1 / 17

NEU 501: From Molecules to Systems

NEU 501: From Molecules to Systems. Module 6: Neural Coding Class 3: Spike-Triggered Covariance Analysis Michael J Berry II Wednesday, Dec. 4, 2013. Determining The LN Model. 1) Find the spike-triggered stimulus average (STA ) 2) Linear filter must be time-reversed STA

amena-morrow
Download Presentation

NEU 501: From Molecules to Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. NEU 501:From Molecules to Systems Module 6: Neural Coding Class 3: Spike-Triggered Covariance Analysis Michael J Berry II Wednesday, Dec. 4, 2013

  2. Determining The LN Model 1) Find the spike-triggered stimulus average (STA) 2) Linear filter must be time-reversed STA 3) Find the effective stimulus, s1(t) 4) Sample s1(t) at the times of spikes 5) Use Bayes’ Rule to find the nonlinear function

  3. Model of Neural Representation • what if the LN model is inadequate? • generalization to more complex dependence on stimulus

  4. Dimensionality Reduction

  5. Linear Response:Convolution = Vector Projection • Algebraic vs. Geometric pictures:

  6. Determining linear features from white noise

  7. Identifying Multiple Stimulus Features • Calculate the covariance matrix: • Subtract off the stimulus covariance in the prior distribution: Spike-triggered stimulus covariance Spike-triggered stimulus average

  8. Covariance Analysis

  9. Identifying Multiple Stimulus Features II • Diagonalize the covariance matrix • Look at the spectrum of eigenvalues: – the number of eigenvaluesthat are significantly different from zero is the number of stimulus features that affect the neuron’s spiking – the corresponding eigenvectors are the relevant stimulus features (or span the relevant stimulus subspace)

  10. Back to the Neural Model • multiple stimulus features from significant eigenvalues • linear filtering = convolution = projection

  11. A Toy Example: Filter-and-Fire Model

  12. Covariance Analysis of Filter-and-Fire Model

  13. Biological Variation & Dimensionality Reduction • Principle Components Analysis (PCA)

  14. Determining linear features from white noise

  15. The Covariance Matrix

  16. Summary • Building coding models using the correlation between stimulus and response • More detailed analysis of this correlation yields richer, more accurate models • Problem sets will explore how to build such models

  17. The END

More Related