hw5 - 10708 Graphical Models: Homework 5 Due November 29th,...

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Unformatted text preview: 10708 Graphical Models: Homework 5 Due November 29th, beginning of class November 16, 2006 Instructions : There are four 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/HW5 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 Gaussian Graphical Models [25 pts] [Khalid] Consider a Gaussian graphical model over three variables x 1 ,x 2 ,x 3 , represented by the fol- lowing multivariate Normal distribution: P ( x 1 ,x 2 ,x 3 ) = 1 (2 π ) 3 / 2 | Σ | 1 / 2 exp- 1 2 ( x- μ ) T Σ- 1 ( x- μ ) where x = ( x 1 x 2 x 3 ) and μ = ( μ 1 μ 2 μ 3 ) are column vectors, and Σ is a 3 × 3 covariance matrix. Let Σ 1 = 2 1 0 1 2 1 0 1 2 , Σ 2 = . 75 0 . 5 0 . 25 . 5 1 . . 5 . 25 0 . 5 0 . 75 (a) Suppose Σ = Σ 1 . Are there any marginal independencies among the components of x ? (b) Suppose Σ = Σ 2 . Are there any marginal independencies among the components of x ? (c) Suppose that the distribution of x can be represented by the Bayes net in Figure 1 with the following parameterization: 1 Figure 1: Structure of Gaussian graphical model....
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This note was uploaded on 05/25/2008 for the course MACHINE LE 10708 taught by Professor Carlosgustin during the Fall '07 term at Carnegie Mellon.

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hw5 - 10708 Graphical Models: Homework 5 Due November 29th,...

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