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Conditional independence, Nave Bayes and Bayesian Networks Jo - PowerPoint PPT Presentation

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Fundamentals of AI Introduction and the most basic concepts Conditional independence, Nave Bayes and Bayesian Networks Jo Joint Probability Distribution Banana -shaped probability distribution Probability of any combination of

  1. Fundamentals of AI Introduction and the most basic concepts Conditional independence, Naïve Bayes and Bayesian Networks

  2. Jo Joint Probability Distribution ‘Banana -shaped probability distribution’ • Probability of any combination of features to happen Conditional Probability Bayes rule Probability density function (PDF)

  3. Event M The story of Andrew (Moore) and Manuela True False Event S True False

  7. Most probable 0.18 0.42 0.12 0.28

  8. Event M False True Event S False True Event L False True

  12. Event R True False

  31. Example from real-life

  32. Example from real-life

  33. Example from real-life

  34. Now, what is naïve Bayesian assumption ? • In simple words, it assumes that all variables (or a set of variables) are all conditionally independent : the Bayesian net is not connected • Or, we have an unconnected Bayesian net connected to a single node x,y,z,t are conditionally independent given C C This construction can be used to predict C from x,y,z,t values: this is Naïve Bayes classifier x y z t

  35. What you should take with you • Conditional independence of evens given other events • Bayesian networks: convenient graphical way to represent known causalities and compute joint probability distribution • Naïve Bayesian assumption is the simplest case: we assume that a set of variables is conditionally independent

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