Instructors: | Mike Landy & Eero Simoncelli |
Teaching Assistants: |
Sarah Master (sm4937 AT nyu DOT edu), Ajay Subramanian (as15003 AT nyu DOT edu), Xinyuan Zhao (xz2556 AT nyu DOT edu), |
Time: |
Lectures: Tuesday/Thursday, 10:00-12:00 Labs: selected Fridays, 9:30-12:00 |
Location: |
Lectures: Meyer 636 Labs: Meyer 636 |
TA Office hours: |
Monday, 4-5pm, Meyer 760 Friday, 1-2pm, Meyer 635 |
Topics include: Linear algebra, least-squares and total-least-squares regression, eigen-analysis and PCA, linear shift-invariant systems, convolution, Fourier transforms, Nyquist sampling, basics of probability and statistics, hypothesis testing, model comparison, bootstrapping, estimation and decision theory, signal detection theory, linear discriminants, classification, clustering, simple models of neural spike generation, white noise (reverse-correlation) analysis.
Prerequisites: Algebra, trigonometry, and calculus. Some experience with matrix algebra and/or computer programming is helpful, but not required. The real prerequisites are an aptitude for logical and geometric reasoning, and a willingness to work hard!
Announcements: This year, we will use brightspace for class announcements and online questions/discussions: https://brightspace.nyu.edu/d2l/home/315787 . Rather than emailing the instructors or TAs, we encourage you to post your questions/comments there, where they can be discussed and/or answered by any of us or your fellow classmates.
Schedule: (Notes: labs are in green, content will appear incrementally, for a preview see last year's course page)
Date | Topic | Handouts | Homework |
---|---|---|---|
Tue, Sep 5 |
Introduction to the course
Linear algebra I: vectors, operations, vector spaces Zoom recording, whiteboard (pdf) |
Course description (pdf)
Notes: Linear Algebra (pdf) Slides: Linear algebra (pdf) |
|
Thu, Sep 7 |
Linear algebra II: inner products, projection, coordinate systems
Zoom recording (sorry, only first 1 hr 20 min, whiteboard (pdf) |
||
Fri, Sep 8 |
Programming Lab: Scripts, conditionals, iteration, functions,
maninpulating matrices and vectors |
Matlab installation (txt)
Matlab primer (pdf) Lab1 (zip) - includes matlab and python. |
|
Tue, Sep 12 |
Linear algbra III: linear systems, orthogonal/diagonal matrices, geometry
Zoom recording (sorry, no audio for first half), whiteboard (pdf) |
||
Thu, Sep 14 |
Linear algebra IV: orthogonal matrices, singular value decomposition
Zoom recording, whiteboard (pdf) |
||
Fri, Sep 15 | [no lab] | ||
Tue, Sep 19 |
Linear algebra V: Null/Range spaces, Trichromacy example
Zoom recording, whiteboard (pdf) |
Slides: Trichromacy (pdf) | Homework 1 (pdf - due 10/3) mat file for question 6 submission instructions |
Thu, Sep 21 |
Regression I: regression, multiple regression, partitioning variance
Zoom recording: part1, part2. whiteboard (pdf) |
Slides: Least squares (pdf) | |
Fri, Sep 22 |
Lab: Regression |
||
Tue, Sep 26 |
Regression II: choosing regressors, weighting, outliers, overfitting
Zoom recording, whiteboard (pdf) |
||
Thu, Sep 28 |
Regression III: incorporating linear constraints, TLS regression
Zoom recording I, whiteboard (pdf) |
||
Fri, Sep 29 | [no lab] | Notes: Least Squares (pdf) | |
Tue, Oct 3 |
Regression IV: TLS regression, PCA, eigenvalues/eigenvectors Zoom recording, whiteboard (pdf) |
Homework 2 (pdf - due 10/19) Data and code files (zip) |
