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)