Andrew W. Moore Probability Densities: Slide 3 Why we should care •Real Numbers occur in at least 50% of database records •Can’t always quantize them •So … … to understand how to describe where they come from•A great way of saying what’s a reasonable range of values•A great way of saying how multiple attributes should reasonably co-occur Copyright © 2001, Andrew W. Moore Probability Densities: Slide 4 Why we should care•Can immediately get us Bayes Classifiers that are sensible with real- …

Probability Densities in Data Mining •Why we should care •Notation and Fundamentals of continuous PDFs •Multivariate continuous PDFs •Combining continuous and discrete random variables hy we should care •Real Numbers occur in at least 50% of database records •Can’t always quantize them •So need to understand how to describe where they come from •A great way of saying what’s a reasonable range of values •A great way of saying how multiple attributes should reasonably co-occur Why we should care •Can immediately get us Bayes Classifiers that are sensible with real-valued data •You’ll need to intimately understand PDFs in order to do kernel methods, clustering with Mixture Models, analysis of variance, time series and many other things •Will introduce us to linear and non-linear regression A PDF of American Ages in 2000 Let X be a continuous random variable. If p(x) is a Probability Density Function for X then… ( ) ? = = ? < b a x dx x p b X a P ) ( ( ) ? = = ? < 50 30 age age ) age ( 50 Age 30 d p P = 0.36 Properties of PDFs That means… h h x X h x P x p ? ? ? ? ? ? + ? < - = ? 2 2 ) ( lim 0 h ( ) ? = = ? < b a x dx x p b X a P ) ( ( ) ) ( x p x X P x = ? ? ?….

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