On the Relation between Kappa Calculus and Probabilistic Reasoning

We study the connection between kappa calculus and probabilistic reasoning in diagnosis applications. Specifically, we abstract a probabilistic belief network for diagnosing faults into a kappa network and compare the ordering of faults computed using both methods. We show that, at least for the example examined, the ordering of faults coincide as long as all the causal relations in the original probabilistic network are taken into account. We also provide a formal analysis of some network structures where the two methods will differ. Both kappa rankings and infinitesimal probabilities have been used extensively to study default reasoning and belief revision. But little has been done on utilizing their connection as outlined above. This is partly because the relation between kappa and probability calculi assumes that probabilities are arbitrarily close to one (or zero). The experiments in this paper investigate this relation when this assumption is not satisfied. The reported results have important implications on the use of kappa rankings to enhance the knowledge engineering of uncertainty models.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

Human-aided Multi-Entity Bayesian Networks Learning from Relational Data

An Artificial Intelligence (AI) system is an autonomous system which emulates human mental and physical activities such as Observe, Orient, Decide, and Act, called the OODA process. An AI system performing the OODA process requires a semantically rich representation to handle a complex real world situation and ability to reason under uncertainty about the situation. Multi-Entity Bayesian Networks (MEBNs) combines First-Order Logic with Bayesian Networks for representing and reasoning about uncertainty in complex, knowledge-rich domains. MEBN goes beyond standard Bayesian networks to enable reasoning about an unknown number of entities interacting with each other in various types of relationships, a key requirement for the OODA process of an AI system. MEBN models have heretofore been constructed manually by a domain expert. However, manual MEBN modeling is labor-intensive and insufficiently agile. To address these problems, an efficient method is needed for MEBN modeling. One of the methods is to use machine learning to learn a MEBN model in whole or in part from data. In the era of Big Data, data-rich environments, characterized by uncertainty and complexity, have become ubiquitous. The larger the data sample is, the more accurate the results of the machine learning approach can be. Therefore, machine learning has potential to improve the quality of MEBN models as well as the effectiveness for MEBN modeling. In this research, we study a MEBN learning framework to develop a MEBN model from a combination of domain expert's knowledge and data. To evaluate the MEBN learning framework, we conduct an experiment to compare the MEBN learning framework and the existing manual MEBN modeling in terms of development efficiency

Reasoning From Data in the Mathematical Theory of Evidence

Mathematical Theory of Evidence (MTE) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its foundation, many questions remain open. One of the most important open questions seems to be the relationship between frequencies and the Mathematical Theory of Evidence. The theory is blamed to leave frequencies outside (or aside of) its framework. The seriousness of this accusation is obvious: no experiment may be run to compare the performance of MTE-based models of real world processes against real world data. In this paper we develop a frequentist model of the MTE bringing to fall the above argument against MTE. We describe, how to interpret data in terms of MTE belief functions, how to reason from data about conditional belief functions, how to generate a random sample out of a MTE model, how to derive MTE model from data and how to compare results of reasoning in MTE model and reasoning from data. It is claimed in this paper that MTE is suitable to model some types of destructive processesComment: presented as poster M.A. K{\l}opotek: Reasoning from Data in the Mathematical Theory of Evidence. [in:] Proc. Eighth International Symposium On Methodologies For Intelligent Systems (ISMIS'94), Charlotte, North Carolina, USA, October 16-19, 1994. arXiv admin note: text overlap with arXiv:1707.0388

Inference Networks and the Evaluation of Evidence: Alternative Analyses

Inference networks have a variety of important uses and are constructed by persons having quite different standpoints. Discussed in this paper are three different but complementary methods for generating and analyzing probabilistic inference networks. The first method, though over eighty years old, is very useful for knowledge representation in the task of constructing probabilistic arguments. It is also useful as a heuristic device in generating new forms of evidence. The other two methods are formally equivalent ways for combining probabilities in the analysis of inference networks. The use of these three methods is illustrated in an analysis of a mass of evidence in a celebrated American law case.Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999

