hw4 - 10708 Graphical Models Homework 4 Due November 15th...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
10708 Graphical Models: Homework 4 Due November 15th, beginning of class October 27, 2006 Instructions : There are six questions on this assignment. Each question has the name of one of the TAs beside it, to whom you should direct any inquiries regarding the question. The last problem involves coding. Do not attach your code to the writeup. Instead, copy your implementation to /afs/andrew.cmu.edu/course/10/708/your_andrew_id/HW4 Refer to the web page for policies regarding collaboration, due dates, and extensions. Note : Please put your name and Andrew ID on the first page of your writeup. 1 Markov Network Representations [5 pts] [Khalid] Figure 1 is a Markov Random Field where the potentials are defined on all cliques of three variables. A B C D 1 1 8 1 1 22 1 0 14 0 1 1 12 0 1 0 0 1 1 7 0 0 1 1 0 1 0 5 0 15 0 0 Ψ (A,B,C) C B A 1 1 1 1 1 2 1 0 15 0 1 1 13 0 1 0 0 1 1 11 0 0 9 1 0 1 0 3 0 6 0 0 Ψ (B,C,D) D C B Figure 1: A chordal (triangulated) Markov network (a) Convert the triangle graph on ( A, B, C ) with potential Ψ( A, B, C ) into a pairwise Markov Random Field by introducing a new variable X. Show the graph, as well as the node and edge potentials in table form ( i.e. , compute the values of the potentials in the pairwise MRF) 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
(b) Convert the graph on ( A, B, C, D ) with potentials Ψ( A, B, C ) and Ψ( B, C, D ) into a pairwise Markov Random Field. Is the graph chordal ? ( Note : You do not have to compute the pairwise MRF potentials in your solution). 2 Hammersley-Clifford [10 pts] [Ajit] Complete the analysis of Example 5.4.3 (Koller & Friedman, pg 199), showing that the distribution P defined in the example does not factorize over H . ( Hint : Use a proof by contradiction). 3 Importance Sampling [20 pts] [Khalid] To do this question you need to read (Koller & Friedman, 10.2.2). The likelihood weighting of an importance sampler is defined as w ( x ) = P ( x ) /Q ( x ) where P is the distribution we want to sample from and Q is a proposal distribution. (a) Why is computing the probability of a complete instantiation of the variables in a Markov Random Field computationally intractable ? Your answer should be brief.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern