15-260 Statistics and Computing (SnC), Spring 2022, 3 Units

This is a "micro" class, which allows you to get credit for having covered the Statistics you need to receive an ML minor or do an ML concentration. You will not be able to register for 15-260 until a month AFTER PnC starts. The registrar insists on this because they want to make sure that only people who are in PnC get into 15-260. Everyone who is in PnC will be eligible for 15-260. People who are not in PnC are ineligible to take 15-260.

Lectures: Mondays 7:00 pm - 8:20 pm in GHC 4307.

Grading:

Weekly homework (~2 problems/homework) -- 60%
Three quizzes -- 40%
We will drop your 1 lowest homework score and 1 lowest quiz score
Usual grade breakdowns: A (90-100%); B (80-90%); C (70 - 80%); D (60 - 70%); R (<60%)

Syllabus:

March 21: Statistical Estimation and Inference

Basics of statistics: data generating models, common problem formulations and goals
Point estimation of parameters
Likelihood function, log likelihood
Maximum likelihood estimator (MLE)

March 28: Bayesian estimation

Priors
Bayes update, maximum a posteriori (MAP) estimator
Error metrics, minimum mean square error (MMSE) estimator

April 4: Hypothesis testing

Hypotheses, samples
Type I and type II errors
ML decision rule, MAP decision rule
Minimum cost testing

April 11: Confidence intervals

Point estimation vs interval estimation
Sampling theory
Connection with hypothesis testing
Prediction

April 18: Classification

Problem formulation, classifiers
Error rate, empirical/training error
Bayes classfier, regression functions
Plug-in classifier
Classifiers used in practice

April 25: Regression

Linear regression, least squared error
Linear regression of a random variable on a random variable
Least squared error (LSE) estimator
Linear regression with Gaussian noise