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Probability Theory Review for Machine Learning

Probability Theory Review for Machine LearningSamuel IeongNovember 6, 20061 Basic ConceptsBroadly speaking, Probability Theory is the mathematical study of uncertainty. It plays acentral role in Machine Learning , as the design of Learning algorithms often relies on proba-bilistic assumption of the data. This set of notes attempts to cover some basic probabilitytheory that serves as a background for the Probability SpaceWhen we speak about Probability , we often refer to the Probability of aneventof uncertainnature taking place. For example, we speak about the Probability of rain next , in order to discuss Probability Theory formally, we must first clarify what thepossible events are to which we would like to attach , aprobability spaceis defined by the triple ( ,F, P), where is thespace of possible outcomes(oroutcome space), F 2 (the power set of ) is thespace of (measurable) events(orevent space), Pis theprobability measure(orprobability distribution) that maps an

Probability Theory Review for Machine Learning Samuel Ieong November 6, 2006 1 Basic Concepts Broadly speaking, probability theory is the mathematical study of uncertainty. It plays a central role in machine learning, as the design of learning algorithms often relies on proba-

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