Sample syllabus: Topics in Neural Data Analysis
Course Instructor:
Alex Williams (alex.h.williams@nyu.edu)
Course Description:
Research into the neural basis of cognition, perception, and behavior is increasingly predicated on complex data modeling pipelines. Interpreting and critiquing data analyses within recent publications is challenging, even for those with some training in “the fundamentals” of mathematical and computational analysis.
This course combines instructor-led lectures and student-led paper discussions to introduce and then apply advanced mathematical concepts to understand complex neural and behavioral data.
Prerequisites: MathTools (NEURL-GA.2201) or permission of the instructor.
Location / Time:
Lectures - on Wednesdays, 1:30-3pm, Meyer 1010
Paper Discussions - on Thursdays, 1:30-3pm, Meyer 1010
Office Hours - on weeks where there is no one to lead paper discussion, the Thursday slot is converted into office hours.
Grading:
Paper presentation (35%)
Students will lead discussion (potentially in teams of two) once during the semester.
Pedagogical literature review / blog post (35%)
Students will write a short piece of writing explaining a computational method or statistical model in modern neuroscience. This piece can be, but does not have to be, a review of a particular paper discussed in class. Here are some blog posts that I wrote as a graduate student that can serve as inspiration: http://alexhwilliams.info/itsneuronalblog/
Attendance and participation in paper discussion (30%)
Students are expected to attend paper discussions scheduled (roughly) every other week of the class. Permission to miss a discussion section should be requested in advance as much as possible.
Dates / Topics:
- Jan 25 - Mathematical Background
- Feb 1 - Nonnegative Matrix Factorization
- Feb 8 - Tensor Factorization
- Feb 15 - Covariance Estimation / Noise Correlations
- Feb 22 - Canonical Correlations Analysis
- Mar 1 - Work on Literature Review / Blog Posts
- Mar 8 - Clustering
- Mar 15 - Spring Break
- Mar 22 - Topological Data Analysis / Persistent Homology
- Mar 29 - tSNE / UMAP
- Apr 5 - Variational Autoencoders (guest lecture)
- Apr 12 - Hidden Markov Models
- Apr 19 - State Space Models
- Apr 26 - Time Warping
FULL READING LIST
You are not expected to read the background material prior to each class, but you may find these materials to be useful references if you have questions about lecture material or the primary reading.
You are expected to briefly read each paper for discussion each week, and you are obviously expected to read the paper carefully when you are assigned to lead the discussion.
We will not have paper discussion every week. Our aim will be to have discussion sections approximately every other week. Students will volunteer to lead discussions from the options listed below. If necessary, students will present in teams of two.
Jan 25 - Mathematical Background
- May 3 - Finish Literature Review / Blog Posts
Lecture Materials:
(Chapters 1-8) Murphy (2022). Probabilistic Machine Learning: An Introduction. MIT Press. https://probml.github.io/pml-book/book1.html
N/A
Feb 1 - Nonnegative Matrix Factorization
Lecture Materials:
Paper Discussion:
Liu et al. Inference of neuronal functional circuitry with spike-triggered non-negative matrix factorization. Nat Commun 8, 149 (2017). https://doi.org/10.1038/s41467-017-00156-9
Feb 8 - Tensor Factorization
Lecture Materials:
Kolda, T. G., & Bader, B. W. (2009). Tensor Decompositions and Applications. SIAM Review, 51(3), 455–500. https://doi.org/10.1137/07070111X
Williams et al. (2018). Unsupervised discovery of demixed,
low-dimensional neural dynamics across multiple timescales through tensor components analysis. Neuron. 98(6):1099–1115.e8 https://doi.org/10.1016/j.neuron.2019.10.020
Paper Discussion:
Lecture Materials:
Ledoit & Wolf (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2), 365–411. https://doi.org/10.1016/S0047-259X(03)00096-4
Paper Discussion:
Rumyantsev et al. (2020). Fundamental bounds on the fidelity of sensory cortical coding. Nature, 580(7801), 100-105. https://doi.org/10.1038/s41586-020-2130-2
Feb 22 - Canonical Correlations Analysis / Communication Subspace
Lecture Materials:
Uurtio,et al. (2017). A Tutorial on Canonical Correlation Methods. ACM Comput Surv. 50(6). https://doi.org/10.1145/3136624
Semedo et al. (2022). Feedforward and feedback interactions between visual cortical areas use different population activity patterns. Nat Commun 13, 1099. https://doi.org/10.1038/s41467-022-28552-w
Mar 1 - Work on Literature Review / Blog Posts
Mar 8 - Clustering
Lecture Materials:
Kleinberg, J. (2002). An impossibility theorem for clustering. Advances in neural information processing systems, 15. https://proceedings.neurips.cc/paper/2002/hash/43e4e6a6f341e00671e12 3714de019a8-Abstract.html
Towards a Statistical Theory of Clustering https://cs.uwaterloo.ca/~shai/LuxburgBendavid05.pdf
Paper Discussion:
Grün et al. (2015). Single-cell messenger RNA sequencing reveals rare intestinal cell types. Nature, 525(7568), 251-255.
Mar 15 - Spring Break
Mar 22 - Topological Data Analysis / Persistent Homology
Lecture Materials:
Paper Discussion:
Lecture Materials:
Paper Discussion:
Bohm et al. (2022) Unsupervised visualization of image datasets using contrastive learning. https://arxiv.org/abs/2210.09879
Apr 5 - Variational Autoencoders (Guest Lecture - Amin Nejatbakhsh)
Lecture Materials:
Kingma & Welling (2019), "An Introduction to Variational Autoencoders",
Foundations and Trends® in Machine Learning: Vol. 12: No. 4, pp 307-392. http://dx.doi.org/10.1561/2200000056
Doersch (2016). Tutorial on variational autoencoders. https://arxiv.org/abs/1606.05908
Paper Discussion:
Goffinet et al. (2021) Low-dimensional learned feature spaces quantify individual and group differences in vocal repertoires. eLife 10:e67855. https://doi.org/10.7554/eLife.67855
Apr 12 - Hidden Markov Models (HMMs)
Lecture Materials:
Paper Discussion:
Ashwood et al. (2022) Mice alternate between discrete strategies during perceptual decision-making. Nat Neurosci 25, 201–212 (2022). https://doi.org/10.1038/s41593-021-01007-z
Apr 19 - State Space Models / Switching Linear Dynamical Systems
Lecture Materials:
Paper Discussion:
Lecture Materials:
Williams et al (2020). Discovering precise temporal patterns in large-scale neural recordings through robust and interpretable time warping. Neuron. 105(2):246-259.e8 https://doi.org/10.1016/j.neuron.2019.10.020
Paper Discussion:
Willet et al. (2021) High-performance brain-to-text communication via handwriting. Nature 593, 249–254 (2021). https://doi.org/10.1038/s41586-021-03506-2
May 3 - Finish Literature Review / Blog Posts
Possible papers / topics for literature reviews:
Chung et al. (2017). A fully automated approach to spike sorting. Neuron, 95(6), 1381-1394. https://doi.org/10.1016/j.neuron.2017.08.030
Carlsson, G. E., & Mémoli, F. (2010). Characterization, stability and convergence of hierarchical clustering methods. J. Mach. Learn. Res., 11(Apr), 1425-1470.
Kiselev et al. (2019) Challenges in unsupervised clustering of single-cell RNA-seq data. Nat Rev Genet 20, 273–282. https://doi.org/10.1038/s41576-018-0088-9