1 4 using the intuition in part 33 design a dynamic

Info icon This preview shows pages 3–5. Sign up to view the full content.

View Full Document Right Arrow Icon
described in part 3.1. 4. Using the intuition in part 3.3, design a dynamic programming algorithm (caching partial results) which computes P ( X i , X j ) for all n choose 2 choices of i and j in time asymptotically much lower than the complexity you described in part 3.2. What is the asymptotic running time of your algorithm? 4 Belief Propagation Two graduate students in University of Tehran have gotten into an argument over the weather. One thinks summer is over and Autumn has already come, while the other thinks it is still summer. In Tehran, there are four seasons – Spring (S), Summer (M), Autumn (A), and Winter (W). Given the season the previous day, the season on a day is conditionally 3
Image of page 3

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

View Full Document Right Arrow Icon
independent of the season on all previous days. The weather is either Hot (H), Rainy (R) or Freezing (F). Given the season on any given day, the weather that day is independent of all other variables. More formally, if we let C i denote the season on the i–th day (taking values S, M, A, W) and O i denote the observed weather pattern (one of H, R, F). We have j < i - 1 , C i C j | C i - 1 and X, O i X | C i where X is any random variable other than C i , O i . 1. Draw a graphical model over C 1 . . . C N , O 1 . . . O N that satisfies the conditional inde- pendencies listed above. 2. Implement sum-product and max-product algorithms in MATLAB for this graphical model. 3. We has made 20 observation of the weather over the last few months (i.e., O 1 . . . O N ) : { R, F, F, H, F, H, H, H, H, H, H, H, H, R, H, H, H, R, H, H } Some of the values for the conditional probability table (CPT) are as follows.
Image of page 4
Image of page 5
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