator and at least one non-evidence variable not in the separator. This paper considers the use of different tree structures to guide the message passing in SP and reports on an experimental analysis using a set of real-world Bayesian networks.