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Neural characterization Ingredients:
- stimuli
- response model
- estimation method
Characterization of Neural Responses with Stochastic Stimuli Eero - - PowerPoint PPT Presentation
Characterization of Neural Responses with Stochastic Stimuli Eero - - PowerPoint PPT Presentation
Characterization of Neural Responses with Stochastic Stimuli Eero P. Simoncelli Howard Hughes Medical Institute Center for Neural Science, and Courant Institute of Mathematical Sciences New York University http://www.cns.nyu.edu/ eero
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Stochastic stimuli and the spike-triggered ensemble
response stimulus t
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Stochastic stimuli and the spike-triggered ensemble
response stimulus t stimulus component 1 stimulus component 2
6×8 stimulus block
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Stochastic stimuli and the spike-triggered ensemble
response stimulus t stimulus component 1 stimulus component 2
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Stochastic stimuli and the spike-triggered ensemble
response stimulus t stimulus component 1 stimulus component 2
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Stochastic stimuli and the spike-triggered ensemble
response stimulus t stimulus component 1 stimulus component 2
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Standard V1 models
Simple cell Complex cell +
Linear → Nonlinear → Poisson (LNP)
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Spike-triggered average (STA)
response stimulus t stimulus component 1 stimulus component 2
STA
Simple LNP characterization:
- STA can provide an unbiased estimate of the linear filter
- Nonlinearity can be estimated thereafter ...
[Chichilnisky, ’01]
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Estimating the firing rate nonlinearity
firing rate
- rthogonal axis response
# stimuli # spikes # stimuli # spikes firing rate STA response
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Failure for symmetric nonlinearity
+ Complex cell model
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Spike-triggered covariance (STC)
10 20 30 40 1 1.5 2 eigenvalue number variance e1 e26 e1 e26
[deRuyter & Bialek, ’88; Schwartz, Chichilnisky & Simoncelli, ’01]
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Spike-triggered covariance, complex cell model
10 20 30 40 1 1.5 2 eigenvalue number variance e1 e2 e26 e1 e2
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Estimating the (2D) firing rate nonlinearity
e2 response e1 response
firing rate # stimuli # spikes # stimuli # spikes histogram firing rate histogram
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V1 simple cell
space sf
STA
time tf
[Rust, Schwartz, Movshon & Simoncelli, CNS*03]
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V1 simple cell
space sf eigenvalue number 50 100 150 200 250 0.2 0.6 1 1.6 1.8
STA
variance time tf
STC [Rust, Schwartz, Movshon & Simoncelli, CNS*03]
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V1 complex cell
50 100 150 200 250 0.2 0.4 1 1.6 1.8 eigenvalue number space sf
STA
variance time tf
STC [Rust, Schwartz, Movshon & Simoncelli, CNS*03]
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V1 population statistics
1 2 3 4 5 6 5 15 5 15 1 2 3 4 5 6 5 15 5 15 Simple (n = 15) Complex (n = 20) # Excitatory eigenvectors # Suppressive eigenvectors = Predictions of standard models
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Pairwise firing rate nonlinearities
- Simple
Complex
e1 response ST A response e255 response e255 response e1 response e2 response e254 response e254 response
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Excitatory/suppressive pooling model
Sum
- f
squares Sum
- f
squares
?
(STA)
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Simple cell
1.00 0.52 0.27 0.27 0.78 0.78 1.00 1.00
Subtractive Divisive
Pooled suppressive signal Pooled excitatory signal Sum
- f
squares Sum
- f
squares
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Complex cell
1.00 0.98 0.75 0.73 0.58 0.58 0.62 0.67 0.77 0.82 0.94 1.00 0.45 Subtractive Divisive
Sum
- f
squares Pooled suppressive signal Pooled excitatory signal Sum
- f
squares
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Conclusions
- STC characterization with stochastic stimuli can yield a more
complete description of neural response
- Direction-selective V1 simple/complex cells exhibit multiple
excitatory and suppressive components
- These components are combined in a simple fashion
- To do:
– Model validation with optimized stimuli – Modified analysis for non-Poisson spiking models – Application to other areas (retina, V2, V4, MT)
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