Estimate Conditional Probabilities for Continuous Attributes (Additional Notes) ο Notes: 1 π ππ π = π¦π = 2ππππ2 π ππ βπππ β 2 2πππ 2 Probability density function ο The probability density function is continuous, the P(y|x) probability that the random variable Xi takes a particular value xi is zero. 1 xk x Estimate Conditional Probabilities for Continuous Attributes (Additional Notes) ο Instead, we should compute π₯π +π π π₯π β€ ππ β€ π₯π + π π = π¦π = οΏ½ P(y|x) π₯π xk xk+Ξ΅ x β 1 2ππππ2 1 2ππππ2 π π ππ βπππ β 2 2πππ ππ βπππ β 2 2πππ 2 2 πππ ×π ο Since Ι appears as a constant multiplicative factor for each class, it cancels out when normalizing the posterior probability for P(Y|X). 2 Estimate Conditional Probabilities for Continuous Attributes (Additional Notes) ο Therefore, we can still apply the following equation to approximate the class-conditional probability, π ππ = π₯π |π = π¦π π ππ = π₯π π = π¦π = 3 1 2ππππ2 π π₯π βπππ β 2 2πππ 2
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