42-590 / 18-699
Neural signal processing
Spring 2010

12 units

Class time and location:
Tues / Thurs 10:30-11:50am
Scaife Hall 220


Byron Yu
B204 Hamerschlag Hall
(412) 268-9658
Office hours: Tues / Thurs noon-1pm


Jinyin Zhang
(412) 268-5251
Office hours: Fri 12:30-2pm
Location: 2139 Hamerschlag Hall

Matt Golub
(412) 268-3738
Office hours: Wed 4:15-5pm, Thurs 5:15-6pm
Location: B200 Hamerschlag Hall

Course management assistant:

Bara Ammoura
D200 Hamerschlag Hall
(412) 268-6595
Office hours: Mon-Fri 8:30am-5pm

Course description:

The brain is among the most complex systems ever studied. Underlying the brain's ability to process sensory information and drive motor actions is a network of roughly 10^11 neurons, each making 10^3 connections with other neurons. Modern statistical and machine learning tools are needed to interpret the plethora of neural data being collected, both for (1) furthering our understanding of how the brain works, and (2) designing biomedical devices that interface with the brain.

This course will cover a range of statistical methods and their application to neural data analysis. The statistical topics include latent variable models, dynamical systems, point processes, dimensionality reduction, Bayesian inference, and spectral analysis. The neuroscience applications include neural decoding, firing rate estimation, neural system characterization, sensorimotor control, spike sorting, and field potential analysis.

Course goals:

There are two primary goals for the course: (1) to introduce the statistical tools used to study large-scale neural activity, and (2) to bring out the real-world challenges of working with experimental data. By the end of the course, students should be able to ask research-level questions in neural signal processing, as well as develop new statistical tools for problems in their own research. In short, this course serves as a stepping stone to research in neural signal processing.


This course is ideally suited for students with a solid background in basic probability and linear algebra. Prior knowledge of neuroscience is welcome, but not required. Students with experience in neuroscience should be aware that the first 3 weeks will cover basic neuroscience.

Students should already be familiar with concepts such as:

Probability -- independence, conditional probability, Bayes rule, multivariate Gaussian distribution, Poisson distribution, Poisson process

Linear algebra -- basic matrix operations (sums and products), matrix inversion, eigenvectors and eigenvalues, singular value decomposition

For those unfamiliar with the concepts above, I would recommend Statistical Methods for Neuroscience and Psychology (36-746), and Probability Theory and Random Processes (36-217).

If you are unsure whether this class is for you, please talk with me.

Required textbook:

Pattern Recognition and Machine Learning
Christopher Bishop. Springer, 2006.

Optional textbooks:

Principles of Neural Science
Eric Kandel, James Schwartz, Thomas Jessell. McGraw-Hill Medical, 2000.

Theoretical Neuroscience
Peter Dayan and L.F. Abbott. MIT Press, 2001.

Information Theory, Inference, and Learning Algorithms
David J.C. MacKay. Cambridge University Press, 2003.

Matlab for Neuroscientists
Pascal Wallisch, Michael Lusignan, Marc Benayoun, Tanya I. Baker, Adam S. Dickey, and Nicholas G. Hatsopoulos. Academic Press, 2009.

Assignments and exams:

There will be approximately 8 problem sets during the semester and regular reading assignments. There will be a midterm exam in class on Thursday, March 4. There will be a final exam the week of May 3, date TBD.

Most problem sets will have a Matlab component, in which students will implement various algorithms and apply them to neural data. This link has information about how to obtain Matlab software.

Students may work on problem sets together, but each student must turn in his/her own solutions. You may not simply copy another student's work. All students are bound by the CMU Academic Integrity Code.

Late policy for problem sets: Each student is allowed two late problem sets during the semester (up to 24 hours after the deadline). Problem sets that are turned in outside of this grace period will receive zero credit.

Grading breakdown:

Problem sets 30%
Midterm exam 30%
Final exam 40%

Course Outline:

  1. What is neural signal processing?
    (1 lecture)

  2. Neuroscience basics. Membrane potential. Action potential. Synaptic transmission.
    (5 lectures)
    PNS Ch 1, 2, 7
    Excerpts from PNS Ch 9, 10, 12

  3. Spike train analysis. Spike histogram. Tuning curve. Poisson process.
    (2 lectures)
    TN Ch 1

  4. Fundamentals of probabilistic machine learning. Maximum likelihood parameter estimation. Priors and likelihood functions.
    (2 lectures)
    PRML Ch 1 and 2

  5. Classification. Linear discriminant analysis. Naive Bayes.
    Neuroscience application: discrete neural decoding
    (2 lectures)
    PRML Ch 4

  6. Graphical models.
    (1 lecture)
    PRML Ch 8.1-8.2

  7. Mixture models. Expectation-maximization.
    Neuroscience application: spike sorting
    (3 lectures)
    PRML Ch 9

  8. Principal components analysis. Factor analysis.
    Neuroscience applications: dimensionality reduction, discrete neural decoding
    (3 lectures)
    PRML Ch 12

  9. Hidden Markov model. Kalman filter. Linear filter.
    Neuroscience application: continuous neural decoding
    (5 lectures)
    PRML Ch 13

  10. Cross-validation. Bayesian model selection.
    Neuroscience applications: dimensionality reduction, spike sorting
    (2 lectures)
    PRML Ch 1.3, 3.4
    MacKay Ch 28

  11. Point processes. Conditional intensity functions. Time-rescaling algorithm for point processes. Goodness-of-fit.
    Neuroscience application: spike train models
    (2 lectures)