1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]
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Transcript of 1 2 Spike Coding Adrienne Fairhall Summary by Kim, Hoon Hee (SNU-BI LAB) [Bayesian Brain]
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2 Spike Coding2 Spike Coding
Adrienne FairhallSummary by Kim, Hoon Hee (SNU-BI LAB)
[Bayesian Brain]
(C) 2007 SNU CSE Biointelligence Lab
Spike CodingSpike Coding
Spikes information Single Sequences
Spike encoding Cascade model Covariance Method
Spike decoding
Adaptive spike coding
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(C) 2007 SNU CSE Biointelligence Lab 3
Spikes: What kind of Code?Spikes: What kind of Code?
(C) 2007 SNU CSE Biointelligence Lab
Spikes: Timing and InformationSpikes: Timing and Information
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Entropy
Mutual Information S: stimulus, R: response
Total Entropy Noise Entropy
(C) 2007 SNU CSE Biointelligence Lab
Spikes: Information in Single Spikes Spikes: Information in Single Spikes
Spike (r=1) No spike (r=0)
Noise Entropy
Information
Information per spike
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(C) 2007 SNU CSE Biointelligence Lab
Spikes: Information in Spike Sequences (1)Spikes: Information in Spike Sequences (1)
A spike train and its representation in terms of binary “letters.” N bins : N-letter binary words, w.
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P(w)
P(w|s(t))
(C) 2007 SNU CSE Biointelligence Lab
Spikes: Information in Spike Sequences (2)Spikes: Information in Spike Sequences (2)
Two parameters dt: bin width L=N*dtTotal :
duration of the word
The issue of finite sampling poses something of a problem for information-theoretic approaches
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Information rate
(C) 2007 SNU CSE Biointelligence Lab
Encoding and Decoding : Linear DecodingEncoding and Decoding : Linear Decoding
Optimal linear kernel K(t) Crs : spike-triggered average (STA) Css : autocorrelation
Using white noise stimulus
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(C) 2007 SNU CSE Biointelligence Lab
Encoding and Decoding: Cascade ModelsEncoding and Decoding: Cascade Models
Cascade Models
Decision function EX)
Two principal weakness It is limited to only one linear feature The model as a predictor for neural output is that it generate
only a time-varying probability, or rate. Poisson spike train (Every spike is independent.)
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(C) 2007 SNU CSE Biointelligence Lab
Encoding and Decoding: Cascade ModelsEncoding and Decoding: Cascade Models
Modified cascade model
Integrate-and-fire model
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(C) 2007 SNU CSE Biointelligence Lab
Encoding and Decoding: Finding Multiple FeaturesEncoding and Decoding: Finding Multiple Features
Spike-triggered covariance matrix
Eigenvalue decomposition of : Irrelevant dimensions : eigenvalues close to zero Relevant dimensions : variance either less than the
prior or greater.
Principal component analysis (PCA)
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(C) 2007 SNU CSE Biointelligence Lab
Examples of the Application of Covariance Methods (1)Examples of the Application of Covariance Methods (1)
Neural Model Second filter
Two significant modes(negative) STA is linear combination of f and f’. Noise effect Spike interdependence
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(C) 2007 SNU CSE Biointelligence Lab
Examples of the Application of Covariance Methods (2)Examples of the Application of Covariance Methods (2)
Leaky integrate-and-fire neuron (LIF)
C: capacitance, R: resistance, Vc: theshold, V: membrane potential Causal exponential kernel
Low limit of integration
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(C) 2007 SNU CSE Biointelligence Lab
Examples of the Application of Covariance Methods (3)Examples of the Application of Covariance Methods (3)
How change in the neuron’s biophysics Nucleus magnocellularis(NM) DTX effect
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Reverse correlation
(C) 2007 SNU CSE Biointelligence Lab
Using Information to Assess DecodingUsing Information to Assess Decoding
Decoding : to what extent has one captured what is relevant about the stimulus?
Use Bayse rule N-dimensional model Single-spike information
1D STA-based model recovers ~ 63%, 2D model recovers ~75%.
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(C) 2007 SNU CSE Biointelligence Lab
Fly large monopolar cells
Adaptive Spike Coding (1)Adaptive Spike Coding (1)
Adaptation (cat’s toepad)
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(C) 2007 SNU CSE Biointelligence Lab
Adaptive Spike Coding (2)Adaptive Spike Coding (2)
Although the firing rate is changing, we can use a variant of the information methods.
White noise stimulus Standard deviation
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Input/output relation