Positive dependence in qualitative probabilistic networks

Qualitative probabilistic networks (QPNs) combine the conditional independence assumptions of Bayesian networks with the qualitative properties of positive and negative dependence. They formalise various intuitive properties of positive dependence to allow inferences over a large network of variables. However, we will demonstrate in this paper that, due to an incorrect symmetry property, many inferences obtained in non-binary QPNs are not mathematically true. We will provide examples of such incorrect inferences and briefly discuss possible resolutions.Comment: 10 pages, 3 figure

CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements

Information about user preferences plays a key role in automated decision making. In many domains it is desirable to assess such preferences in a qualitative rather than quantitative way. In this paper, we propose a qualitative graphical representation of preferences that reflects conditional dependence and independence of preference statements under a ceteris paribus (all else being equal) interpretation. Such a representation is often compact and arguably quite natural in many circumstances. We provide a formal semantics for this model, and describe how the structure of the network can be exploited in several inference tasks, such as determining whether one outcome dominates (is preferred to) another, ordering a set outcomes according to the preference relation, and constructing the best outcome subject to available evidence

Generalized belief change with imprecise probabilities and graphical models

We provide a theoretical investigation of probabilistic belief revision in complex frameworks, under extended conditions of uncertainty, inconsistency and imprecision. We motivate our kinematical approach by specializing our discussion to probabilistic reasoning with graphical models, whose modular representation allows for efficient inference. Most results in this direction are derived from the relevant work of Chan and Darwiche (2005), that first proved the inter-reducibility of virtual and probabilistic evidence. Such forms of information, deeply distinct in their meaning, are extended to the conditional and imprecise frameworks, allowing further generalizations, e.g. to experts' qualitative assessments. Belief aggregation and iterated revision of a rational agent's belief are also explored

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Proceedings of the Fifth European Workshop on Probabilistic Graphical Models

Peer reviewe

Transformation of graphical models to support knowledge transfer

Menschliche Experten verfügen über die Fähigkeit, ihr Entscheidungsverhalten flexibel auf die jeweilige Situation abzustimmen. Diese Fähigkeit zahlt sich insbesondere dann aus, wenn Entscheidungen unter beschränkten Ressourcen wie Zeitrestriktionen getroffen werden müssen. In solchen Situationen ist es besonders vorteilhaft, die Repräsentation des zugrunde liegenden Wissens anpassen und Entscheidungsmodelle auf unterschiedlichen Abstraktionsebenen verwenden zu können. Weiterhin zeichnen sich menschliche Experten durch die Fähigkeit aus, neben unsicheren Informationen auch unscharfe Wahrnehmungen in die Entscheidungsfindung einzubeziehen. Klassische entscheidungstheoretische Modelle basieren auf dem Konzept der Rationalität, wobei in jeder Situation die nutzenmaximale Entscheidung einer Entscheidungsfunktion zugeordnet wird. Neuere graphbasierte Modelle wie Bayes\u27sche Netze oder Entscheidungsnetze machen entscheidungstheoretische Methoden unter dem Aspekt der Modellbildung interessant. Als Hauptnachteil lässt sich die Komplexität nennen, wobei Inferenz in Entscheidungsnetzen NP-hart ist. Zielsetzung dieser Dissertation ist die Transformation entscheidungstheoretischer Modelle in Fuzzy-Regelbasen als Zielsprache. Fuzzy-Regelbasen lassen sich effizient auswerten, eignen sich zur Approximation nichtlinearer funktionaler Beziehungen und garantieren die Interpretierbarkeit des resultierenden Handlungsmodells. Die Übersetzung eines Entscheidungsmodells in eine Fuzzy-Regelbasis wird durch einen neuen Transformationsprozess unterstützt. Ein Agent kann zunächst ein Bayes\u27sches Netz durch Anwendung eines in dieser Arbeit neu vorgestellten parametrisierten Strukturlernalgorithmus generieren lassen. Anschließend lässt sich durch Anwendung von Präferenzlernverfahren und durch Präzisierung der Wahrscheinlichkeitsinformation ein entscheidungstheoretisches Modell erstellen. Ein Transformationsalgorithmus kompiliert daraus eine Regelbasis, wobei ein Approximationsmaß den erwarteten Nutzenverlust als Gütekriterium berechnet. Anhand eines Beispiels zur Zustandsüberwachung einer Rotationsspindel wird die Praxistauglichkeit des Konzeptes gezeigt.Human experts are able to flexible adjust their decision behaviour with regard to the respective situation. This capability pays in situations under limited resources like time restrictions. It is particularly advantageous to adapt the underlying knowledge representation and to make use of decision models at different levels of abstraction. Furthermore human experts have the ability to include uncertain information and vague perceptions in decision making. Classical decision-theoretic models are based directly on the concept of rationality, whereby the decision behaviour prescribed by the principle of maximum expected utility. For each observation some optimal decision function prescribes an action that maximizes expected utility. Modern graph-based methods like Bayesian networks or influence diagrams make use of modelling. One disadvantage of decision-theoretic methods concerns the issue of complexity. Finding an optimal decision might become very expensive. Inference in decision networks is known to be NP-hard. This dissertation aimed at combining the advantages of decision-theoretic models with rule-based systems by transforming a decision-theoretic model into a fuzzy rule-based system. Fuzzy rule bases are an efficient implementation from a computational point of view, they can approximate non-linear functional dependencies and they are also intelligible. There was a need for establishing a new transformation process to generate rule-based representations from decision models, which provide an efficient implementation architecture and represent knowledge in an explicit, intelligible way. At first, an agent can apply the new parameterized structure learning algorithm to identify the structure of the Bayesian network. The use of learning approaches to determine preferences and the specification of probability information subsequently enables to model decision and utility nodes and to generate a consolidated decision-theoretic model. Hence, a transformation process compiled a rule base by measuring the utility loss as approximation measure. The transformation process concept has been successfully applied to the problem of representing condition monitoring results for a rotation spindle

