"Graphical models" and "gene finding and diagnosis of diseases" ? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T00:36:05Z http://mathoverflow.net/feeds/question/94931 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/94931/graphical-models-and-gene-finding-and-diagnosis-of-diseases "Graphical models" and "gene finding and diagnosis of diseases" ? Alexander Chervov 2012-04-23T12:13:53Z 2012-04-23T15:14:26Z <p><a href="http://en.wikipedia.org/wiki/Graphical_model#Applications" rel="nofollow">Quote Wikipedia</a>: Applications of <a href="http://en.wikipedia.org/wiki/Graphical_model" rel="nofollow">graphical models</a> include ... gene finding and diagnosis of diseases...</p> <p>Unfortunately there is no comment what are these applications... Can one comment on this ?</p> <p><strong>Background</strong></p> <p>A <a href="http://en.wikipedia.org/wiki/Graphical_model" rel="nofollow">graphical models</a> is a probabilistic model for which a graph denotes the conditional independence structure between random variables. </p> <p>The so-called <a href="http://en.wikipedia.org/wiki/Belief_propagation" rel="nofollow">belief propagation</a> is an algorithm for calculations of various probabilities in graphical models. It is used for decoding of error-correcting codes, calculations of free-energy for Ising type model etc. See e.g. the answer to this question: <a href="http://mathoverflow.net/questions/93765/correlation-function-for-random-graph-ising-model" rel="nofollow">http://mathoverflow.net/questions/93765/correlation-function-for-random-graph-ising-model</a></p> http://mathoverflow.net/questions/94931/graphical-models-and-gene-finding-and-diagnosis-of-diseases/94936#94936 Answer by Felix Goldberg for "Graphical models" and "gene finding and diagnosis of diseases" ? Felix Goldberg 2012-04-23T12:36:10Z 2012-04-23T12:36:10Z <p>Do you mean something like this?</p> <p><a href="http://www-devel.cs.ubc.ca/~murphyk/Papers/ismb99.pdf" rel="nofollow">http://www-devel.cs.ubc.ca/~murphyk/Papers/ismb99.pdf</a></p> http://mathoverflow.net/questions/94931/graphical-models-and-gene-finding-and-diagnosis-of-diseases/94950#94950 Answer by Noah Stein for "Graphical models" and "gene finding and diagnosis of diseases" ? Noah Stein 2012-04-23T14:48:05Z 2012-04-23T14:48:05Z <p>Wikipedia is likely referring to examples like the one in <a href="http://mitpress.mit.edu/books/chapters/0262013193chap1.pdf" rel="nofollow">the introduction</a> to Koller and Friedman's book. In such examples one forms a directed graphical model with variables for underlying causes of diseases, variables for diseases themselves, and variables for symptoms. These are connected based on which causes could lead to which diseases and which diseases lead to which symptoms, using known data on the conditional probabilities involved. One then takes symptoms as given and, conditioned on these, infers the states of the hidden disease variables.</p> http://mathoverflow.net/questions/94931/graphical-models-and-gene-finding-and-diagnosis-of-diseases/94955#94955 Answer by Joseph O'Rourke for "Graphical models" and "gene finding and diagnosis of diseases" ? Joseph O'Rourke 2012-04-23T15:14:26Z 2012-04-23T15:14:26Z <p>This supplements Noah Stein's answer. Judea Pearl has written extensively on causal models, both in his book <em><a href="http://bayes.cs.ucla.edu/BOOK-2K/" rel="nofollow">Causality</a></em>, and in individual papers, such as "Causal Diagrams for Empirical Research," <em>Biometrika</em>, 82(4), 669-710, 1995, from which this figure is taken: <br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="http://cs.smith.edu/~orourke/MathOverflow/PearlFig1.jpg" alt="Fig1"></p>