$\DeclareMathOperator{\p}{Pr}$ $\DeclareMathOperator{\P}{Pr}$ $\DeclareMathOperator{\c}{^C}$ $\DeclareMathOperator{\or}{ or}$ $\DeclareMathOperator{\and}{ and}$ $\DeclareMathOperator{\var}{Var}$ $\DeclareMathOperator{\E}{E}$ $\DeclareMathOperator{\std}{Std}$ $\DeclareMathOperator{\Ber}{Bern}$ $\DeclareMathOperator{\Bin}{Bin}$ $\DeclareMathOperator{\Poi}{Poi}$ $\DeclareMathOperator{\Uni}{Uni}$ $\DeclareMathOperator{\Exp}{Exp}$ $\DeclareMathOperator{\N}{N}$ $\DeclareMathOperator{\R}{\mathbb{R}}$ $\newcommand{\d}{\, d}$

Schedule

The class starts by providing a fundamental grounding in combinatorics, and then quickly moves into the basics of probability theory. We will then cover many essential concepts in probability theory, including particular probability distributions, properties of probabilities, and mathematical tools for analyzing probabilities. Finally, the last third of the class will focus on data analysis and Machine Learning as a means for seeing direct applications of probability in this exciting and quickly growing subfield of computer science.

Overview of Topics


Counting Theory

Core Probability

Random Variables

Probabilistic Models

Uncertainty Theory

Machine Learning

Lecture Plan

Lecture content is subject to change by the management at any time.

1
# Weekday Date Topic Notes
Week 1
3
1 Monday Sept 20 Counting
4
2 Wednesday Sept 22 Combinatorics PSet 1 out
5
3 Friday Sept 24 What is Probability?
Week 2
7
4 Monday Sept 27 Conditional Probability and Bayes
8
5 Wednesday Sept 29 Independence
9
6 Friday Oct 1 Random Variables and Expectation PSet 1 in / PSet 2 out
Week 3
11
7 Monday Oct 4 Variance Bernoulli Binomial
12
8 Wednesday Oct 6 Poisson
13
9 Friday Oct 8 Continuous Random Variables
Week 4
15
10 Monday Oct 11 Normal Distribution PSet 2 in / PSet 3 out
16
11 Wednesday Oct 13 Joint Distributions
17
12 Friday Oct 15 Continuous Joint
Week 5
19
13 Monday Oct 18 Inference
14 Wednesday Oct 20 Modelling
15 Friday Oct 22 General Inference PSet 3 in
Week 6
16 Monday Oct 25 No Class
- Tuesday Oct 26 Midterm Midterm: 7 - 9pm
17 Wednesday Oct 27 Mixture Models PSet 4 out
18 Friday Oct 29 Central Limit Theorem
Week 7
19 Monday Nov 1 Great Expectations
20 Wednesday Nov 3 Bootstraping and P-Values
21 Friday Nov 5 Beta Distributions PSet 4 in / PSet 5 out
Week 8
22 Monday Nov 8 M.L.E.
23 Wednesday Nov 10 M.A.P.
24 Friday Nov 12 Naive Bayes
Withdraw deadline
Week 9
25 Monday Nov 15 Ethics in Machine Learning PSet 5 in / PSet 6 out
26 Wednesday Nov 17 Optimization
27 Friday Nov 19 Logistic Regression
Week 10
28 Monday Nov 29 Deep Learning Challenge in
29 Wednesday Dec 1 Future of Probability PSet 6 in
30 Friday Dec 3 No Class Final: Thurs, Dec 9th, 12:15 - 3:15pm

Readings

This quarter we are writing a Course Reader for CS109 which is free (but will be constructed as we go)! You can optionally read from Sheldon Ross, A First Course in Probability (10th Ed.), Prentice Hall, 2018. The corresponding readings can be found Win 21 schedule. The textbook's 8th and 9th editions have the same readings and section headers.