On risk-based decision-making for structural health monitoring

Structural health monitoring (SHM) technologies seek to detect, localise, and characterise damage present within structures and infrastructure. Arguably, the foremost incentive for developing and implementing SHM systems is to improve the quality of operation and maintenance (O&M) strategies for structures, such that safety can be enhanced, or greater economic benefits can be realised. Given this motivation, SHM systems can be considered primarily as decision-support tools. Although much research has been conducted into damage identification and characterisation approaches, there has been relatively little that has explicitly considered the decision-making applications of SHM systems. In light of this fact, the current thesis seeks to consider decision-making for SHM with respect to risk. Risk, defined as a product of probability and cost, can be interpreted as an expected utility. The keystone of the current thesis is a general framework for conducting risk-based, SHM generated by combining aspects of probabilistic risk assessment (PRA) with the existing statistical pattern recognition paradigm for SHM. The framework, founded on probabilistic graphical models (PGMs), utilises Bayesian network representations of fault-trees to facilitate the flow of information between observations of discriminative features to failure states of structures of interest. Using estimations of failure probabilities in conjunction with utility functions that capture the severity of consequences enables risk assessments -- these risks can be minimised with respect to candidate maintenance actions to determine optimal strategies. Key elements of the decision framework are examined; in particular, a physics-based methodology for initialising a structural degradation model defining health-state transition probabilities is presented. The risk-based framework allows aspects of SHM systems to be developed with explicit consideration for the decision-support applications. In relation to this aim, the current thesis proposes a novel approach to learn statistical classification models within an online SHM system. The approach adopts an active learning framework in which descriptive labels, corresponding to salient health states of a structure, are obtained via structural inspections. To account for the decision processes associated with SHM, structural inspections are mandated according to the expected value of information for data-labels. The resulting risk-based active learning algorithm is shown to yield cost-effective improvements in the performance of decision-making agents, in addition to reducing the number of manual inspections made over the course of a monitoring campaign. Characteristics of the risk-based active learning algorithm are further investigated, with particular focus on the effects of \sampling bias. Sampling bias is known to degrade decision-making performance over time, thus engineers have a vested interest in mitigating its negative effects. On this theme, two approaches are considered for improving risk-based active learning; semi-supervised learning, and discriminative classification models. Semi-supervised learning yielded mixed results, with performance being highly dependent on base distributions being representative of the underlying data. On the other hand, discriminative classifiers performed strongly across the board. It is shown that by mitigating the negative effects of sampling bias via classifier and algorithm design, decision-support systems can be enhanced, resulting in more cost-effective O&M strategies. Finally, the future of risk-based decision-making is considered. Particular attention is given to population-based structural health monitoring (PBSHM), and the management of fleets of assets. The hierarchical representation of structures used to develop the risk-based SHM framework is extended to populations of structures. Initial research into PBSHM shows promising results with respect to the transfer of information between individual structures comprising a population. The significance of these results in the context of decision-making is discussed. To summarise, by framing SHM systems as decision-support tools, risk-informed O&M strategies can be developed for structures and infrastructure such that safety is improved and costs are reduced

Probabilistic Modeling of Process Systems with Application to Risk Assessment and Fault Detection

Three new methods of joint probability estimation (modeling), a maximum-likelihood maximum-entropy method, a constrained maximum-entropy method, and a copula-based method called the rolling pin (RP) method, were developed. Compared to many existing probabilistic modeling methods such as Bayesian networks and copulas, the developed methods yield models that have better performance in terms of flexibility, interpretability and computational tractability. These methods can be used readily to model process systems and perform risk analysis and fault detection at steady state conditions, and can be coupled with appropriate mathematical tools to develop dynamic probabilistic models. Also, a method of performing probabilistic inference using RP-estimated joint probability distributions was introduced; this method is superior to Bayesian networks in several aspects. The RP method was also applied successfully to identify regression models that have high level of flexibility and are appealing in terms of computational costs.Ph.D., Chemical Engineering -- Drexel University, 201

Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks

Semi-qualitative probabilistic networks (SQPNs) merge two important graphical model formalisms: Bayesian networks and qualitative probabilistic networks. They provade a very Complexity of inferences in polytree-shaped semi-qualitative probabilistic networks and qualitative probabilistic networks. They provide a very general modeling framework by allowing the combination of numeric and qualitative assessments over a discrete domain, and can be compactly encoded by exploiting the same factorization of joint probability distributions that are behind the bayesian networks. This paper explores the computational complexity of semi-qualitative probabilistic networks, and takes the polytree-shaped networks as its main target. We show that the inference problem is coNP-Complete for binary polytrees with multiple observed nodes. We also show that interferences can be performed in time linear in the number of nodes if there is a single observed node. Because our proof is construtive, we obtain an efficient linear time algorithm for SQPNs under such assumptions. To the best of our knowledge, this is the first exact polynominal-time algorithm for SQPn. Together these results provide a clear picture of the inferential complexity in polytree-shaped SQPNs.CNP

Statistical Fusion of Multi-aspect Synthetic Aperture Radar Data for Automatic Road Extraction

In this dissertation, a new statistical fusion for automatic road extraction from SAR images taken from different looking angles (i.e. multi-aspect SAR data) was presented. The main input to the fusion is extracted line features. The fusion is carried out on decision-level and is based on Bayesian network theory