Anders L. Madsen

Bayesian Networks and Influence Diagrams

Bayesian networks and influence diagram , Bayesian networks and influence diagram , کتابخانه دیجیتال جندی شاپور اهواز

LAZY propagation: a junction tree inference algorithm based on lazy evaluation

Abstract In this paper we present a junction tree based inference architecture exploiting the structure of the original Bayesian network and independence relations induced by evidence to improve the efficiency of inference. The efficiency improvements are obtained by maintaining a multiplicative decomposition of clique and separator potentials. Maintaining a multiplicative decomposition of clique and separator potentials offers a tradeoff between off-line constructed junction trees and on-line exploitation of barren variables and independence relations induced by evidence. We consider the impact of the proposed architecture on a number of commonly performed Bayesian network tasks. The tasks we consider include cautious propagation of evidence, determining a most probable configuration, and fast retraction of evidence a long with a number of other tasks. The general impression is that the proposed architecture increases the computational efficiency of performing these tasks. The efficiency improvement offered by the proposed architecture is emphasized through empirical evaluations involving large real-world Bayesian networks. We compare the time and space performance of the proposed architecture with non-optimized implementations of the Hugin and Shafer–Shenoy inference architectures.

Applications of object-oriented Bayesian networks for condition monitoring, root cause analysis and decision support on operation of complex continuous processes ☆

Abstract The increasing complexity of large-scale industrial processes and the struggle for cost reduction and higher profitability means automated systems for processes diagnosis in plant operation and maintenance are required. We have developed a methodology to address this issue and have designed a prototype system on which this methodology has been applied. The methodology integrates decision-theoretic troubleshooting with risk assessment for industrial process control. It is applied to a pulp digesting and screening process. The process is modeled using generic object-oriented Bayesian networks (OOBNs). The system performs reasoning under uncertainty and presents to users corrective actions, with explanations of the root causes. The system records users’ actions with associated cases and the BN models are prepared to perform sequential learning to increase its performance in diagnostics and advice.

THE HUGIN TOOL FOR PROBABILISTIC GRAPHICAL MODELS

As the framework of probabilistic graphical models becomes increasingly popular for knowledge representation and inference, the need for efficient tools for its support is increasing. The Hugin Tool is a general purpose tool for construction, maintenance, and deployment of Bayesian networks and influence diagrams. This paper surveys the key functionality of the Hugin Tool and reports on new advances of the tool. Furthermore, an empirical analysis reports on the efficiency of the Hugin Tool on common inference and learning tasks.

The Hugin Tool for Learning Bayesian Networks

In this paper, we describe the Hugin Tool as an efficient tool for knowledge discovery through construction of Bayesian networks by fusion of data and domain expert knowledge. The Hugin Tool supports structural learning, parameter estimation, and adaptation of parameters in Bayesian networks. The performance of the Hugin Tool is illustrated using real-world Bayesian networks, commonly used examples from the literature, and randomly generated Bayesian networks.

Maximal prime subgraph decomposition of Bayesian networks

The authors present a method for decomposition of Bayesian networks into their maximal prime subgraphs. The correctness of the method is proven and results relating the maximal prime subgraph decomposition (MPD) to the maximal complete subgraphs of the moral graph of the original Bayesian network are presented. The maximal prime subgraphs of a Bayesian network can be organized as a tree which can be used as the computational structure for LAZY propagation. We also identify a number of tasks performed on Bayesian networks that can benefit from MPD. These tasks are: divide and conquer triangulation, hybrid propagation algorithms combining exact and approximative inference techniques, and incremental construction of junction trees. We compare the proposed algorithm with standard algorithms for decomposition of undirected graphs into their maximal prime subgraphs. The discussion shows that the proposed algorithm is simpler, more easy to comprehend, and it has the same complexity as the standard algorithms.

Variations over the message computation algorithm of lazy propagation

Improving the performance of belief updating becomes increasingly important as real-world Bayesian networks continue to grow larger and more complex. In this paper, an investigation is done on how variations over the message-computation algorithm of lazy propagation may impact its performance. Lazy propagation is a junction-tree-based inference algorithm for belief updating in Bayesian networks. Lazy propagation combines variable elimination (VE) with a Shenoy-Shafer message-passing scheme in an attempt to exploit the independence properties induced by evidence in a junction-tree-based algorithm. The authors investigate, the use of arc reversal (AR) and symbolic probabilistic inference (SPI) as alternative algorithms for computing clique-to-clique messages in lazy propagation. The paper presents the results of an empirical evaluation of the performance of lazy propagation using AR, SPI, and VE as the message-computation algorithm. The results of the empirical evaluation show that no single algorithm outperforms or is outperformed by the other two alternatives. In many cases, there is no significant difference in the performance of the three algorithms.

Improvements to message computation in lazy propagation

Even though existing algorithms for belief update in Bayesian networks (BNs) have exponential time and space complexity, belief update in many real-world BNs is feasible. However, in some cases the efficiency of belief update may be insufficient. In such cases minor improvements in efficiency may be important or even necessary to make a task tractable. This paper introduces two improvements to the message computation in Lazy propagation (LP): (1) we introduce myopic methods for sorting the operations involved in a variable elimination using arc-reversal and (2) extend LP with the any-space property. The performance impacts of the methods are assessed empirically.

A factorized representation of independence of causal influence and lazy propagation

The efficiency of algorithms for probabilistic inference in Bayesian networks can be improved by exploiting independence of causal influence. The factorized representation of independence of causal influence offers a factorized decomposition of certain independence of causal influence models. We describe how lazy propagation - a junction tree based inference algorithm easily can be extended to take advantage of the decomposition offered by the factorized representation. We introduce two extensions to the factorized representation easing the knowledge acquisition task and reducing the space complexity of the representation exponentially in the state space size of the effect variable of an independence of causal influence model. Finally, we describe how the factorized representation can be used to solve tasks such as calculating the maximum a posteriori hypothesis, the maximum expected utility: and the most probable configuration.

Solving linear-quadratic conditional Gaussian influence diagrams

This paper considers the problem of solving Bayesian decision problems with a mixture of continuous and discrete variables. We focus on exact evaluation of linear-quadratic conditional Gaussian influence diagrams (LQCG influence diagrams) with additively decomposing utility functions. Based on new and existing representations of probability and utility potentials, we derive a method for solving LQCG influence diagrams based on variable elimination. We show how the computations performed during evaluation of a LQCG influence diagram can be organized in message passing schemes based on Shenoy-Shafer and Lazy propagation. The proposed architectures are the first architectures for efficient exact solution of LQCG influence diagrams exploiting an additively decomposing utility function.