1 / 6

Graphical Models and Belief Propagation in Learning Algorithms

Explore the application of graphical models, empirical probabilities, and belief propagation in solving the learning problem through optimization. Maximize likelihood using examples and probabilities to improve model application. Learn about conditional random fields and random variables for efficient processing. Understanding CRF, MRF, and optimization techniques for better learning on GP units.

evat
Download Presentation

Graphical Models and Belief Propagation in Learning Algorithms

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. Graphical Models • The learning problem:max likelihood • Empirical probabilities • Belief propagation • Optimization • Model application • P mass fn • Phi • Beispiel für phi • Likelihood • Optimierung (gradient von emp. – BP) • BP • Max BP macht model application

  2. Given data are subsequences of system calls: 1,open,1812,179,178,201,200,firefox,/etc/hosts,524288,438,7 2,read,1812,179,178,201,200,firefox,/etc/hosts,4096, 361 3,read,1812,179,178,201,200,firefox,/etc/hosts,4096, 0 4,close,1812,179,178,201,200,firefox,/etc/hosts timestamp, syscall, thread-id, process-id,parent, user, group, exec, file, parameters (optional), 361 to 0: file is read completely to end of file zero transition zero transition Full transition state firefox-bin/firefox-bin, cookies.sqlite-journal/default/hosts ?/firefox-bin, ?/?/cookies.sqlite-journal firefox-bin/firefox-bin, ?/cookies.sqlite-journal/default

  3. Graphical ModelsConditional Random Fields • Random variablesX= {X1, …,Xr}Y= {Y1, …, Yl}|Y|= l • dom(Xi)={x1i,…,xki}|Xi|= ki • Parameters: Sequence length: T Node + transition + prior Storage need: d + full examples • X = {exec, file} • Y = {full, read, zero} • |Y| = 3 = l • dom(exec)= {?/firefox, firefox/firefox, …} kexec=20 • dom(file)={?/?/cookies, ?/cookies/default, cookies/default/host,…} kfile= 25 • d=20*3 + 25*3 + 20*9 + 25*9 + 3=60+75+180+225 = 540

  4. Learning on GP Graphics Processing Units: CRF • Read batch of B examples counting frequencies for every instance of state/transition features fk. Create a thread for each class and example, B |Y| threads. Each thread calculates for this fixed x and y the msgsof belief propagation. • Deshalbergibtsich: • Z(x) • p(y,y’|x) • p(y|x) • Lookup frequencies fkand use calculations for fixed x from 1. for updating the model. K threads. • Optimization l(q)=p(y,x). Bthreads.

  5. Markov Random Fields • Each node is one random variable: V={lights, rain, jam} • X = (red,yellow,green) x (dry,wet) x (jam, free) • Examples: x1:(red,dry,free) x2:(yellow,dry,free) x3:(green,dry,free) x4:(yellow,dry,jam) • d = 3+2+2 + 3*2 + 3*2 + 2*2 = 23node states+edges values • Random variablesV= {X1, …,Xn}dom(Xi)={x1i,…,xki}|Xi|= ki X = dom(X1) x dom(X2) x …dom(Xn) • Examples: x in X f: X {0,1}d • Parameters for pairwise MRF: Nodes + Edges {dry, wet} Rain Lights Jam {red,yellow,green} {jam, free}

  6. fNodes, Edges f(x): ( /* Nodes*/ • red, /*dom(lights)*/ • yellow, • green, • wet, /*dom(rain)*/ • dry, • jam, /*dom(jam)*/ • free, /*Edges*/ • red, dry, /* edge lights-rain*/ • yellow, dry, • green, dry, • red, wet, • yellow, wet, • green, wet, • red, jam, /*edge lights-jam*/ • yellow, jam, • green, jam, • red, free, • yellow, free, • green, free, • dry, free, /*edge rain-jam*/ • dry, jam, • wet, free, • wet, jam) ) • x1:(red,dry,free) • f(x1)=(1,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0) • d = 23 Rain {dry, wet} Lights Jam {red,yellow,green} {jam, free}

More Related