1 / 4

Mixture models: datapoint has nonzero probs to belong to multiple k distributions

EM. Mixture models: datapoint has nonzero probs to belong to multiple k distributions So Hidden Var in each datapoint: e.g for k=2 <x i z i1 z i2 > hypothesis h about parameters of ,say, k Gaussians. Estimate posterior : E (P(D|h’) | x, h) Maximize : argmax E(P(D|h’)|x, h)

nasya
Download Presentation

Mixture models: datapoint has nonzero probs to belong to multiple k distributions

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. EM • Mixture models: datapoint has nonzero probs to belong to multiple k distributions • So Hidden Var in each datapoint: e.g for k=2 <xi zi1 zi2> • hypothesis h about parameters of ,say, k Gaussians. • Estimateposterior: E (P(D|h’) | x, h) • Maximize : argmax E(P(D|h’)|x, h) • Result: priors on distribution, mean and variance binary membership var, hidden Analytical for multivariate normal distr

  2. VQ • vector quantization • map a set of M coding vectors (red) to a cloud of N data points (not shown) : Q(xi)=cj • ..using neighboring relations (Euclidian distance) • http://www.data-compression.com/vq.html

  3. SOM • M “neurons”= M coding vectors (cfr. VQ) • But.. neurons are CONNECTED, so they form an “elastic net”. • Elasticity or mutual influence determined by a kernel function that is defined on a 2D grid • the coding vectors and their “projection (visualization)” on the 2D grid constitute the SOM

  4. Useful Code • sDpima = som_read_data('d:\\patrick\\projects\\oefn_johan\\PIMADATAsorted2.txt'); • sDpima=som_normalize(sDpima, 'var') • sMap=som_make(…) • sMap=som_autolabel(sMap, sDpima, 'vote') • som_show(sMap,'norm','d') % basic visualization • som_show(sMap,'umat','all','empty','Labels') % UMatrix • som_show_add('label',sMap,'Textsize',8,'TextColor','r','Subplot',2) %labels • SORT DATASET (file) according to labels with e.g. spreadsheet program • % h1 = som_hits(sMap,sDpima.data(1:500,:));  -1’s • % h2 = som_hits(sMap,sDpima.data(501:768,:));  +1’s • % som_show_add('hit',[h1, h2],'MarkerColor',[1 0 0; 0 1 0],'Subplot',1)

More Related