Mathematical Tools for Neural Science
| Instructor: | Eero Simoncelli |
| Teaching Assistant: | Mehrdad Jazayeri |
| Lectures: | Monday/Wednesday, 9:10-10:55am |
| Location: | Meyer Hall (4 Wash. Pl.), rm 809 |
 |
| Instructor: | Eero Simoncelli |
| Teaching Assistant: | Mehrdad Jazayeri |
| Lectures: | Monday/Wednesday, 9:10-10:55am |
| Location: | Meyer Hall (4 Wash. Pl.), rm 809 |
|
|
| Date | Topic | Handouts | Homework |
| Wed, Sep 6 | Linear Algebra I: vectors, inner products |
Course Description (pdf) Background Poll (pdf) |
|
| Fri, Sep 8 3:30-5:30, rm 460 |
Matlab session I | Matlab Primer (pdf) |
HW01(pdf) due 18 Sep |
| Mon, Sep 11 | No Class (Eero at HHMI) | ||
| Wed, Sep 13 1:30-3:30, rm 460 |
Matlab session IIa | ||
| Fri, Sep 15 3:30-5:30, rm 460 |
Matlab session IIb |
HW02(pdf) due 25 Sep |
|
| Mon, Sep 18 | Linear algebra II: Linear stystems, matrics |
Linear algebra notes (pdf) See also resources below |
|
| Wed, Sep 20 | Linear algebra III: diagonal and orthogonal matrices, SVD | ||
| Thu, Sep 21 3:45-5:45, rm 460 |
Matlab session III | ||
| Mon, Sep 25 |
Linear algebra IV: inverses, nullspace Trichromacy and color matching |
HW03 (pdf) mtxExamples (mat), plotVec (m) due 4 Oct, extended to 5 Oct |
|
| Wed, Sep 27 |
Trichromacy and color matching | ||
| Mon, Oct 2 | No Class (Yom Kippur) | ||
| Wed, Oct 4 | Regression I: Least squares, fitting with a basis |
Least Squares notes (pdf) See also resources below |
HW04 (pdf) colmatch (mat), due 12 Oct |
| Mon, Oct 9 | No Class (Eero at ICIP) | ||
| Wed, Oct 11 | No Class (Eero at ICIP) | ||
| Thu, Oct 12 1:00-3:00 Meyer Hall, Room 1024 |
Regression II: Total least squares, eigenvalues | ||
| Mon, Oct 16 | No Class (SfN meeting) | ||
| Wed, Oct 18 | No Class (SfN meeting) | ||
| Thu, Oct 19 3:00-5:00 Meyer Hall, Room 1024 |
Eigenvalues/Eigenvectors | ||
| Mon, Oct 23 |
Linear shift invariant systems I: definition, properties, sinusoids |
HW05 (pdf) due 1 Nov - extended to Nov 6. |
|
| Wed, Oct 25 |
Linear shift invariant systems II: Fourier transform | ||
| Mon, Oct 30 | Convolution Theorem | ||
| Wed, Nov 1 | Fourier examples/properties I: amplitude/phase, symmetries, periodicities, shifting | ||
| Mon, Nov 6 | Fourier examples/properties II: sinuoisoids, Gaussian, scaling, Gabor | ||
| Wed, Nov 8 | Sampling |
LSI notes (pdf) |
|
| Mon, Nov 13 | Two-dimensional LSI/Fourier | David Heeger's linear system notes | |
| Wed, Nov 15 | Probability intro: densities, marginals, conditionals, Bayes |
HW06 (pdf) problem 1 (2.35/2.36) cconv2 (m), mkRamp (m), mkSine (m) due 22 Nov. |
|
| Mon, Nov 20 | Probability: independence, cumulatives, transformations | ||
| Wed, Nov 22 | Probability: Expectation, mean, covariance, Gaussians | ||
| Mon, Nov 27 | Probability: Gaussians | ||
| Wed, Nov 29 | Probability: Estimation |
HW07 (pdf) due 11 Dec. [problem 3 optional] |
|
| Mon, Dec 4 | No Class (Eero at NIPS) | ||
| Wed, Dec 6 | Decision / Signal Detection theory [Mehrdad] | ||
| Mon, Dec 11 | Estimation under additive noise, standard errors |
HW08 (pdf) mat and m files in Homework directory due 18 Dec. |
|
| Wed, Dec 13 |
Bootstrapping Spike-triggered average and the LNP model |
||
| Thu, Dec 14 1pm, Meyer 1024 |
Spike-triggered average and the LNP model | ||
| Mon, Dec 18 Meyer 1024 |
Decisions based on neural response Fisher linear discriminant |
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.
|
| ||
| Revised: 11 December 2006. |
Feedback/comments to: |
Top of page |