CSCI B 609 Foundations of Data Science Lecture
CSCI B 609: “Foundations of Data Science” Lecture 1: Intro Slides at http: //grigory. us/data-science-class. html Grigory Yaroslavtsev http: //grigory. us
Disclaimers • A lot of Math!
Disclaimers • No programming!
Class info • • Advanced graduate class, not an intro-level class Primary audience: Ph. D. students MW 16: 00 – 17: 15, THA 201 Grading: – Class attendance/participation (20%) – Homework assignments (40%) • Only accepted via e-mail in La. Te. X-generated PDF format • No handwritten homework accepted – Project (40%) • Text: Blum-Hopcroft-Kannan, “Foundations of Data Science” – http: //grigory. us/files/bhk-book. pdf – 06/09/16 version • Office hours announced later • Slides & videos will be posted
Plan for today • Today’s lecture: – Basic probability – Inequalities for random variables – Concentration bounds
Expectation •
Expectation •
Variance •
Variance •
Independence •
Conditional Probabilities •
Union Bound •
Independence and Linearity of Expectation/Variance •
Part 2: Inequalities • Markov inequality • Chebyshev inequality • Chernoff bound
Markov’s Inequality •
Markov’s Inequality •
Markov Inequality: Example •
Markov Inequality: Example •
Chebyshev’s Inequality •
Chebyshev’s Inequality •
Chebyshev: Example •
Chebyshev: Example •
Chebyshev: Example •
Chernoff bound •
Chernoff bound (corollary) •
Chernoff: Example •
Chernoff: Example •
Chernoff v. s Chebyshev: Example •
Chernoff v. s Chebyshev: Example •
- Slides: 29