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Course plan is approximate.
Lecture 1: Course Overview
Lecture 2: Review of Probability Inequalities and Limit Theorems (References: EE178 notes or Sections 1.6.(1-2) and 1.7.(1-3) from Gallager)
Lecture 3-4: Concentration Inequalities, Moment Generating Function, Sub-Gaussian Random Variables (References: Chapter 2 Vershynin and Appendix B of Shalev-Shwartz & Ben-David)
Lecture 5-6: Machine Learning, Empirical Risk Minimization, Learning via Uniform Convergence (Reference: Chapters 2-3-4 of Shalev-Shwartz & Ben-David)
Lecture 7: Random Vectors, Mean and Covariance Matrix (Reference: Sections 3.1 to 3.4 of Gallager)
Lecture 8: Properties of a Covariance Matrix, Spectral Decomposition, Karhunen-Loeve Expansion (Reference: Sections 3.1 to 3.4 of Gallager)
Lecture 9: Principal Component Analysis, Gaussian Random Vectors (Reference: Sections 3.1 to 3.4 of Gallager)
Lecture 10: Gaussian Random Vectors (Reference: Sections 3.1 to 3.4 of Gallager)
Lecture 11: Detection/Hypothesis Testing (Reference: Sections 8.1 to 8.2 of Gallager)
Lecture 12: Detection/Hypothesis Testing: Examples (Reference: Sections 8.1 to 8.2 of Gallager)
Lecture 13: No class. Democracy day!
Lecture 14: Midterm
Lecture 15: Detection/Hypothesis Testing for Vector Gaussian Channel, Estimation (Reference: Sections 8.1 to 8.2, Sections 10.1-10.2 of Gallager)
Lecture 16: MMSE Estimation, Sufficient Statistics (Sections 10.1-10.2 of Gallager)
Lecture 17: Recursive Estimation and Kalman Filtering (Sections 10.1-10.2 of Gallager)
Lecture 18: Random Processes, Stationarity (Section 3.6 of Gallager)
Lecture 19: Gaussian Random Processes, Auto-Correlation Function (Section 3.6 of Gallager)
Lecture 20: Power Spectral Density
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