Fall 2026 Course Topics
The course will cover the following topics.
Detection and Hypothesis Testing Mean and conditional expectation, variance, covariance, correlation, and moment generating functions Random vectors, covariance matrices, and linear transformations Inequalities: Markov, Chebyshev, Hoeffding, and general concentration inequalities MSE estimation; linear estimation and the orthogonality principle Covariance matrices: whitening and coloring, Gaussian random vectors, vector detection and MSE estimation; Kalman filtering and innovations Convergence and limit theorems: Law of Large Numbers, Central Limit Theorem, and applications Random processes: definition and examples of discrete and continuous random processes; IID processes, random walk, independent increment processes, Poisson process, Gaussian random processes, stationarity, autocorrelation function, and power spectral density White noise, bandlimited processes, and response of linear systems to random inputs Linear filtering; infinite smoothing, causal estimation, spectral factorization, and Wiener filtering
Tentative Fall 2026 Lecture Plan
This lecture plan, including both midterm dates, is tentative and subject to change. Exam arrangements will be announced. Lecture numbers include the no-class dates below.
Lectures meet on Tuesdays and Thursdays. University holidays and recess dates follow the Stanford academic calendar.
Lecture 1 (September 22): Course Overview
Lecture 2 (September 24): 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 (September 29): Concentration Inequalities and Moment Generating Functions (References: Chapter 2 Vershynin and Appendix B of Shalev-Shwartz & Ben-David)
Lecture 4 (October 1): Sub-Gaussian Random Variables and Concentration Bounds (References: Chapter 2 Vershynin and Appendix B of Shalev-Shwartz & Ben-David)
Lecture 5 (October 6): Machine Learning and Empirical Risk Minimization (Reference: Chapters 2-3-4 of Shalev-Shwartz & Ben-David)
Lecture 6 (October 8): Midterm 1 (tentative; week 3).
Lecture 7 (October 13): Learning via Uniform Convergence (Reference: Chapters 2-3-4 of Shalev-Shwartz & Ben-David)
Lecture 8 (October 15): Random Vectors, Mean and Covariance Matrix (Reference: Sections 3.1 to 3.4 of Gallager)
Lecture 9 (October 20): Properties of a Covariance Matrix, Spectral Decomposition, Karhunen-Loeve Expansion (Reference: Sections 3.1 to 3.4 of Gallager)
Lecture 10 (October 22): Principal Component Analysis and Gaussian Random Vectors (Reference: Sections 3.1 to 3.4 of Gallager)
Lecture 11 (October 27): Detection/Hypothesis Testing (Reference: Sections 8.1 to 8.2 of Gallager)
Lecture 12 (October 29): Detection/Hypothesis Testing: Examples (Reference: Sections 8.1 to 8.2 of Gallager)
Lecture 13 (November 3): Democracy Day — no classes university-wide.
Lecture 14 (November 5): Midterm 2 (tentative; week 7).
Lecture 15 (November 10): Detection/Hypothesis Testing for Vector Gaussian Channel, Estimation (Reference: Sections 8.1 to 8.2, Sections 10.1-10.2 of Gallager)
Lecture 16 (November 12): MMSE Estimation, Sufficient Statistics (Sections 10.1-10.2 of Gallager)
Lecture 17 (November 17): Recursive Estimation and Kalman Filtering (Sections 10.1-10.2 of Gallager)
Lecture 18 (November 19): Random Processes, Stationarity (Section 3.6 of Gallager)
Lecture 19 (November 24): Thanksgiving recess — no class.
Lecture 20 (November 26): Thanksgiving recess — no class.
Lecture 21 (December 1): Gaussian Random Processes, Auto-Correlation Function (Section 3.6 of Gallager)
Lecture 22 (December 3): Power Spectral Density
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