{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 38 Wed April 22

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

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
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