DA241M-2022

DA 241M: Mathematical foundations of data science (July-Nov 2022)

The is a B.Tech. (3rd Semester) minor course.

Lectures:

4 PM – 4.55 PM, Wednesday

4 PM - 4.55 PM, Thursday

4 PM- 4.55 PM, Friday


Lectures are being held offline in Room No 4005 (in Core 4).

Instructor:

Prof. Ratnajit Bhattacharjee (Pre-Midsem)
Dr. Arghyadip Roy (Post-Midsem)



Course Content/ Syllabus:

Fundamentals: Review of linear algebra and multi-variate calculus from data science perspective.

Probability and random variables: Basics of Probability Theory, Conditional Probability, Bayes’ Theorem, Random Variables, Discrete and Continuous Distributions, Moments, Law of large numbers and Central Limit Theorem.

Statistical inference: Parametric and nonparametric methods, Point estimation, Confidence Intervals, Maximum Likelihood Estimators; Hypothesis testing; Bayesian Inference.

Optimization: Unconstrained and Constrained optimization for single and multiple variables: Gradient descent methods, Newton’s method, Simplex method; Convexity and duality


Textbooks:

  • Wasserman, L., All of statistics: a concise course in statistical inference, 1st Ed., Springer, New York, 2004.

  • Pishro-Nik, Hossein. Introduction to probability, statistics, and random processes. (2016).

  • Stephen P. Boyd, and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.

  • Kochenderfer, Mykel J., and Tim A. Wheeler. Algorithms for optimization. MIT Press, 2019.


References:

  • Lecture notes, Joshua M. Tebbs, Mathematical Statistics, Department of Statistics, University of South Carolin

  • Ross, Sheldon M. Introduction to probability and statistics for engineers and scientists. Academic press, 2020.


Grading Scheme:

Pre-Midsem Quiz: 10%

Midsem: 30%

Post-Midsem Quiz: 10%

Endsem: 50% (10 marks (pre-midsem), 40 marks (post-midsem))



Lecture Schedule:

Lecture 1: Introduction to Statistical Inference

Lecture 2: Nonparametric Estimation

Lecture 3: Statistical Functional

Lecture 4: Maximum Likelihood Estimator

Lecture 5: Sufficient Statistics

Lecture 6: Minimal Sufficient Statistics

Lecture 7: Hypothesis Testing

Lecture 8: LRT

Lecture 9: Bayesian Inference

Lecture 10: MAP Estimation

Lecture 11: Bayesian Hypothesis testing

Lecture 12: Optimization Basics

Lecture 13: Duality

Lecture 14: KKT Conditions

Lecture 15: Gradient Descent

Lecture 16: Newton's Method

Lecture 17: Direct Method



Problem Set:

Problem Set 1: Statistical Inference

Problem Set 2: Optimization

Examinations:

Quiz 2: 9 th Nov (5-6 PM)

Endsem: 29 th Nov (9:00-12:00)