Neural and Cognitive Data Science

PSYC 499
University of Southern California, Fall 2026
Time: M/W 2:00–3:50 pm
Location: KAP 165
Office Hours: W 4:00–6:00 pm in HNB 316
Instructor: Sam Nastase (snastase@usc.edu)
Syllabus: Syllabus
GitHub: GitHub
Scratch: Scratch

This course introduces students to the mathematical and data scientific tools at the core of research in cognitive and computational neuroscience. The course aims to familiarize students with topics in linear algebra, statistics, and machine learning, with practical, hands-on applications to cognition and neuroscience. Lectures on each topic will develop the relevant mathematical background with links to foundational applications in the field. Coursework will focus primarily on problem sets requiring the implementation of models and analyses in Python. The course will equip students with a practical proficiency in various computational methods, including programming skills in data analysis and visualization that are increasingly important to scientific inquiry in general, and neuroscience in particular. The intended audience for this course is later-stage undergraduate students (or graduate students) who want to develop their expertise in data science, machine learning, and computational approaches to understanding brain and behavior. Some experience with Python programming, linear algebra, or neuroscience will be helpful, but is not strictly required.

Course schedule

Date	Topic	Materials	Optional readings
M 8/24	Introduction to cognitive computational neuroscience	`Lecture 0` `Code 0` `Homework 0`	Marr, 1982, Vision, Ch. 1, pp. 8–38 `PDF` McClelland et al., 1986, PDP, Ch. 1, pp. 3–44 `PDF`
W 8/26	Introduction to linear algebra	`Lecture 1` `Code 1`	Jordan, 1986, PDP, Ch. 9, pp. 365–373 `PDF` Simoncelli, 1999, NYU `PDF`
M 8/31	Linear combination and vector spaces	`Lecture 2` `Code 2` `Homework 1`	Jordan, 1986, PDP, Ch. 9, pp. 374–385 `PDF` Shepard, 1987, Science `PDF` Mikolov et al., 2013, NAACL `PDF`
W 9/2	Application: trichromatic vision	`Lecture 3` `Code 3`	Maxwell, 1855, Trans. R. Soc. Edinburgh `PDF` Baylor et al., 1987, J. Physiol. `DOI` Ruderman et al., 1998, JOSA A `DOI`
M 9/7	No class (Labor Day Holiday)
W 9/9	Matrix multiplication and linear systems	`Lecture 4` `Code 4`	Jordan, 1986, PDP, Ch. 9, pp. 385–395 `PDF`
M 9/14	Application: local and distributed representation	`Lecture 5` `Code 5` `Homework 2`	Kanwisher et al., 1997, J. Neurosci. `DOI` Haxby et al., 2001, Science `DOI`
W 9/16	The four fundamental subspaces	`Lecture 6` `Code 6`	Strang, 2023, MIT, Ch. 3, pp. 84–88 `PDF` Kaufman et al., 2014, Nat. Neurosci. `PDF`
M 9/21	Application: neural population codes	`Lecture 7` `Code 7`	Ebitz & Hayden, 2021, Neuron `PDF` Churchland & Shenoy, 2024, Nat. Rev. Neurosci. `PDF` Panichello & Buschman, 2021, Nature `PDF`
W 9/23	Singular value decomposition (SVD)	`Lecture 8` `Code 8`	Jordan, 1986, PDP, Ch. 9, pp. 399–403 `PDF` Saxe et al., 2019, PNAS `PDF`
M 9/28	Principal component analysis (PCA)	`Lecture 9` `Code 9` `Homework 3`	Abdi & Williams, 2010, WIREs `PDF` Cunningham & Yu, 2014, Nat. Neurosci. `PDF`
W 10/30	~~Application: visualizing high-dimensional neural activity~~ No class
M 10/5	Application: visualizing high-dimensional neural activity	`Lecture 10` `Code 10`	Fusi et al., 2016, Curr. Opin. Neurobiol. `PDF` Stringer et al., 2019, Nature `PDF` Williamson et al., 2019, Curr. Opin. Neurobiol. `PDF`
W 10/7	~~Application: univariate regression in fMRI~~ No class
M 10/12	Least-squares regression	`Lecture 11` `Code 11` `Homework 4`	Strang, 2023, MIT, Ch. 4, pp. 163–169 `PDF`
W 10/14	Application: univariate regression in fMRI	`Lecture 12` `Code 12`	Epstein & Kanwisher, 1998, Nature `PDF` Daw et al., 2011, Neuron `PDF`
M 10/19	Introduction to probability and statistics	`Lecture 13` `Code 13`	Poldrack, 2019, Statistical Thinking, Ch. 5–6 `link`
W 10/21	Statistical tests as linear models	`Lecture 14` `Code 14`	Poldrack, 2019, Statistical Thinking, Ch. 7 `link` Lindeløv & Ho, 2019 `link`
M 10/26	Application: representational similarity analysis	`Lecture 15` `Code 15` `Homework 5`	Kriegeskorte & Kievit, 2013, TICS `PDF` Cichy et al., 2014, Nat. Neurosci. `PDF`
W 10/28	Permutation tests and the bootstrap	`Lecture 16` `Code 16`	Good, 1994, Permutation Tests, Ch. 1, pp. 1–9 `PDF` Griffiths et al., 2010, TICS `PDF`
M 11/2	Overfitting and out-of-sample prediction	`Lecture 17` `Code 17`	Yarkoni & Westfall, 2017, PPS `PDF` Rokem & Yarkoni, 2023, DSfN, Ch. 17, pp. 263–271 `link`
W 11/4	Regularized regression	`Lecture 18` `Code 18`	Rokem & Yarkoni, 2023, DSfN, Ch. 21, pp. 311–319 `link` Naselaris et al., NeuroImage `PDF` Wager et al., 2013, NEJM `PDF`
M 11/9	Application: encoding models in fMRI	`Lecture 19` `Code 19` `Homework 6`	Huth et al., 2016, Nature `PDF` de Heer et al., 2017, J. Neurosci. `PDF` Zada et al., 2024, Neuron `PDF`
W 11/11	No class (Veterans Day Holiday)
M 11/16	Classification analysis
W 11/18	Application: neural decoding
M 11/23	Artificial neural networks
W 11/25	No class (Thanksgiving Holiday)
M 11/30	Application: deep learning
W 12/2	Final exam

