Course content and aim
This course will provide a broad introduction to basic mathematical and computational tools for a quantitative analysis of neural systems. Integrated lectures, MATLAB sessions, and homework sets will introduce techniques and help us learn to apply them. We will cover a range of topics, including neural encoding and decoding, population codes, filtering, correlation, convolution, spike-triggered averaging (reverse correlation), deconvolution, and dimensionality reduction, clustering, and spike-sorting through principal components analysis, as well as some probability and Bayesian inference, as used in neuroscience. The goal is to help develop a level of intuitive and practical comfort with quantitative methods and visualization of complex data.
Time & Place
Tuesday/Thursday 11:00 a.m. 12:30 p.m. GDC 5.304, 3:30 p.m. 5:00 p.m. WEL 2.128.
Tuesday 5:00p.m.-6:00p.m. and Thursday 12:30p.m.-13.30p.m. @ NHB 4.344.
|01.21.2020||Preliminaries: introduction to course aims.||Cercal System Review, MATLAB tutorial1, NR_movie, NRiter1, NRiter2, NRiter3, NRiter4, NRiter5, ComplexGrid, MatlabIntro|
|01.24.2020||Linear algebra: vector, inner product, system of equations||MATLAB tutorial2, LinAlgNotes1||PS1|
|01.28.2020||Linear algebra: vector space, basis, matrix product, rank||MATLAB tutorial3, LinAlgSlide1, linAlgNotes2|
|01.30.2020||Overfitting and cross-validation.||FittingSlides|
|02.04.2020||Variance, covariance, and the Pearson correlation coefficient.||StatSlides||PS2|
|02.06.2020||Time-series: cross- and auto-correlation.||CorrSlides1|
|02.11.2020||Analyzing temporal structure in spike trains.||CorrSlides2||PS3, c1p8.mat , gridcell_halfmsbins.mat|
|02.18.2020||Convolution and applications: Mach bands, edge-detection in the retina.||ConvSlides||MarrHildreth80|
|02.20.2020||Wiener-Hopf equations.||WH_Slides1||PS4, generate_STAdata.mt|
|02.25.2020||Reverse correlation analysis.||WH_Slides2|
|03.03.2020||Linear least-squares regression.||LSR_Notes|
|03.05.2020||Eigenvalues, eigenvectors, and the spectral theorem.|
|03.10.2020||Review, more examples, Q&A for midterm.|
|03.26.2020||Review on eigenvalues, eigenvectors, and the spectral theorem.|
|03.31.2020||PCA: theory.||PCA1_Notes||PS5, clusters_generate_fake_3d.m|
|04.02.2020||PCA: application (dimensionality reduction, denoising)||PCA2_Notes||PCATutorial_Shlens|