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Unformatted text preview: Computational functional genomics (Spring 2005: Lecture 10) David K. Gifford (Adapted from a lecture by Tommi S. Jaakkola) MIT CSAIL Topics Basic classification approaches decisions estimation variable selection Examples More advanced methods Classification We can divide the large variety of classification approaches into roughly two main types 1. Generative build a generative statistical model e.g., mixture model 2. Discriminative directly estimate a decision rule/boundary e.g., logistic regression Generative approach to classification A mixture of two Gaussians, one Gaussian per class choice of class P ( class = 1) P ( class = 0) X N ( 1 , 1 ) X N ( , ) where X corresponds to, e.g., a tissue sample (expression levels across the genes). Three basic problems we need to address: 1. decisions 2. estimation 3. variable selection Mixture classifier contd Examples X (tissue samples) are classified on the basis of which Gaussian better explains the new sample (cf. likelihood ratio test) log P ( X  1 , 1 ) P ( class = 1) > class = 1 (1) P ( X  , ) P ( class = 0) class = (2) where the prior class probabilities P ( class ) bias our decisions to wards one class or the other. Decision boundary log P ( X  1 , 1 ) P ( class = 1) = (3) P ( X  , ) P ( class = 0) Mixture classifier: decision boundary Equal covariances X N ( 1 , ) , class = 1 (4) X N ( , ) , class = (5) The decision rule is linear Mixture...
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This note was uploaded on 11/11/2011 for the course BIO 7.344 taught by Professor Bobsauer during the Spring '08 term at MIT.
 Spring '08
 BobSauer
 Genomics

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