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

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
2
 1 Monday Sept 23 Counting
3
 2 Wednesday Sept 25 Combinatorics PSet 1 out
4
 3 Friday Sept 27 What is Probability?
Week 2
5
 4 Monday Sept 30 Conditional Probability and Bayes
6
 5 Wednesday Oct 2 Independence
7
 6 Friday Oct 4 Random Variables and Expectation PSet 1 in / PSet 2 out
Week 3
8
 7 Monday Oct 7 Variance Bernoulli Binomial
9
 8 Wednesday Oct 9 Poisson
10
 9 Friday Oct 11 Continuous Random Variables
Week 4
11
 10 Monday Oct 14 Normal Distribution PSet 2 in / PSet 3 out
12
 11 Wednesday Oct 16 Joint Distributions
13
 12 Friday Oct 18 Inference
Week 5
14
 13 Monday Oct 21 Inference II
15
 14 Wednesday Oct 23 General Inference
16
 15 Friday Oct 25 Beta PSet 3 in
Week 6
17
 - Monday Oct 28 No Class (Break)
16 Tuesday Oct 29 Midterm Midterm: 7 - 9pm
18
 16 Wednesday Oct 30 Adding PSet 4 out
19
 17 Friday Nov 1 Central Limit Theorem
Week 7
20
 18 Monday Nov 4 Bootstrapping and P-Values
21
 19 Wednesday Nov 6 Algorithmic Analysis
22
 20 Friday Nov 8 Entropy and Divergence PSet 4 in / PSet 5 out
Week 8
23
 21 Monday Nov 11 M.L.E.
24
 22 Wednesday Nov 13 Optimisation
25
 23 Friday Nov 15 Logistic Regression Withdraw deadline
Week 9
26
 24 Monday Nov 18 Comparing Classifiers PSet 5 in / PSet 6 out
27
 25 Wednesday Nov 20 Beyond Classification
28
 26 Friday Nov 22 Deep Learning
Week 10
29
 27 Monday Dec 2 Diffusion Challenge in
30
 28 Wednesday Dec 4 Final Lecture PSet 6 in
31
 - Friday Dec 6 No Class Final: Tue, Dec 10th, 8:30a

Readings

This quarter we are writing a Course Reader for CS109 which is free and written for the course. 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.