| Instructors: | Nathaniel Daw & Eero Simoncelli |
| Teaching Assistant: | Deep Ganguli (dganguli AT cns DOT nyu DOT edu) |
| Lectures: | Monday/Wednesday, 9:10-10:55am |
| Location: | Meyer Hall (4 Washington Place), Rm. 809 |
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| Date | Topic | Handouts | Homework |
| Wed, Sep 3 (Eero) |
Linear Algebra I: vectors, inner products |
Course Description (pdf) Background Poll (pdf) Linear Algebra handout (pdf) |
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| Fri, Sep 5 3:30-5:30, rm 460 |
Matlab session I: interpreter, syntax, basic commands, plotting |
Matlab Primer (pdf) (also, see links below) |
hw1 (pdf), due 12 Sep |
| Mon, Sep 8 (Eero) |
Linear Algebra II: linear systems, matrices, orthogonal transforms | ||
| Wed, Sep 10 (Eero) |
Linear Algebra III: diagonal matrices, SVD | ||
| Mon, Sep 15 (Eero/Nathaniel) |
Linear Algebra IV: nullspaces, inverses Intro to Trichromacy |
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| Tue, Sep 16 3:30-5:30, rm 460 |
Matlab session II: loops, scripts, functions, recursion |
hw2 (pdf), due 23 Sep |
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| Wed, Sep 17 (Nathaniel) |
Trichromacy |
hw3 (pdf), mat files: colmatch, mtxExamples due 1 Oct |
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| Mon, Sep 22 (Nathaniel) |
Regression I: least-squares data fitting | Least Squares handout (pdf) | |
| Wed, Sep 24 (Nathaniel) |
Regression II: incorporating linear or quadratic constraints | ||
| Mon, Sep 29 (Nathaniel) |
Regression III: Total least squares, quadratic constraints | ||
| Wed, Oct 1 (Eero) |
Elliptical geometry of TLS regression | ||
| Mon, Oct 6 (Eero) |
Principal Component Analysis, Eigenvectors |
hw4 (pdf), mat files: regress1, regress2, wtdDataSet, PCA, outlierData, constrainedLS due 20 Oct |
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| Wed, Oct 8 (Eero) |
Intro to linear shift-invariant systems | ||
| Mon, Oct 13 | No Class (Columbus day holiday) | ||
| Wed, Oct 15 (Deep) |
LSI systems and sinusoids The Fourier Transform |
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| Mon, Oct 20 (Eero) |
The Convolution theorem | ||
| Wed, Oct 22 (Eero) |
Convolution Theorem II, Fourier examples | ||
| Mon, Oct 27 (Eero) |
Complex exponentials, 2D Fourier transformas | LSI/Fourier handout (pdf) |
hw5 (pdf), m-files: unknownSystem1, unknownSystem2, cconv2 due: 10 Nov. |
| Wed, Oct 29 (Nathaniel) |
Probability intro: densities, marginals, conditionals, Bayes rule | ||
| Mon, Nov 3 (Nathaniel) |
Probability II: transformations, sums of random variables, expectation, moments | ||
| Wed, Nov 5 (Nathaniel) |
Probability III: Gaussian densities, central limit theorem | ||
| Mon, Nov 10 (Nathaniel) |
Statistical estimation: ML, MAP, Bayes | Probability & decision handout (pdf) | |
| Wed, Nov 12 (Nathaniel) |
Statistical Estimation: examples | ||
| Mon, Nov 17 | No class: SfN meeting | ||
| Wed, Nov 19 | No class: SfN meeting |
hw6 (pdf), m-files: blackBox, due: 5 Dec |
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| Mon, Nov 24 (Eero) |
Example: neural characterization | ||
| Wed, Nov 26 (Eero) |
Bias, variance | ||
| Mon, Dec 1 (Eero) |
Example continued: neural characterization | ||
| Wed, Dec 3 (Eero/Nathaniel) |
Bootstrapping / Decision theory intro |
Review article on spike-triggered averaging:
Chichilnisky01 Two chapters on bootstrapping: Efron93 |
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| Mon, Dec 8 (Nathaniel) |
Decision, Signal Detection Theory |
hw7 (pdf), m-files: neurometricData, simulateSNL, makeWhiteNoise, fisherData due: 17 Dec |
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| Wed, Dec 10 (Nathaniel) |
Multi-dimensional decisions, Fisher linear discriminants |
Electrons:
- Online matlab help at The MathWorks | at MIT | at U. Florida | at U. Utah
- Linear Algebra Appendix from PDP series, by Michael Jordan. (pdf - 3Mbytes)
- 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:
- Linear Algebra / Least Squares:
Linear Algebra and Its Applications, by Gilbert Strang. Academic Press, 1980.- Linear (shift-invariant) Systems
Discrete-time Signal Processing, by Alan Oppenheim and Ron Schafer. Prentice Hall, 1989.- Probability/Statistics:
Probability and Statistics, by Morris DeGroot and Mark Schervish. Addison-Wesley, 2002.- 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.- Computationa/Theoretical Neuroscience:
Theoretical Neuroscience , by Peter Dayan and Larry Abbott. MIT Press, 2001.
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