Probabilistic Graphical Models, Spring 2015

[cwyoo]

Class related materials, discussions, Q&A will be posted here.

[cwyoo]

Syllabus of the course. This will be the syllabus of the independent study if this course get canceled.

[cwyoo]

Explain using Bayes' theorem the following fact:

One prisoner will be executed tomorrow among the three prisoners X, Y, and Z and only a sincere guard G knows who will be executed. Prisoner X knows that

P(X) = 1/3 given that X represents "X will be executed tomorrow".

Prisoner X asks the guard G whether he can tell him who will not be executed between Y and Z. The guard thinks about the request and concludes that he is not revealing the most crucial information and tells X, "Y will not be executed". However, after hearing this, X thinks now his probability to being executed tomorrow just increased from 1/3 to 1/2, since only one will be executed between X and Z.

Who is correct, the guard or X? Find it out by calculating P(X|G=not Y) where G=not Y represent "G tells X, Y will not be executed".

[meninonas]

Dr. Yoo,

Please find the d-connectivity applet below:

http://www.phil.cmu.edu/~wimberly/dsep/dSep.html

[qja0428]

There is another way to construct a Bayesian Network, using the SAMIAM software package to design. You can find the program and more information at this website:

http://reasoning.cs.ucla.edu/samiam/index.php

The SAMIAM program can be found on the course website. There are separate files for each operating system (Linux, Windows, and Mac), so just use whichever is appropriate for the machine you are on. SAMIAM relies on Java, so if you do not already have a Java runtime installed on your machine (or you receive errors that no java executable is found, or the program does not start), you should download one from:

http://java.com/en/download/manual.jsp

When constructing your network, you will be using Edit Mode to add edges to your network. To engage Edit Mode, go to the Mode menu and simply select Edit Mode; if the option is greyed out, SAMIAM is already in this mode. To add an edge, go to Edit, Add Edge, click on whichever node you want to be the parent, and then click on the node you want to be the child. To change the node’s properties, double click on it. You should only change the CPDs for the nodes; all other properties should be left the same, as changing any of the other properties will cause problems with the automatic grading system. You can edit the CPD for the selected node by clicking on the Probabilities tab, double clicking on any of the values, and simply inputting your own value. Remember that you should edit the CPD for the
child node whenever you add an edge. You may wish to use Query Mode to monitor the marginals of nodes in this network. Go to the Mode menu and select Query Mode. On the left you should have a list of nodes. Clicking on one will reveal the values that node can take on. Clicking one of these values will assign it to have that observed value. Clicking again will free the node to be unobserved. To view a node’s marginal, right click and select Monitor. You can
also display all marginals by going to the Query menu, then Show monitors, and selecting Show All.

[cwyoo]

Please read the article titled Micro-Macro Analysis of Complex Networks (2015) that is posted under Theory and Concepts > Graph Theory.