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

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 Tuesday Jun 24 Counting PSet 1 out
4
2 Thursday Jun 26 Combinatorics
4
3 Friday Jun 27 What is Probability?
Week 2
5
4 Tuesday Jul 1 Bayes Theorem and Independence PSet 1 in / PSet 2 out
7
5 Thursday Jul 3 Random Variables
8
- Friday Jul 4 No class
Week 3
9
6 Tuesday Jul 8 Expectation and Variance PSet 2 in / PSet 3 out
11
7 Thursday Jul 10 Continuous Random Variables
12
8 Friday Jul 11 Joint Distributions
Week 4
13
9 Tuesday Jul 15 Probabilistic Models PSet 3 in / PSet 4 out
15
10 Thursday Jul 17 Inference
16
11 Friday Jul 18 General Inference
Week 5
17
12 Tuesday Jul 22 Beta PSet 4 in / PSet 5 out
19
13 Thursday Jul 24 Adding Variables, Convolutions
14 Friday Jul 25 Sampling
Week 6
15 Tuesday Jul 29 Bootstrapping PSet 5 in / PSet 6 out
16 Thursday Jul 31 Algorithmic Analysis
17 Friday Aug 1 Maximum Likelihood Estimation
Week 7
18 Tuesday Aug 5 Maximum A Posteriori PSet 6 in / PSet 7 out
19 Thursday Aug 7 Logistic Regression
20 Friday Aug 8 Comparing Classifiers
Week 8
21 Tuesday Aug 12 Beyond Classification PSet 7 in
22 Thursday Aug 14 Final Review Session
- Saturday Aug 16 Final Exam 3:30p - 6:30p