G80.3042.002 -- Fall, 2007

Statistical Analysis and Modeling of Neural Data

Instructors: Bijan Pesaran & Eero Simoncelli
Time: Mondays and Wednesdays, 9:15-10:55 am
Location: Meyer Hall, rm 815, 4 Washington Place
Prerequisites: Content of Mathematical Tools for Neural Science, including: calculus, linear algebra, linear systems theory, basic probability/statistics, basic estimation/decision, some matlab programming experience.

Brief Description:

A graduate course covering advanced tools for analysis and modeling of neural systems and data. The goal of the course is to provide fundamental mathematical, statistical and computational tools necessary to solve data analysis and modeling problems, the transformations of raw data into a form in which these tools may be utilized, and the interpretation of such analyses. Broadly speaking, the course will be divided into three sections: (1) Neural Encoding; (2) Neural Decoding; (3) Unsupervised Learning/Estimation. Lectures on each topic will include mathematical background, derivation of basic results, and examples relavent to neural science.

Schedule (updated incrementally):

 
Date Lecturer Topic Handouts Homework
5 Sep Pesaran/Simoncelli Intro to course
Some examples from the literature 		Course description
Student info sheet 		 
10 Sep Simoncelli Spiking models, fitting/estimation, nonparametric case Paper: Spike-triggered analysis (pdf)  
12 Sep Simoncelli Parametric models, maximum likelihood methods, optimization Slides (pdf)
Paper: Max likelihood fitting (pdf)   		 
17 Sep Pesaran Probabilistic models of point processes Slides (ppt)  
19 Sep Pesaran Point processes: measures of association I Slides (ppt)    
24 Sep Pesaran Point processes: measures of association II,
Spectral representation		 Slides (ppt)  
26 Sep Pesaran Point process coherence. Model validation. Slides (ppt) HW1 (pdf)
data file (mat)
Due: 10 Oct
1 Oct Simoncelli Fitting an LNP model  
3 Oct Simoncelli Fitting a GLM model Slides (pdf)  
8 Oct Columbus Day Holiday
10 Oct Simoncelli Decoding I: decisions from one neuron  
15 Oct Simoncelli Decoding II: multi-neuron decisions, estimation  
17 Oct Pesaran Temporal decoding I HW2 (pdf)
dmtspec.m, dpsschk.m
data file (mat)
Due: 31 Oct
22 Oct Pesaran Temporal decoding II: Kalman filter  
24 Oct Simoncelli Kalman: Interpretation & Examples  
29 Oct Simoncelli Estimation from neural responses:
ML, linear, Cramer-Rao bounds		 Slides (pdf)  
31 Oct Souheil Inati Estimation of brain activity from fMRI BOLD measurements Slides (pdf), Readings (zip)  
5 Nov No class: SfN meeting  
7 Nov No class: SfN meeting  
12 Nov Pesaran Spectral estimation I Slides (ppt)  
14 Nov Pesaran Spectral estimation II  
19 Nov Simoncelli Introduction to Information Theory  
21 Nov Jonathan Victor Information Theory: Experimental Data Analysis Slides (pdf)  
26 Nov Simoncelli Efficient Coding  
28 Nov Nathaniel Daw Models of Reinforcement Learning Slides (ppt) HW3 (pdf)
data file (mat)
Due: 7 Dec
3 Dec Simoncelli Efficient Coding  
5 Dec Pesaran Spike sorting Slides (ppt)  
10 Dec Pesaran Unsupervised learning  
12 Dec Simoncelli HW4 (pdf)
data file (mat)
Due: 17 Dec

Relevant Books:

  • Theoretical Neuroscience , by Dayan and Abbott. MIT Press, 2001.
  • Spikes: Exploring the Neural Code, by Rieke, Warland, de Ruyter, & Bialek. MIT Press, 1997.
  • Spiking Neuron Models: Single Neurons, Populations, Plasticity, by Gerstner and Kistler. Cambridge University Press, 2002.
  • Pattern Classification, by Duda, Hart and Storck. Wiley, 2001.
  • All of Statistics, by Larry Wasserman.

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