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Sequences II

Sequences II. Prof. Noah Snavely CS1114 http://cs1114.cs.cornell.edu. Administrivia. Assignments: A5P2 due on Friday Quiz Tuesday, 4/24 Final project proposals due on CMS by this Thursday. Google’s PageRank. H. Start at a random page, take a random walk. Where do we end up?. A. E. I.

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Sequences II

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  1. Sequences II Prof. Noah Snavely CS1114 http://cs1114.cs.cornell.edu

  2. Administrivia • Assignments: • A5P2 due on Friday • Quiz Tuesday, 4/24 • Final project proposals due on CMS by this Thursday

  3. Google’s PageRank H Start at a random page, take a random walk. Where do we end up? A E I D B C F J G

  4. Google’s PageRank H Add 15% probability of moving to a random page. Now where do we end up? A E I D B C F J G

  5. Google’s PageRank H PageRank(P) = Probability that a long random walk ends at node P A E I D B C F J G

  6. Example (The ranks are an eigenvector of the transition matrix)

  7. Modeling Texture • What is texture? • An image obeying some statistical properties • Similar structures repeated over and over again • Often has some degree of randomness

  8. A D X B C • Higher order MRF’s have larger neighborhoods * * * * * * * * X * * * X * * * * * * * * * Markov Random Field • A Markov random field (MRF) • generalization of Markov chains to two or more dimensions. • First-order MRF: • probability that pixel X takes a certain value given the values of neighbors A, B, C, and D:

  9. Texture Synthesis [Efros & Leung, ICCV 99] • Can apply 2D version of text synthesis

  10. More Synthesis Results • Increasing window size

  11. More Results • aluminum wire • reptile skin

  12. Image-Based Text Synthesis

  13. Author recognition • Simple problem: Given two Markov chains, say Austen (A) and Dickens (D), and a string s (with n words), how do we decide whether A or D wrote s? • Idea: For both A and D, compute the probability that a random walk of length n generates s

  14. Probability of a sequence • What is the probability of a given n-lengthsequence s? s = s1 s2 s3 … sn • Probability of generating s = the product of transition probabilities: Probability that a sequence starts with s1 Transition probabilities

  15. Likelihood • Compute this probability for A and D Jane Austen wrote s “likelihood” of A Charles Dickens wrote s “likelihood” of D ???

  16. Problems with likelihood • Most strings of text (of significant length) have probability zero • Why? • Even if it’s not zero, it’s probably extremely small • What’s 0.01 * 0.01 * 0.01 * … (x200) … * 0.01? • According to Matlab, zero • How can we fix these problems?

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