We introduce a Probabilistic Grammar-Markov Model (PGMM) which couples probabilistic context-free grammars and Markov Random Fields. These PGMMs are generative models defined over attributed features and are used to detect and classify objects in natural images. PGMMs are designed so that they can perform rapid inference, parameter learning, and the more difficult task of structure induction. PGMMs can deal with unknown 2D pose (position, orientation, and scale) in both inference and learning, different appearances, or aspects of the model. The PGMMs can be learned in an unsupervised manner, where the image can contain one of an unknown number of objects of different categories or even be pure background. We first study the weakly supervised case, where each image contains an example of the (single) object of interest, and then generalize to less supervised cases. The goal of this paper is theoretical, but, to provide proof of concept, we demonstrate results from this approach on a subset of the Caltech data set (learning on a training set and evaluating on a testing set). Our results are generally comparable with the current state of the art and our inference is performed in less than five seconds.

Unsupervised Learning of Probabilistic Grammar-Markov Models for Object Categories

Bayesian networks have been at the core of the research pertaining to probabilistic reasoning. Several machine learning algorithms and techniques highly rely on Bayesian networks for their reasoning capabilities. Since several decades Bayesian networks proved to be the essential tool in the hands of researchers working in artificial intelligence domain. Yet Bayesian networks do have certain limitations [1], Bayesian networks need extensions to be more expressive and functional for probabilistic reasoning needs of various domains. Multi Entity Bayesian Networks (MEBN) is a theory combining expressivity of first-order logic principles and probabilistic reasoning of Bayesian networks. The paper thoroughly introduces the MEBN theory with an example modeling for a problem description and discusses various other works which included MEBN theory as a core of their research. The study in this paper concludes with the current highlights and challenges in MEBN and future developments.

https://www.ijarcs.info/index.php/Ijarcs/article/download/3954/3735

Survey of Multi Entity Bayesian Network (MEBN) and its applications in probabilistic reasoning.

Multi-Entity Bayesian Network (MEBN) is a knowledge representation formalism combining Bayesian Networks (BNs) with First-Order Logic (FOL). MEBN has sufficient expressive power for general-purpose knowledge representation and reasoning, and is the logical basis of Probabilistic Web Ontology Language (PR-OWL), a representation language for probabilistic ontologies. Developing an MEBN model to support a given application is a challenge, requiring definition of entities, relationships, random variables, conditional dependence relationships, and probability distributions. When available, data can be invaluable both to improve performance and to streamline development. By far the most common format for available data is the relational database (RDB). Relational databases describe and organize data according to the Relational Model (RM). Developing an MEBN model from data stored in an RDB therefore requires mapping between the two formalisms. This paper presents MEBN-RM, a set of mapping rules between key elements of MEBN and RM. We identify links between the two languages (RM and MEBN) and define four levels of mapping from elements of RM to elements of MEBN. These definitions are implemented in the MEBN-RM algorithm, which converts a relational schema in RM to a partial MEBN model. Through this research, the software has been released as an MEBN-RM open-source software tool. The method is illustrated through two example use cases using MEBN-RM to develop MEBN models: a Critical Infrastructure Defense System and a Smart Manufacturing System. Both systems are proof-of-concept systems used for situation awareness, where data coming from various sensors are stored in RDBs and converted into MEBN models through the MEBN-RM algorithm. In these use cases, we evaluate the performance of the MEBN-RM algorithm in terms of mapping speed and quality to show its efficiency in MEBN modeling.

MEBN-RM: A Mapping between Multi-Entity Bayesian Network and Relational Model

The web of things (WoT) uses web technologies to connect embedded objects to each other and to deliver services to stakeholders. The context of these interactions (situation) is a key source of information which can be sometimes uncertain. In this paper, we focus on the development of intelligent web services. The main requirements for intelligent service are to deal with context diversity, semantic context representation and the capacity to reason with uncertain information. From this perspective, we propose a framework for intelligent services to deal with various contexts, to reactively respond to real-time situations and proactively predict future situations. For the semantic representation of context, we use PR-OWL, a probabilistic ontology based on multi-entity Bayesian networks. PR-OWL is flexible enough to represent complex and uncertain contexts. We validate our framework with an intelligent plant watering use case to show its reasoning capabilities.

