Advanced Methods for Biomedical Signal Analysis
This is a graduate-level course. Students from engineering, physics, mathematics, statistics, and neuroscience are all welcome to attend, provided that the prerequisites are satisfied.
Biomedical signals like ECG, EEG, and LFP are typically non-stationary and have complex features often masked by noise and other interfering signals. The course will introduce advanced statistical methods to deal with these characteristics and to properly model and analyze biomedical signals in various domains of application. The students will get hands-on experience in applying the methods learnt in class to real world problems and a course project will provide the opportunity to explore current problems in biomedical signal analysis, with specific application to neural and ECG data. Topics will include multivariate probability distributions, estimation, model uncertainty, bootstrap, sequential hypothesis test, nonlinear regression, Poisson and generalized point processes, Markov chains, and Bayesian estimation.
Course Objectives and Outcomes:
The objective of this course is to learn the basic concepts and tools for modeling and analyzing biomedical signals, with specific focus on nonstationary and multivariate physiological time series (e.g., EEG, ECG, single unit neural recordings, and local field potentials). Through a mix of lectures and hands-on experiences, the students will learn how to use advanced statistical tools and numerical methods to describe the temporal dynamics of biomedical signals, how to validate data-driven predictive models, and how to use these models to simulate physiological time series.
Random vectors; Maximum likelihood estimation; Generalized linear models; Poisson processes; Point processes; Time-rescaling theorem and Kolmogorov tests; ROC analysis; Nonlinear regression; Nonparametric models; Bayesian estimation; Adaptive filtering; Markov chains and hidden Markov models; Change-point detection; Neural networks and graph models; Numerical analysis in MATLAB.
Prerequisite: Undergraduate-level knowledge of probability theory, signal processing, electromagnetism, biomedical instrumentation, and MATLAB (equivalent to CSE 1010, ECE 3101, STAT3025Q, and BME 3500).
Required, Elective, or Selected Elective: Elective.
Lectures: 1 lecture per week (3 hours)
Grading: Homework: 10%; Microteaching Assignment: 10%; Midterm Project: 40%; Final Project: 40%
A syllabus can be found here.
[TB] Robert E. Kass, Uri Eden, Emery N. Brown (2014) Analysis of Neural Data. ISBN: 978-1-4614-9602-1
Other Recommended References:
[R1] Alexander Tartakovsky, Igor Nikiforov, Michele Basseville (2015) Sequential Analysis: Hypothesis Testing and Changepoint Detection. ISBN: 978-1-4398-3820-4
[R2] L. R. Rabiner (1989) “A tutorial on hidden Markov models and selected applications in speech recognition,” Proc. of the IEEE, vol. 77 (2), pp. 257-286. DOI: 10.1109/5.18626
[R3] David J. C. MacKay (2003) Information Theory, Inference, and Learning Algorithms. ISBN: 978-0-5216-4298-9
Plan of Lectures and Assignments
|1||Probability and Random Variables||Lecture Notes. R1: Ch. 1-3||Homework 1|
|2||Random Vectors||Lecture Notes. TB: Ch. 4, 6||–|
|3||Maximum Likelihood Estimation||Lecture Notes. TB: Ch. 5, 7-8||Homework 2|
|4||Generalized Linear Models||Lecture Notes. TB: Ch. 12, 14-15|
|5||Point Process Theory||Lecture Notes. TB: Ch. 14, 19||–|
|6||Point Process GLM Fitting||Lecture Notes. TB: Ch. 10, 19. A1, A2, A3, A4, & A5||–|
|7||MIDTERM PROJECT DISCUSSION||–||–|
|8||Adaptive Filtering and Decoding||Lecture Notes. TB: Ch. 16. A1 & A2||Homework 3|
|9||Changepoint Detection||Lecture Notes. R1: Ch. 1-2||–|
|10||Theory of Markov Chains||Lecture Notes. R2||Homework 4|
|11||Hidden Markov Models and Algorithms||Lecture Notes. R2||–|
|12||Artificial Neural Networks||Lecture Notes. R3: Ch. 38-42||–|
|14||FINAL PROJECT DISCUSSION||–||–|
|MATERIAL DEVELOPED WITH THE SUPPORT OF THE US NATIONAL SCIENCE FOUNDATION:||
“EAGER: Modeling Network Dynamics in the Epileptic Brain to Develop Translational Tools for Seizure Localization and Detection”