{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 38 Wed April 22

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

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

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern