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

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Presentation transcript:

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

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

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

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

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

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

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

Markov Random Field A Markov random field (MRF) First-order 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: D C X A B X * Higher order MRF’s have larger neighborhoods

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

More Synthesis Results Increasing window size

More Results reptile skin aluminum wire

Image-Based Text Synthesis

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

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

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

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?