Proactive and reactive context reasoning architecture for smart web services

During the past quarter-century, situation awareness (SAW) has become a critical research theme, because of its importance. Since the concept of SAW was first introduced during World War I, various versions of SAW have been researched and introduced. Predictive Situation Awareness (PSAW) focuses on the ability to predict aspects of a temporally evolving situation over time. PSAW requires a formal representation and a reasoning method using such a representation. A Multi-Entity Bayesian Network (MEBN) is a knowledge representation formalism combining Bayesian Networks (BN) with First-Order Logic (FOL). MEBN can be used to represent uncertain situations (supported by BN) as well as complex situations (supported by FOL). Also, efficient reasoning algorithms for MEBN have been developed. MEBN can be a formal representation to support PSAW and has been used for several PSAW systems. Although several MEBN applications for PSAW exist, very little work can be found in the literature that attempts to generalize a MEBN model to support PSAW. In this research, we define a reference model for MEBN in PSAW, called a PSAW-MEBN reference model. The PSAW-MEBN reference model enables us to easily develop a MEBN model for PSAW by supporting the design of a MEBN model for PSAW. In this research, we introduce two example use cases using the PSAW-MEBN reference model to develop MEBN models to support PSAW: a Smart Manufacturing System and a Maritime Domain Awareness System.

Reference Model of Multi-Entity Bayesian Networks for Predictive Situation Awareness.

Probabilistic context free grammars (PCFG) have been the core of the probabilistic reasoning based parsers for several years especially in the context of the NLP. Multi entity Bayesian networks (MEBN) a First Order Logic probabilistic reasoning methodology is widely adopted and used method for uncertainty reasoning. Further upper ontology like Probabilistic Ontology Web Language (PR-OWL) built using MEBN takes care of probabilistic ontologies which model and capture the uncertainties inherent in the domain's semantic information. The paper attempts to establish a link between probabilistic reasoning in PCFG and MEBN by proposing a formal description of PCFG driven by MEBN leading to the usage of PR-OWL modeled ontologies in PCFG parsers. Furthermore, the paper outlines an approach to resolve the prepositional phrase (PP) attachment ambiguity using the proposed mapping between PCFG and MEBN.

Syntactico-Semantic Reasoning using PCFG, MEBN & PP Attachment Ambiguity

Probabilistic context free grammars (PCFG) have been the core of the probabilistic reasoning based parsers for several years especially in the context of the NLP. Multi entity bayesian networks (MEBN) a First Order Logic probabilistic reasoning methodology is widely adopted and used method for uncertainty reasoning. Further upper ontology like Probabilistic Ontology Web Language (PR-OWL) built using MEBN takes care of probabilistic ontologies which model and capture the uncertainties inherent in the domain's semantic information. The paper attempts to establish a link between probabilistic reasoning in PCFG and MEBN by proposing a formal description of PCFG driven by MEBN leading to usage of PR-OWL modeled ontologies in PCFG parsers. Furthermore, the paper outlines an approach to resolve prepositional phrase (PP) attachment ambiguity using the proposed mapping between PCFG and MEBN.

The paper proposes a formal approach for parsing grammatical derivations in the context of the principle of semantic compositionality by defining a mapping between Probabilistic Context Free Grammar (PCFG) and Multi Entity Bayesian Network (MEBN) theory, which is a first-order logic for modelling probabilistic knowledge bases. The principle of semantic compositionality states that meaning of compound expressions is dependent on meanings of constituent expressions forming the compound expression. Typical pattern analysis applications focus on syntactic patterns ignoring semantic patterns governing the domain in which pattern analysis is attempted. The paper introduces the concepts and terminologies of the mapping between PCFG and MEBN theory. Further the paper outlines a modified version of CYK parser algorithm for parsing PCFG derivations driven by MEBN. Using Kullback– Leibler divergence an outline for proving properness and consistency of the PCFG mapped with MEBN is discussed.

Properness and Consistency of Syntactico-Semantic Reasoning using PCFG and MEBN

Probabilistic context free grammars (PCFG) have been the core of the probabilistic reasoning based parsers for several years especially in the context of the NLP. Multi entity bayesian networks (MEBN) a First Order Logic probabilistic reasoning methodology and is widely adopted and used method for uncertainty reasoning. Further upper ontology like Probabilistic Ontology Web Language (PR-OWL) built using MEBN takes care of probabilistic ontologies which model and capture the uncertainties inherent in the domain's semantic information. The paper attempts to establish a link between probabilistic reasoning in PCFG and MEBN by proposing a formal description of PCFG driven by MEBN leading to usage of PR-OWL modeled ontologies in PCFG parsers.

Shrinivasan Patnaikuni

Papers

Survey of Multi Entity Bayesian Network (MEBN) and its applications in probabilistic reasoning.

Syntactico-Semantic Reasoning using PCFG, MEBN & PP Attachment Ambiguity

Syntactico-Semantic Reasoning using PCFG, MEBN & PP Attachment Ambiguity

Properness and Consistency of Syntactico-Semantic Reasoning using PCFG and MEBN

Syntactico-Semantic Reasoning using PCFG, MEBN, and PR-OWL.