1 / 3

conditional entropy, mutual information

H ( X|Y ). I ( X;Y ). H ( Y|X ). H ( X ). H ( Y ). conditional entropy, mutual information. X and Y are independent. X is determined by Y. H ( X | Y ) = H ( X ) I ( X ; Y ) = 0. H ( X | Y ) = 0 I ( X ; Y ) = H ( X ). example: evolution. [Adami 2002].

christoffer-carus
Download Presentation

conditional entropy, mutual information

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. H(X|Y) I(X;Y) H(Y|X) H(X) H(Y) conditional entropy, mutual information X and Y are independent X is determined by Y H(X|Y) = H(X) I(X;Y) = 0 H(X|Y) = 0 I(X;Y)= H(X)

  2. example: evolution [Adami 2002] • consider information in the genome in the context of information in the environment • same genome in a differentenvironment wouldn’t be as fit • evolution is increasing mutual information • fitter organisms exploittheir environment better,so must contain more info about their env • (total information in a genome can change, as genome changes size, etc) G1 H(G1|E) G2 increasing fitness of genome G in Env E G3 Env E I(G3;E)

  3. example: emergence [Weeks et al 2007] • consider information in the high level description S in the context of information in the low level description E • same high level model in a differentlow level environment wouldn’t be as good • modelling /engineering as increasing mutual information • small H(S|E)  good model / impl • large H(E|S)  redundancy • use I as a fitness functionto search for better models / impls ? increasing fit of model S to Env E S1 S2 S3 H(S1|E) I(S3;E) Env E

More Related