E0 315: Measure Theoretic Probability, January Term 2022
E0 315: Measure Theoretic Probability
Department of Computer Science & Automation
Indian Institute of Science
Mid Term: 30 Marks
Assignments: 20 Marks
Endsem: 50 Marks
- First one-month classes will be held online
The objective of the course is to provide students with a measure-theoretic understanding of probability that is normally not taught in Engineering departments. The hope is this would equip students with deeper concepts and tools in probability theory that would help them in understanding deeper concepts in Machine Learning, Reinforcement Learning, Analysis of Stochastic Approximation Algorithms etc.
Basic Probability and Analysis
As students of IISc, we expect you to adhere to the highest standards of academic honesty and integrity.
Elements of the course are designed to support your learning of the
subject. Copying will not help you (in the exams or in the real world),
so don't do it. If you have difficulties learning some of the topics or
lack some background, try to form study groups where you can bounce off
ideas with one another and try to teach each other what you understand.
You're also welcome to talk to any of us and we'll be glad to help you.
If any exam/assignment is found to be copied, it will automatically
result in a zero grade for that exam/assignment and a warning note to
your advisor. Any repeat instance will automatically lead to a failing
grade in the course.
Sigma-Field, Construction of Probability Spaces and Measures, Random Variables and Measurability, Independence, Integration and Expectation, Monotone Convergence, Dominated Convergence, almost sure, and in-probability convergence, Convergence in Distribution, Central Limit Theorem, Conditional Expectation and Martingales.
- G.R.Shorack, Probability for Statisticians, Springer, Second Edition, 2017
- R.Ash and C. Doleans-Dade, Probability and Measure Theory, 1999