The content of this course is inspired by related courses designed by Jonathan Pillow, Eero Simoncelli, Michael Landy, Ella Batty, and Tal Yarkoni.

Resources and references

“Welcome to Colab” introduction to browser-based interactive Jupyter Notebooks hosted by Google Colab: Welcome to Colab

Jupyter ecosystem documentation: Jupyter Documentation Jupyter Markdown Cells

Pyplot tutorial and Matplotlib documentation: Pyplot Tutorial Matplotlib Documentation

Pandas and Seaborn documentation: Pandas Seaborn

Scikit-learn’s User Guide and Examples: User Guide Examples

Managing Python environments and installing software using conda: Conda Documentation

Neuromatch computational neuroscience tutorials: Neuromatch

Neurohackademy summer school lecture archive: Neurohackademy

“Introduction to Linear Algebra” textbook materials available online at Gilbert Strang’s website: website
— Strang, G. (2023). Introduction to Linear Algebra (6th ed.). Wellesley-Cambridge Press.

“Parallel Distributed Processing” (PDP) book chapters available at Jay McClelland’s website: website
— Rumelhart, D. E., McClelland, J. L., & the PDP Research Group. (1986). Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Volume 1: Foundations. MIT Press.

“The Elements of Statistical Learning” textbook available online at Trevor Hastie’s website: website PDF
— Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd ed.). Springer.

“Statistical Thinking for the 21st Century” online book by Russ Poldrack: website
— Poldrack, R. A. (2023). Statistical Thinking: Analyzing Data in an Uncertain World. Princeton University Press.

“Neuroimaging and Data Science” online book and interactive tutorials: website
— Rokem, A., & Yarkoni, T. (2023). Data Science for Neuroimaging: An Introduction. Princeton University Press.

“Experimentology“ online book by Michael C. Frank and colleagues: website
— Frank, M. C., Braginsky, M., Cachia, J., Coles, N. A., & Hardwicke, T. E. (2025). Experimentology: An Open Science Approach to Experimental Psychology Methods. MIT Press.

“Theoretical Neuroscience” book by Peter Dayan and Larry Abbott: PDF
— Dayan, P., & Abbott, L. F. (2001). Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. MIT Press.

“Computational Foundations of Cognitive Neuroscience” online book by Sam Gershman: website
— Gershman, S. J. (2025). Computational Foundations of Cognitive Neuroscience.