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Bayesian Network and Influence Diagram A Guide to Construction And Analysis

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Chapter 1

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Introduction This chapter provides brief accounts on the context of Probabilistic Networks, what they are and when to use them The main topic covered are – Expert Systems – Rule-Based Systems – Bayesian Networks

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Expert Systems A system that is able to perform tasks that are intellectually demanding often said to exhibit an Expert System if the system’s problem solving ability is restricted to particular area The techniques that enable us to construct devices and services that are able to – Perform reasoning and decision making under uncertainty – Acquire knowledge from data/experience – Solve problems efficiently and respond to new situation

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Representation of Uncertainty Randomness and uncertain judgment is inherent in most real world decision problems We need a method to automate reasoning and decision making under uncertain statements and conditions and method to combining the measures such that reasoning and decision making under uncertainty can be automated Probability theory is the prevailing method for dealing with uncertainty and is the focus of this book Alternative method to probability theory are Belief Theory and Fuzzy Methods

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Normative Expert Systems Earlier the expert system is design to mimic human behavior Today a model of the problem domain is created instead of model of the expert Normative expert systems uses classical probability calculus and decision theory as their basis of reasoning and decision making under uncertainty

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Rule-Based Systems One of the earliest methods of knowledge representation and manipulation was logical rules of the form R1: if s1 then s2 – S2 can be concluded with certainty when s1 is observed R2: if s2 then s3 – S3 can be concluded through forward chaining involving R1 and R2 once s1 is known These rules are asymmetric

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Causality Occurrence of some event c is known to cause the effect e, relationship between c & e is deterministic If c then e, rather then e then c We can conclude that rules like R1 and R2 express causal relationship Rule based system represent the problem domain only up to some precision Smoking → bronchitis → dyspnoea

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Causality Contd. R3: if smoking then bronchitis R4: if bronchitis then dyspnoea R4’: if dyspnoea then bronchitis

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Uncertainty in Rule-Based Systems The vast majority of cause-effect mechanism of interest in our attempts to model parts of the world in the expert systems are uncertain A method of rule-based system with uncertainty was developed in the 1970s Certainty Factor CF [-1,+1] indicates the strength of the conclusion of the rule whenever it’s condition is satisfied

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Explaining Away C1 C2 E1E2 C1 can cause event E1 & E2, and C2 can cause event E2

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Bayesian Networks Due to serious limitations in the rule-based systems with certainty factor as a method for knowledge representation, researchers turned their attention towards probabilistic interpretation of certainty factor, leading to Bayesian Network Bayesian can be defined as acyclic directed graph DAG which defines a factorization of a joint probability distribution over the variables that are represented by nodes of the DAG, factorization is given by directed links of the DAG

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Bayesian Networks Contd. A joint probability distribution over the set of variables can be represented as P(U) = ∏ P(A i | pa(A i )),

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Inference in Bayesian Networks Contrary to rule-base systems, inference in Bayesian network is consistent Efficiency of inference is highly dependent on structure of DAG Posterior Probability distribution P(X|Y=y) – P(X|Y=y) = P(Y=y|X)P(X) P(Y=y)

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Construction of Bayesian Networks Bayesian networks can be describe in terms of a qualitative component consisting of a DAG, and a quantitative component, consisting of joint probability distribution The construction of Bayesian networks runs in two phases – Identification of relevant variables and causal relation among them – The resulting DAG specifies a set of dependent and independent assumptions that will be enforced on joint probability distribution specifying a set of conditional probability distributions

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An Example Fuel Spark-Plugs Fuel-gauge Start?

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