CS 177: Applications of Probability in Computer Science

Instructor: Professor Charless Fowlkes
Lectures: MWF, 2:00 to 2:50, 1300 DBH
Office Hours: Monday, 3:00 to 4:00, 4076 DBH
Course Code: 34360

TA: Nathan Sutter (TA Web page)
Discussion Section: Friday 1:00 to 1:50 in DBH 1300
TA Office Hours:Tuesday, 3:00 to 4:00, DBH 4059

In this course students will build on the basic probability concepts learned in Math 67 and learn how these ideas can be applied to a broad range of problems in modern computer science. The methods and models used will be mathematical in nature, but will be illustrated using real-world applications. Among the application areas that we will discuss are modeling of text and Web data, network traffic modeling, probabilistic analysis of algorithms and graphs, reliability modeling, simulation algorithms, data mining, and speech recognition. The mathematical methods that we will use to analyze these applications will include basic principles of probability such as Bayes rule, conditional probability, random variables, expectation, and Markov chains.

Note that Mathematics 67, Introduction to Probability and Statistics for Computer Scientists, is a prerequisite for this class.

The required text is Probability, Statistics, and Stochastic Processes, by Peter Olofsson, John Wiley and Sons, 2005, which is in stock at the bookstore. ISBN 0471679690.

• Week 1 : [3/31] Review of basic concepts in probability, random variables, expectation of a random variable, examples and applications.
  
  
  • Homework 1: due Wed, April 9th
  
  
  • MATLAB code for Homework 1
  • MATLAB access and tutorials
  • An interesting paper from researchers at Google about modeling the probability of disk failures.
  
  
• Week 2 : [4/6] Multiple random variables, joint distributions (for discrete random variables), factorization, law of total probability, conditional probability, Bayes rule.
  
  
  • Homework 2: due Wed, April 16th
  
  
  • MATLAB code and data for Homework 2
  • A short tutorial paper on Power-law distributions
  • research paper on Power Laws and related ideas
  • Scale-free networks (and how they relate to power-laws)
    
    
• Week 3 : [4/13] Independence and conditional independence. Applications to data mining and text classification, including discussion of classifying spam emails.
  
  
  • Homework 3 due electronically, Wed, April 23rd
  • Data files for Homework 3
  
  
  • Galton's paradox, as described by Sir Francis Galton in 1894
  • Two useful articles on building a spam email detector using Bayes rule: A plan for spam and Better Bayesian filtering
• Research papers from the 2007 Conference on Email and Anti-Spam
  
  
• Week 4 : [4/21] Entropy and Coding, basic principles of Markov Chains and examples.
  
  
  • Homework 4 due in class, Wed, April 30th
  
  
  • Prediction and Entropy of Printed English, Claude Shannon, 1950
  
  
  
• Week 5: [4/28] Mid-term recap
  
  
  • Sample midterm questions
  • Solutions to sample midterm questions
    
  • In class midterm exam on Wednesday 4/30/08
  • No class on Friday 5/2/08
  
  
• Week 6: [5/5] Markov Chains (continued), stationary distributions, applications to ranking of Web pages.
  
  
  • Homework 5 due electronically, Wed, May 14th
  
  
  
• Week 7: [5/12] Continuous random variables: uniform, Gaussian/Normal. Central Limit Theorem.
  
  
  • Homework 6 due Wed, May 21st
  
  
  
• Week 8: [5/19]The exponential model, memoryless waiting times, and the Poisson process.
  
  
  • Homework 7 due Wed, May 28th
  • disk failure data used for homework 7
  
  
  
• Week 9: [5/26] Introduction to Queueing Theory: analysis of a simple M/M/1 queueing model.
  
  
  • No class on Memorial day, 5/26/08
  • Homework 8
  
  
  
• Week 10: [6/2] Simulation Techniques: pseudorandom number generators, algorithms and methods for generating non-uniform random variates. Applications of Monte Carlo simulation methods.
  • An interesting paper [pdf] on linear congruential random number generation
  • Sample questions for the final exam
  • Note that the final will be Wednesday, June 11 from 10:30-12:30pm
    
    

The grading for this class will be based on:
30% for the N-1 best out of N homeworks (your lowest homework score will be dropped)
30% for the midterm exam
40% for the final exam

There will be approximately 8 homeworks during the quarter. Each homework due by the end of class on the due date. Late homeworks will not be graded so please just hand in whatever you have completed by the end the class that it is due.  The lowest homework score for each student for the quarter will not be counted. Solutions will be provided after homeworks have been graded each week. 

You will be required to use MATLAB for some of your homework problems. MATLAB is available on about 34 machines in the CS 364 lab - the machines are in 3 rows front of the lab assistant's desk and to the left of this desk as you face away from it. Nathan will be providing a tutorial on how to use MATLAB in the first discussion session.

For questions relating to homeworks and grading please email the TA Nathan directly with your questions. If Nathan cannot answer your question, he will pass it along to Professor Fowlkes. For other more general questions about the class, please email Professor Fowlkes directly.

In all emails about this class, please start the subject line with "[cs 177]....." so that we can easily keep track of class-related emails.

We will try to respond to emails as quickly as is practical, but there may occasionally be a delay of a day or so, especially on the weekends.

You are asked to be respectful of your student colleagues and instructor in class, not being disruptive or otherwise distracting others in the classroom. This includes turning off cell-phones and not using your laptops during class.

Academic honesty is taken seriously. For homework problems or programming assignments you are allowed to discuss the problems or assignments verbally with other class members, but under no circumstances can you look at or copy anyone else's written solutions or code relating to homework problems or programming assignments. All problem solutions submitted must be material you have personally written during this quarter. Failure to adhere to this policy can result in a student receiving a failing grade in the class. It is the responsibility of each student to be familiar with UCI's current academic honesty policies. Please take the time to read the current UCI Senate Academic Honesty Policies (in Spring Schedule of Classes, a few pages from the end). Also you may want to look at the ICS Department's policies on academic honesty .

CS 177: Applications of Probability in Computer Science (4). Application of probability to real-world problems in computer science. Typical topics include analysis of algorithms and graphs, probabilistic language models, network traffic modeling, data compression, and reliability modeling. Prerequisites: Math 2A-B and 67; either ICS 6A or Math 6B; Math 6D and either Math 3A or 6C