Study of MEBN Learning for Relational Model

One of the major weaknesses of current research on the Semantic Web (SW) is the lack of proper means to represent and reason with uncertainty. A number of recent efforts from the SW community, the W3C, and others have recently emerged to address this gap. Such efforts have the positive side effect of bringing together two fields of research that have been apart for historical reasons, the artificial intelligence and the SW communities. One example of the potential research gains of this convergence is the current development of Probabilistic OWL (PR-OWL), an extension of the OWL Web Ontology Language that provides a framework to build probabilistic ontologies, thus enabling proper representation and reasoning with uncertainty within the SW context. PR-OWL is based on Multi-Entity Bayesian Networks (MEBN), a first-order probabilistic logic that combines the representational power of first-order logic (FOL) and Bayesian Networks (BN). However, PR-OWL and MEBN are still in development, lacking a software tool that implements their underlying concepts. The development of UnBBayes-MEBN, an open source, Java-based application that is currently in alpha phase (public release March 08), addresses this gap by providing both a GUI for building probabilistic ontologies and a reasoner based on the PR-OWL/MEBN framework. This work focuses on the major challenges of UnBBayes-MEBN implementation, describes the features already implemented, and provides an overview of the major algorithms, mainly the one used for building a Situation Specific Bayesian Network (SSBN) from a MEBN Theory.

Although classical first-order logic is the de facto standard logical foundation for artificial intelligence, the lack of a built-in, semantically grounded capability for reasoning under uncertainty renders it inadequate for many important classes of problems. Probability is the bestunderstood and most widely applied formalism for computational scientific reasoning under uncertainty. Increasingly expressive languages are emerging for which the fundamental logical basis is probability. This paper presents Multi-Entity Bayesian Networks (MEBN), a first-order language for specifying probabilistic knowledge bases as parameterized fragments of Bayesian networks. MEBN fragments (MFrags) can be instantiated and combined to form arbitrarily complex graphical probability models. An MFrag represents probabilistic relationships among a conceptually meaningful group of uncertain hypotheses. Thus, MEBN facilitates representation of knowledge at a natural level of granularity. The semantics of MEBN assigns a probability distribution over interpretations of an associated classical first-order theory on a finite or countably infinite domain. Bayesian inference provides both a proof theory for combining prior knowledge with observations, and a learning theory for refining a representation as evidence accrues. A proof is given that MEBN can represent a probability distribution on interpretations of any finitely axiomatizable first-order theory.

2005

This paper addresses a major weakness of current technologies for the Semantic Web, namely the lack of a principled means to represent and reason about uncertainty. This not only hinders the realization of the original vision for the Semantic Web, but also creates a barrier to the development of new, powerful features for general knowledge applications that require proper treatment of uncertain phenomena. We propose to extend OWL, the ontology language recommended by the World Wide Web Consortium (W3C), to provide the ability to express probabilistic knowledge. The new language, PROWL , will allow legacy ontologies to interoperate with newly developed probabilistic ontologies. PROWL will move beyond the current limitations of deterministic classical logic to a full first-order probabilistic logic. By providing a principled means of modeling uncertainty in ontologies, PROWL will serve as a supporting tool for many applications that can benefit from probabilistic inference within an ontology language, thus representing an important step toward the W3C's vision for the Semantic Web.

Proceedings of the 11th International Conference on Pattern Recognition Applications and Methods

Exploiting experts' domain knowledge represented in the ontology can significantly enhance the quality of the Bayesian network (BN) structure learning. However, in practice, using such information is not a trivial task. In fact, knowledge encompassed in ontologies doesn't share the same semantics as those represented in a BN. To tackle this issue, a large effort has been devoted to create a bridge between both models. But, as far as we know, most state-of-the-art approaches require a Bayesian network-specific ontology for which the BN structure could be easily derived. In this paper, we propose a generic method that allows deriving knowledge from ontology to enhance the learning process of BN. We provide several steps to infer dependencies as well as orientations of some edges between variables. The proposition is implemented and applied to the wind energy domain.

2016

Multi-Entity Bayesian Network (MEBN) is an expressive first-order probabilistic logic that represents the domain using parameterized fragments of Bayesian networks. Probabilistic-OWL (PR-OWL) uses MEBN to add uncertainty support to OWL, the main language of the Semantic Web. The reasoning in MEBN is made by the construction of a Situation-Specific Bayesian Network (SSBN), a minimal Bayesian network sufficient to compute the response to queries. A Bottom-Up algorithm has been proposed for generating SSBNs in MEBN. However, this approach presents scalability problems since the algorithm starts from all the query and evidence nodes, which can be a very large set in real domains. To address this problem, we present a new scalable algorithm for generating SSBNs based on the Bayes-Ball method, a well-known and efficient algorithm for discovering d-separated nodes of target sets in Bayesian networks. The novel SSBN algorithm used together with Resource Description Framework (RDF) databases...

This paper addresses a major weakness of current technologies for the Semantic Web, namely the lack of a principled means to represent and reason about uncertainty. This not only hinders the realization of the original vision for the Semantic Web, but also creates a barrier to the development of new, powerful features for general knowledge applications that require proper treatment of uncertain phenomena. We propose to extend OWL, the ontology language recommended by the World Wide Web Consortium (W3C), to provide the ability to express probabilistic knowledge. The new language, PR-OWL, will allow legacy ontologies to interoperate with newly developed probabilistic ontologies. PR-OWL will move beyond the current limitations of deterministic classical logic to a full first-order probabilistic logic. By providing a principled means of modeling uncertainty in ontologies, PR-OWL will serve as a supporting tool for many applications that can benefit from probabilistic inference within an ontology language, thus representing an important step toward the W3C's vision for the Semantic Web.

2000

My work is on learning Probabilistic Relational Models (PRMs) from structured data (eg, data in a relational database, an object-oriented database or a frame-based system). This work has as a starting point the framework of Probabilistic Relational Models, introduced in [5, 7]. We adapt and extend the machinery that has been developed over the years for learning Bayesian networks from data [1, 4, 6] to the task of learning PRMs from structured data.

Draft Version, 2005

An introduction is provided to Multi-Entity Bayesian Networks (MEBN), a logic system that integrates First Order Logic (FOL) with Bayesian probability theory. MEBN extends ordinary Bayesian networks to allow representation of graphical models with repeated sub-structures. Knowledge is encoded as a collection of Bayesian network fragments (MFrags) that can be instantiated and combined to form highly complex situation-specific Bayesian networks. A MEBN theory (MTheory) implicitly represents a joint probability distribution over possibly unbounded numbers of hypotheses, and uses Bayesian learning to refine a knowledge base as observations accrue. MEBN provides a logical foundation for the emerging collection of highly expressive probability-based languages. A running example illustrates the representation and reasoning power of the MEBN formalism.

Lecture Notes in Computer Science, 2009

We propose a learning approach for integrating formal knowledge into statistical inference by exploiting ontologies as a semantically rich and fully formal representation of prior knowledge. The logical constraints deduced from ontologies can be utilized to enhance and control the learning task by enforcing description logic satisfiability in a latent multi-relational graphical model. To demonstrate the feasibility of our approach we provide experiments using real world social network data in form of a SHOIN (D) ontology. The results illustrate two main practical advancements: First, entities and entity relationships can be analyzed via the latent model structure. Second, enforcing the ontological constraints guarantees that the learned model does not predict inconsistent relations. In our experiments, this leads to an improved predictive performance.

The increasing availability of large RDF datasets offers an exciting opportunity to use such data to build predictive models using machine learning algorithms. However, the massive size and distributed nature of RDF data calls for approaches to learning from RDF data in a setting where the data can be accessed only through a query interface, e.g., the SPARQL endpoint of the RDF store. In applications where the data are subject to frequent updates, there is a need for algorithms that allow the predictive model to be incrementally updated in response to changes in the data. Furthermore, in some applications, the attributes that are relevant for specific prediction tasks are not known a priori and hence need to be discovered by the algorithm. We present an approach to learning Relational Bayesian Classifiers (RBCs) from RDF data that addresses such scenarios. Specifically, we show how to build RBCs from RDF data using statistical queries through the SPARQL endpoint of the RDF store. We compare the communication complexity of our algorithm with one that requires direct centralized access to the data and hence has to retrieve the entire RDF dataset from the remote location for processing. We establish the conditions under which the RBC models can be incrementally updated in response to addition or deletion of RDF data. We show how our approach can be extended to the setting where the attributes that are relevant for prediction are not known a priori, by selectively crawling the RDF data for attributes of interest. We provide open source implementation and evaluate the proposed approach on several large RDF datasets.