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Learning with Bayesian Networks David Heckerman Presented by Colin Rickert Introduction to Bayesian Networks Bayesian networks represent an advanced form of general Bayesian probability A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest1 The model has several advantages for data analysis over rule based decision trees1 Outline Bayesian vs. classical probability methods Advantages of Bayesian techniques The coin toss prediction model from a Bayesian perspective Constructing a Bayesian network with prior knowledge Optimizing a Bayesian network with observed knowledge (data) Exam questions Bayesian vs. the Classical Approach The Bayesian probability of an event x, represents the person’s degree of belief or confidence in that event’s occurrence based on prior and observed facts. Classical probability refers to the true or actual probability of the event and is not concerned with observed behavior. Bayesian vs. the Classical Approach Bayesian approach restricts its prediction to the next (N+1) occurrence of an event given the observed previous (N) events. Classical approach is to predict likelihood of any given event regardless of the number of occurrences. Example Imagine a coin with irregular surfaces such that the probability of landing heads or tails is not equal. Classical approach would be to analyze the surfaces to create a physical model of how the coin is likely to land on any given throw. Bayesian approach simply restricts attention to predicting the next toss based on previous tosses. Advantages of Bayesian Techniques Handling of Incomplete Data Imagine a data sample where two attribute values are strongly anti-correlated With decision trees both values must be present to avoid confusing the learning model Bayesian networks need only one of the values to be present and can infer the absence of the other: Imagine two variables, one for gun-owner and the other for peace activist. Data should in