Lecture 38 Wed April 22

Lecture 38 Wed April 22 - CS 485: Mathematical Foundations...

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CS 485: Mathematical Foundations for the Information Age Lecture 38 April 22, 2009 Jeff Davidson (jpd236) and Jeff Pankewicz (jhp36) Approximate Counting Algorithm: Problem – in a data stream, count the number of occurrences of a given symbol. If there are n occurrences, this takes log n bits. We can approximate a solution by storing k where n = 2 k . This only takes log log n bits. The trick is to probabilistically increment k by flipping a coin with probability of heads equal to 1/2 k . Then at any given point, it will take an expected 2 k coin flips to actually increase k (and double the estimation), so the estimate is kept roughly close to the actual value. Hidden Markov Models: 1. A finite state graph with transition probabilities 2. Initial state probability distribution π 3. Transition probabilities a ij 4. Output symbol probability distribution for each state A move consists of two steps: When in a given state, flip a coin to go to another state. Then, flip another coin to select an output according to the probability distribution of that output (this
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Lecture 38 Wed April 22 - CS 485: Mathematical Foundations...

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