| Instructor(s): | Nathaniel Daw & Eero Simoncelli |
| Teaching Assistant(s): |
Catherine Olsson (catherio AT nyu DOT edu), and Alexander Rich (asr443 AT nyu DOT edu) |
| Time: |
Lectures: Monday/Wednesday, 10:00-11:50am Labs: selected Fridays, 9:30-noon |
| Location: |
Lectures: Meyer Hall (4 Washington Place), Rm. 771 Labs: Meyer Hall, Rm. 815 |
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, 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 prerequisite is an aptitude for
logical and geometric reasoning, and a willingness to work hard!
Class discussions/information are communicated within
Piazza
| Date | Topic | Handouts | Homework |
|---|---|---|---|
| Wed, Sep 3 |
Introduction to the course Linear algebra I: vectors, vector spaces, inner products |
Course description
(pdf) Matlab primer (pdf) (also, see links below) |
|
| Fri, Sep 5 | Lab: Matlab I: variables, operations, basic graphics, scripts |
Lab 1 script file Homework format: instructions, example |
Before lab, install matlab
(info) Homework 0 (optional) (pdf) |
| Mon, Sep 8 | Linear algebra II: projection, linear systems, matrices | ||
| Wed, Sep 10 | Linear Algebra III: orthogonal & diagonal matrices, geometry | Notes: Linear algebra | Homework 1, due: 19 Sep |
| Fri, Sep 12 | Lab: Matlab II: conditionals, iteration, functions |
Lab 2 script file |
|
| Mon, Sep 15 | Linear algebra IV: singular value decomposition, nullspaces, rangespaces | ||
| Wed, Sep 17 | Linear Algebra V: singular value decomposition, rangespace, nullspace, inverse | ||
| Fri, Sep 19 |
Lab 3: geometry of
SVD |
Notes: SVD geometry (scanned PDF) | |
| Mon, Sep 22 | Extended Example: Color-matching and Trichromacy | ||
| Wed, Sep 24 | Regression I | Notes: Least Squares fitting/regression |
Homework 2,
due: 10 Oct Files: colmatch.mat, regress1.mat |
| Fri, Sep 26 | Lab 4: Regression | Blackboard explanations, example code | |
| Mon, Sep 29 | Regression II | ||
| Wed, Oct 1 | Regression III: total least squares, Principal components analysis | ||
| Fri, Oct 3 | [no lab] | ||
| Mon, Oct 6 | Linear Shift Invariant Systems, Convolution | ||
| Wed, Oct 8 | LSI systems and sinusoids, Fourier transform |
Slides:
LSI systems, LSI introduction |
|
| Fri, Oct 10 | Lab 5: Sinusoids, Fourier | ||
| Mon, Oct 13 | [no class - Fall break] | ||
| Wed, Oct 15 | The convolution theorem, examples | ||
| Fri, Oct 17 | Lab 6: More Fourier | ||
| Mon, Oct 20 | Frequency domain, visualization, examples | ||
| Wed, Oct 22 | Probability & Statistics I: Experimental measurements & inference, random variables |
Homework 3,
due: 5 Nov Files: PCA.mat, unknownSystem1.p, unknownSystem2.p, unknownSystem3.p |
|
| Fri, Oct 24 | [no lab] | ||
| Mon, Oct 27 | Prob II: Distributional manipulations, joint/marginal densities (coins) | ||
| Wed, Oct 29 | Prob III: expectation, confidence intervals, moments | ||
| Fri, Oct 31 | Lab: Probability, distributions, simulation | ||
| Mon, Nov 3 | Prob IV: Sample mean, sample variance, Univariate Gaussians | ||
| Wed, Nov 5 | Prob V: multi-variate Gaussians, marginals, conditinals | ||
| Fri, Nov 7 | Mini-lab: review | ||
| Mon, Nov 10 | More Gaussians, regression | ||
| Wed, Nov 12 | Generalized Linear Models | Homework 4, due: 26 Nov | |
| Fri, Nov 14 | [no lab] | ||
| Mon, Nov 17 | [no class - SfN Meeting] | ||
| Wed, Nov 19 | [no class - SfN Meeting] | ||
| Fri, Nov 21 | Lab: debugging | ||
| Mon, Nov 24 | Hierarchical models, GLMs | Notes: Statistics | |
| Wed, Nov 26 | Spike-triggered averages, Classification images | ||
| Fri, Nov 28 | [no lab - Thanksgiving] | ||
| Mon, Dec 1 | Model comparisons, overfitting | ||
| Wed, Dec 3 | More Spike-triggered analysis, Bootstrapping | Handout: Bootstrapping | Homework 5, due: 19 Dec |
| Fri, Dec 5 | Mini-lab: model comparison, bootstrapping, permutation tests |
Electrons:
- Online matlab help at The MathWorks | Tutorial at the MathWorks | Intro video at MIT | Antonia Hamilton's Tutorial | at Indiana U. | at U. Utah
- Linear Algebra Appendix from PDP series, by Michael Jordan. (pdf)
- Online lecture videos from Gilbert Strang's course at MIT
- Todd Will's Interactive Intro to the SVD
- Thomas Minka's On-line Glossary of Statistical Pattern Recognition
- Wolfram Research World of Mathematics
- History of various topics in mathematics
Dead Trees:
- Matlab:
Getting Started with MATLAB; A Quick Introduction for Scientists and Engineers, R. Pratap, Oxford U. Press, 2009.
Matlab for Neuroscientists. An introduction to scientific computing in Matlab, P. Wallisch, M. Lusignan, M. Benayoun, T. Baker, A. Dickey & N. Hatsopoulos, Elsevier Press, 2008.
Mastering MATLAB, B. L. Littlefield & D. C. Hanselman, Prentice-Hall, 2011.- Linear Algebra / Least Squares:
Linear Algebra and Its Applications, by Gilbert Strang. Academic Press, 1980.- Linear (shift-invariant) Systems:
Discrete-time Signal Processing, A. Oppenheim & R. Schafer. Prentice Hall, 1989.
The Fourier transform and its applications, R. Bracewell, McGraw Hill Science, 1999.
Fast Fourier transform and its applications, E. Brigham, Prentice Hall, 1988.- Probability/Statistics:
Statistics, Freedman, Pisani, Purves, Norton, 2007 (4th ed.)
Mathematical statistics, J. E. Freund, Prentice Hall, 1992.- Decision Theory:
Biology: Elementary Signal Detection Theory, by Thomas D. Wickens. Oxford University Press, 2001.
Signal Detection Theory and Psychophysics, by David Green & John Swets. Peninsula Publishing, 1988.
Math: Statistical Decision Theory, by James O. Berger. Springer-Verlag, 1980.
Chapter 2 of Pattern Classification, by Duda, Hart and Storck. Wiley, 2001.- Bootstrap/Resampling:
An Intoduction to the Bootstrap, by Bradley Efron and Robert Tibshirani. Chapman & Hall, 1998.
Resampling Methods: A practical guide to data analysis, by Phillip Good. Birkhäuser, 1999.- Spikes, Neural Coding, Reverse Correlation:
Spikes: Exploring the Neural Code, by Fred Rieke, David Warland, Rob De Ruyter, & Bill Bialek. MIT Press, 1997.- Computational/Theoretical Neuroscience:
Theoretical Neuroscience , by Peter Dayan and Larry Abbott. MIT Press, 2001.
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