Generalized loopy 2U: A new algorithm for approximate inference in credal networks

Credal networks generalize Bayesian networks by relaxing the requirement of precision of probabilities. Credal networks are considerably more expressive than Bayesian networks, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal networks. The algorithm is based on an important representation result we prove for general credal networks: that any credal network can be equivalently reformulated as a credal network with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal network is then updated by L2U, a loopy approximate algorithm for binary credal networks. Overall, we generalize L2U to non-binary credal networks, obtaining a scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences with respect to other state-of-the-art algorithms is evaluated by extensive numerical tests.

Inference in credal networks using multilinear programming

A credal network is a graphical tool for representation and manipulation of uncertainty, where probability values may be imprecise or indeterminate. A credal network associates a directed acyclic graph with a collection of sets of probability measures; in this context, inference is the computation of tight lower and upper bounds for conditional probabilities. In this paper we present new algorithms for inference in credal networks based on multilinear programming techniques. Experiments indicate that these new algorithms have better performance than existing ones, in the sense that they can produce more accurate results in larger networks.

Statistical Tests for Joint Analysis of Performance Measures

Recently there has been an increasing interest in the development of new methods using Pareto optimality to deal with multi-objective criteria (for example, accuracy and architectural complexity). Once one has learned a model based on their devised method, the problem is then how to compare it with the state of art. In machine learning, algorithms are typically evaluated by comparing their performance on different data sets by means of statistical tests. Unfortunately, the standard tests used for this purpose are not able to jointly consider performance measures. The aim of this paper is to resolve this issue by developing statistical procedures that are able to account for multiple competing measures at the same time. In particular, we develop two tests: a frequentist procedure based on the generalized likelihood-ratio test and a Bayesian procedure based on a multinomial-Dirichlet conjugate model. We further extend them by discovering conditional independences among measures to reduce the number of parameter of such models, as usually the number of studied cases is very reduced in such comparisons. Real data from a comparison among general purpose classifiers is used to show a practical application of our tests.

Discrete Conditional Phase-type model (DC_Ph) for patient waiting time with a logistic regression component to predict patient admission to hospital

Discrete Conditional Phase-type (DC-Ph) models are a family of models which represent skewed survival data conditioned on specific inter-related discrete variables. The survival data is modeled using a Coxian phase-type distribution which is associated with the inter-related variables using a range of possible data mining approaches such as Bayesian networks (BNs), the Naïve Bayes Classification method and classification regression trees. This paper utilizes the Discrete Conditional Phase-type model (DC-Ph) to explore the modeling of patient waiting times in an Accident and Emergency Department of a UK hospital. The resulting DC-Ph model takes on the form of the Coxian phase-type distribution conditioned on the outcome of a logistic regression model.

Semiring induced valuation algebras: Exact and approximate local computation algorithms

Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra.There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible.

Probabilistic logic with independence

This paper investigates probabilistic logics endowed with independence relations. We review propositional probabilistic languages without and with independence. We then consider graph-theoretic representations for propositional probabilistic logic with independence; complexity is analyzed, algorithms are derived, and examples are discussed. Finally, we examine a restricted first-order probabilistic logic that generalizes relational Bayesian networks.

Incorporating PGMs into a BDI Architecture

In this paper, we present a hybrid BDI-PGM framework, in which PGMs (Probabilistic Graphical Models) are incorporated into a BDI (belief-desire-intention) architecture. This work is motivated by the need to address the scalability and noisy sensing issues in SCADA (Supervisory Control And Data Acquisition) systems. Our approach uses the incorporated PGMs to model the uncertainty reasoning and decision making processes of agents situated in a stochastic environment. In particular, we use Bayesian networks to reason about an agent’s beliefs about the environment based on its sensory observations, and select optimal plans according to the utilities of actions defined in influence diagrams. This approach takes the advantage of the scalability of the BDI architecture and the uncertainty reasoning capability of PGMs. We present a prototype of the proposed approach using a transit scenario to validate its effectiveness.

Towards a knowledge-based approach for effective decision-making in railway safety

Purpose – This paper aims to contribute towards understanding how safety knowledge can be elicited from railway experts for the purposes of supporting effective decision-making. Design/methodology/approach – A consortium of safety experts from across the British railway industry is formed. Collaborative modelling of the knowledge domain is used as an approach to the elicitation of safety knowledge from experts. From this, a series of knowledge models is derived to inform decision-making. This is achieved by using Bayesian networks as a knowledge modelling scheme, underpinning a Safety Prognosis tool to serve meaningful prognostics information and visualise such information to predict safety violations. Findings – Collaborative modelling of safety-critical knowledge is a valid approach to knowledge elicitation and its sharing across the railway industry. This approach overcomes some of the key limitations of existing approaches to knowledge elicitation. Such models become an effective tool for prediction of safety cases by using railway data. This is demonstrated using passenger–train interaction safety data. Practical implications – This study contributes to practice in two main directions: by documenting an effective approach to knowledge elicitation and knowledge sharing, while also helping the transport industry to understand safety. Social implications – By supporting the railway industry in their efforts to understand safety, this research has the potential to benefit railway passengers, staff and communities in general, which is a priority for the transport sector. Originality/value – This research applies a knowledge elicitation approach to understanding safety based on collaborative modelling, which is a novel approach in the context of transport.

Belief Updating and Learning in Semi-Qualitative Probabilistic Networks

This paper explores semi-qualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NPPP-Complete. We then show that existing qualitative relations in SQPNs (plus probabilistic logic and imprecise assessments) can be dealt effectively through multilinear programming. We then discuss learning: we consider a maximum likelihood method that generates point estimates given a SQPN and empirical data, and we describe a Bayesian-minded method that employs the Imprecise Dirichlet Model to generate set-valued estimates.

A new Jacobian matrix for optimal learning of single-layer neural networks

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

Computationally efficient sequential learning algorithms for direct link resource-allocating networks

Computionally efficient sequential learning algorithms are developed for direct-link resource-allocating networks (DRANs). These are achieved by decomposing existing recursive training algorithms on a layer by layer and neuron by neuron basis. This allows network weights to be updated in an efficient parallel manner and facilitates the implementation of minimal update extensions that yield a significant reduction in computation load per iteration compared to existing sequential learning methods employed in resource-allocation network (RAN) and minimal RAN (MRAN) approaches. The new algorithms, which also incorporate a pruning strategy to control network growth, are evaluated on three different system identification benchmark problems and shown to outperform existing methods both in terms of training error convergence and computational efficiency. (c) 2005 Elsevier B.V. All rights reserved.