42-590 / 18-699
Neural signal processing
Class time and location:
Tues / Thurs 10:30-11:50am
Scaife Hall 220
B204 Hamerschlag Hall
Office hours: Tues / Thurs noon-1pm
Office hours: Fri 12:30-2pm
Location: 2139 Hamerschlag Hall
Office hours: Wed 4:15-5pm, Thurs 5:15-6pm
Location: B200 Hamerschlag Hall
Course management assistant:
D200 Hamerschlag Hall
Office hours: Mon-Fri 8:30am-5pm
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
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.
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
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
Students should already be familiar with concepts such as:
Probability -- independence, conditional probability, Bayes
rule, multivariate Gaussian distribution, Poisson distribution,
Linear algebra -- basic matrix operations (sums and products),
matrix inversion, eigenvectors and eigenvalues, singular value
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.
Pattern Recognition and Machine Learning
Christopher Bishop. Springer, 2006.
Principles of Neural Science
Eric Kandel, James Schwartz, Thomas Jessell. McGraw-Hill Medical, 2000.
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
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
What is neural signal processing?
Neuroscience basics. Membrane potential. Action potential.
PNS Ch 1, 2, 7
Excerpts from PNS Ch 9, 10, 12
Spike train analysis. Spike histogram. Tuning curve. Poisson
TN Ch 1
Fundamentals of probabilistic machine learning. Maximum likelihood
parameter estimation. Priors and likelihood functions.
PRML Ch 1 and 2
Classification. Linear discriminant analysis. Naive Bayes.
Neuroscience application: discrete neural decoding
PRML Ch 4
PRML Ch 8.1-8.2
Mixture models. Expectation-maximization.
Neuroscience application: spike sorting
PRML Ch 9
Principal components analysis. Factor analysis.
Neuroscience applications: dimensionality reduction, discrete
PRML Ch 12
Hidden Markov model. Kalman filter. Linear filter.
Neuroscience application: continuous neural decoding
PRML Ch 13
Cross-validation. Bayesian model selection.
Neuroscience applications: dimensionality reduction, spike sorting
PRML Ch 1.3, 3.4
MacKay Ch 28
Point processes. Conditional intensity functions. Time-rescaling
algorithm for point processes. Goodness-of-fit.
Neuroscience application: spike train models