|
Thu, Oct 5 |
LinSys I: Linear shift-invariant systems, convolution Zoom recording, whiteboard(pdf) |
Slides: Linear systems theory (pdf) | |
Fri, Oct 6 | Lab: Convolution - 1D and 2D + PCA | ||
Tue, Oct 10 | [no class - NYU legislative day] | ||
Thu, Oct 12 |
LinSys II: Sinusoids and LSI systems, Discrete Fourier transform Zoom recording, whiteboard (pdf) |
||
Fri, Oct 13 | [no lab] | ||
Tue, Oct 17 |
LinSys III: Fourier Transforms+LSI Zoom recording, |
||
Thu, Oct 19 |
LinSys IV: Fourier examples, indexing/plotting, sampling Zoom recording, whiteboard(pdf) |
||
Fri, Oct 20 | Lab: Fourier Transform | Homework 3 (pdf - due 11/2) Data and code files (zip) | |
Tue, Oct 24 |
LinSys V: Extended example: Sound, filtering, and the cochlea Zoom recording, whiteboard (pdf) |
Slides: Auditory example (pdf) | |
Thu, Oct 26 |
Stats intro: summary stats, central tendency, disperson, multi-D
Zoom recording, whiteboard (pdf) |
Slides: Probability and statistics (pdf) | |
Fri, Oct 27 | [no lab] | ||
Tue, Oct 31 |
Prob I: histograms, distributions, expectations, moments, cumulatives,
transformations, sampling
Zoom recording (no screenshare), ``live'' whiteboard with audio (mov), whiteboard (pdf) |
||
Thu, Nov 2 |
Prob II: joint distributions, marginals, conditionals, Bayes Rule, independence
Zoom recording, whiteboard (pdf) |
||
Fri, Nov 3 | Lab: Probability/sampling |
Homework 4
(pdf - due 11/16) |
|
Tue, Nov 7 |
Prob III: Gaussians: marginals, conditionals, dependency. correlation
mis-interpretations
Zoom recording , whiteboard (pdf) |
||
Thu, Nov 9 |
Inference I: Averages: 1/N convergence to mean, CLT, significance
tests,p-values, z-test, t-test, permutation tests
Zoom recording, whiteboard (pdf) |
||
Fri, Nov 10 | [no lab] | ||
Tues, Nov 14 |
Inference II: Statistical inference, MLE, examples Zoom recording, whiteboard (pdf) |
Slides: Statistical Inference (pdf) | |
Thur, Nov 16 |
Inference III: MAP, bias-variance, Bayes estimators Zoom recording, whiteboard (pdf) |
||
Fri, Nov 17 |
Lab: Bayes Zoom recording |
Homework 5
(pdf - due 12/1) |
|
Tue, Nov 21 |
Inference IV: Signal Detection theory: ML/MAP/Bayes, d', ROC Zoom recording, whiteboard (pdf) |
Slides: Signal detection theory (pdf) | |
Thu, Nov 23 | [no class - Thanksgiving] | ||
Fri, Nov 24 | [no lab - Thanksgiving break] | ||
Tue, Nov 28 |
Inference V:
Multi-D decision: FLD, SVM, QDA Zoom recording, whiteboard (pdf) |
||
Thu, Nov 30 |
Discriminability, Fisher Information. Model fitting Zoom recording, whiteboard (pdf) |
Slides: model fitting (pdf) | |
Fri, Dec 1 | Lab: Simulations, bootstrapping, cross-validation |
Homework 6
(pdf - due 12/19) Mat files: pychopathy, fisherData |
|
Tue, Dec 5 |
Model fitting: errors, optimization, overfitting, ridge (L2) and LASSO (L1) regression Zoom recording, whiteboard (pdf) |
||
Thu, Dec 7 |
Clustering: K-means, Hierarchical (mixture) models, soft K-means Zoom recording, whiteboard (pdf) |
||
Fri, Dec 8 | Lab: Regularization, classification, clustering | ||
Tue, Dec 12 |
Model fitting: Example: Fitting an LNP model to neural responses via
STA Zoom recording, whiteboard (pdf) |
Slides: model fitting examples (pdf) | |
Thu, Dec 14 |
Encoding/decoding: Spike-triggered analysis, population decoding Zoom recording, whiteboard (pdf) |
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