ECS124_Lecture13 - ECS 124 Theory and Practice of Bioinformatics Lecture 13 Biological Networks Instructor Ilias Tagkopoulos [email protected]

ECS124_Lecture13 - ECS 124 Theory and Practice of...

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Unformatted text preview: ecture 13 : Biological Networks ECS 124 Theory and Practice of Bioinformatics Lecture 13 : Biological Networks Instructor: Ilias Tagkopoulos [email protected] Office: Kemper 3063 and GBSF 5313 5/18/2010 1 UC Davis LAST TIME: Bayes Theorem Posterior Likelihood Prior Evidence = x 5/18/2010 UC Davis 2 g G ¡¢£¤¤ | ¥¦£§¨©¦ ª = g G ¥¦£§¨©¦ | ¡¢£¤¤ª ∙ gG¡¢£¤¤ª gG¥¦£§¨©¦ª LAST TIME: Bayes Discriminant Function c Put new sample in Class 1 if for its feature X we have : g G ¡¢£¤¥¦¢ § | gG¡¢¢£) ∙ ¤ ¥ gG¡¢¢£ ) > ¤ ¥ ¦§¡¨©ª§ « | gG¡¢¢¬) ∙ ¤¥gG¡¢¢¬) 5/18/2010 UC Davis 3 c Or equivalently if G(X)>0, where G(X) is ­ ¥ « ) = G®¯ ¤ ¥ ¦§¡¨©ª§ « | gG¡¢¢£) ∙ ¤¥gG¡¢¢£) ¤ ¥ ¦§¡¨©ª§ « | gG¡¢¢¬) ∙ ¤¥gG¡¢¢¬) LAST TIME: Assumption of independence in naïve bayes c Assume all features are INDEPENDEND c Then our class conditional probability becomes: gG¡¢£¤¥¦¢ § ¨ , ¡¢£¤¥¦¢ § © , … ¡¢£¤¥¦¢ § ª |gG¡¢¢£) = ¤¥¦§¡¨©ª§ « £ |gG¡¢¢£) ¤¥¦§¡¨©ª§ « ¬ |gG¡¢¢£)… ¤¥¦§¡¨©ª§ « ­ |gG¡¢¢£) 5/18/2010 UC Davis 4 c And our discriminant function becomes: = ®¤¥¦§¡¨©ª§ « ¯ |gG¡¢¢£) °¥« £ ,…,« ­ ) = G±² ∏¤¥¦§¡¨©ª§ « ¯ |gG¡¢¢£) ∙ ¤¥gG¡¢¢£) ∏¤¥¦§¡¨©ª§ « ¯ |gG¡¢¢¬) ∙ ¤¥gG¡¢¢¬) Bayesian classification: an example c Some proteins are more expressed in cancerous vs. healthy tissues and thus they can be used as features to classify patients c Assume two classes/categories/labels: lass 1: Cancer 5/18/2010 UC Davis 5 c Class 1: Cancer c Class 2: Healthy c...
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