DS-GA 1002: Statistical and Mathematical Methods

Instructor: Carlos Fernandez-Granda (cfgranda@cims.nyu.edu)
TA: Levent Sagun (sagun@cims.nyu.edu)

This course introduces statistical and mathematical methods needed in the practice of data science. It covers basic principles in probability, statistics, linear algebra, and optimization.

Announcements

  • The final will take place on Monday December 14 from 5pm to 8pm in SILVER 207 (128), not in the usual classroom

Syllabus

  • Probability: Probability basics (axioms of probability, conditional probability, random variables, expectation, independence, etc.), multivariate distributions, introduction to concentration bounds, laws of large numbers, central limit theorem.

  • Statistics: Maximum a posteriori and maximum likelihood estimation, minimum mean-squared error estimation, confidence intervals.

  • Linear algebra: Vector spaces, linear transformations, singular value decomposition, eigendecomposition, principal component analysis, least squares, regression.

  • Optimization: Matrix calculus, gradient descent, coordinate descent, introduction to convex optimization.

Prerequisites

Calculus and linear algebra at the undergraduate level

General Information

Lecture

Monday 5:10-7 pm, CIWW 109

Recitation

Thursday 6:10-7 pm, CIWW 109

Office hours

Carlos: Wednesday 4:30-6 pm, CDS 782
Levent: Thursday 3:30-5 pm, WWH 605

Piazza

We will be using Piazza to answer questions and post announcements about the course. Please sign up here.

Grading policy

Homework (40%) + Midterm (20%) + Final (40%)

Books

We will provide self-contained notes and no other texts are required. However, here are some additional references that could be useful:

  • Probability:

    • A first course in probability by Ross

    • Introduction to Probability by Bertsekas and Tsitsiklis

  • Statistics:

    • Statistical inference by Casella and Berger

    • All of statistics by Wasserman

    • Probability and Statistics by DeGroot and Schervish

    • Statistics by Freedman, Pisani and Purves

  • Linear algebra:

    • Linear Algebra and Its Applications by Strang

  • Optimization: