L09_-_MCMC

Q ok how many steps sufce to be close to uniform top

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Unformatted text preview: central page and do random walk for sufficiently many steps; –  Restart and repeat sufficiently many times; –  then take PageRank(w) ≈ empirical frequency that random walk ended at w. •  Hope that empirical distribution is good approximation to stationary distribution for the right choice of “sufficiently many” above… •  or at least for the top components of the stationary distribution, which are the most important for ranking the top results. Menu •  Random walks on graphs •  Markov Chains •  Examples: –  pagerank –  card-shuffling –  colorings Card Shuffling Q: Why shuffle the deck? A: well, to start from a uniformly random permutation of the cards Q2: How many permutations are there? A: 52! ≈ 2257 ≈ 1077 – how large is that? Q3: Getting a random permutation? -  soln1: dice 1077 faces - soln2: shuffle ≈ dice Example Shuffles: -  top-in-at-random -  riffle-shuffle Shuffling as a Markov Chain Graph: - one node per permutation of the deck. … … - edge (u,v): v is reachable in one move from u (specific to shuffle) While performing the shuff...
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