An Application of Uncertain Reasoning to Requirements Engineering

This paper examines the use of Bayesian Networks to tackle one of the tougher problems in requirements engineering, translating user requirements into system requirements. The approach taken is to model domain knowledge as Bayesian Network fragments that are glued together to form a complete view of the domain specific system requirements. User requirements are introduced as evidence and the propagation of belief is used to determine what are the appropriate system requirements as indicated by user requirements. This concept has been demonstrated in the development of a system specification and the results are presented here.Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999

Of Starships and Klingons: Bayesian Logic for the 23rd Century

Intelligent systems in an open world must reason about many interacting entities related to each other in diverse ways and having uncertain features and relationships. Traditional probabilistic languages lack the expressive power to handle relational domains. Classical first-order logic is sufficiently expressive, but lacks a coherent plausible reasoning capability. Recent years have seen the emergence of a variety of approaches to integrating first-order logic, probability, and machine learning. This paper presents Multi-entity Bayesian networks (MEBN), a formal 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, and can express a probability distribution over models of any consistent, finitely axiomatizable first-order theory. We present the logic using an example inspired by the Paramount Series StarTrek.Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005

Exploring Localization in Bayesian Networks for Large Expert Systems

Current Bayesian net representations do not consider structure in the domain and include all variables in a homogeneous network. At any time, a human reasoner in a large domain may direct his attention to only one of a number of natural subdomains, i.e., there is ?localization' of queries and evidence. In such a case, propagating evidence through a homogeneous network is inefficient since the entire network has to be updated each time. This paper presents multiply sectioned Bayesian networks that enable a (localization preserving) representation of natural subdomains by separate Bayesian subnets. The subnets are transformed into a set of permanent junction trees such that evidential reasoning takes place at only one of them at a time. Probabilities obtained are identical to those that would be obtained from the homogeneous network. We discuss attention shift to a different junction tree and propagation of previously acquired evidence. Although the overall system can be large, computational requirements are governed by the size of only one junction tree.Comment: Appears in Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence (UAI1992

An Importance Sampling Algorithm Based on Evidence Pre-propagation

Precision achieved by stochastic sampling algorithms for Bayesian networks typically deteriorates in face of extremely unlikely evidence. To address this problem, we propose the Evidence Pre-propagation Importance Sampling algorithm (EPIS-BN), an importance sampling algorithm that computes an approximate importance function by the heuristic methods: loopy belief Propagation and e-cutoff. We tested the performance of e-cutoff on three large real Bayesian networks: ANDES, CPCS, and PATHFINDER. We observed that on each of these networks the EPIS-BN algorithm gives us a considerable improvement over the current state of the art algorithm, the AIS-BN algorithm. In addition, it avoids the costly learning stage of the AIS-BN algorithm.Comment: Appears in Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence (UAI2003

Inferring Personalized Bayesian Embeddings for Learning from Heterogeneous Demonstration

For assistive robots and virtual agents to achieve ubiquity, machines will need to anticipate the needs of their human counterparts. The field of Learning from Demonstration (LfD) has sought to enable machines to infer predictive models of human behavior for autonomous robot control. However, humans exhibit heterogeneity in decision-making, which traditional LfD approaches fail to capture. To overcome this challenge, we propose a Bayesian LfD framework to infer an integrated representation of all human task demonstrators by inferring human-specific embeddings, thereby distilling their unique characteristics. We validate our approach is able to outperform state-of-the-art techniques on both synthetic and real-world data sets.Comment: 8 Pages, 7 figure

Computational Advantages of Relevance Reasoning in Bayesian Belief Networks

This paper introduces a computational framework for reasoning in Bayesian belief networks that derives significant advantages from focused inference and relevance reasoning. This framework is based on d -separation and other simple and computationally efficient techniques for pruning irrelevant parts of a network. Our main contribution is a technique that we call relevance-based decomposition. Relevance-based decomposition approaches belief updating in large networks by focusing on their parts and decomposing them into partially overlapping subnetworks. This makes reasoning in some intractable networks possible and, in addition, often results in significant speedup, as the total time taken to update all subnetworks is in practice often considerably less than the time taken to update the network as a whole. We report results of empirical tests that demonstrate practical significance of our approach.Comment: Appears in Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI1997