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Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

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Page 1: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators
Page 2: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Spike Train decoding

Page 3: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Spike Train decoding

Page 4: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Spike Train decoding

Page 5: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Summary

• Decoding of stimulus from response– Two choice case

• Discrimination• ROC curves

– Population decoding• MAP and ML estimators• Bias and variance• Fisher information, Cramer-Rao bound

– Spike train decoding

Page 6: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Chapter 4

Page 7: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Entropy

Page 8: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Entropy

Page 9: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Mutual information

H_noise< H

Page 10: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Mutual information

Page 11: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

KL divergence

Page 12: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Continuous variables

Page 13: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Entropy maximization

Page 14: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Entropy maximization

Page 15: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Population of neurons

Page 16: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Retinal Ganglion Cell Receptive Fields

Page 17: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Retinal Ganglion Cell Receptive Fields

Page 18: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Retinal Ganglion Cell Receptive Fields

Page 19: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Retinal Ganglion Cell Receptive Fields

Page 20: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Retinal Ganglion Cell Receptive Fields

Page 21: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Temporal processing in LGN

Page 22: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Temporal processing in LGN

Page 23: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Temporal processing in LGN

Page 24: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Temporal vs spatial coding

Page 25: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Entropy of spike trains

Page 26: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Entropy of spike trains

Page 27: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Entropy of spike trains

Page 28: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Entropy of spike trains

• Spike train mutual information measurements quantify stimulus specific aspects of neural encoding.

• Mutual information of bullfrog peripheral auditory neurons was estimated– 1.4 bits/sec for broadband noise stimulus– 7.8 bits/sec for bullfrog call-like stimulus

Page 29: Spike Train decoding Summary Decoding of stimulus from response –Two choice case Discrimination ROC curves –Population decoding MAP and ML estimators

Summary

• Information theory quantifies how much a response says about a stimulus– Stimulus, response entropy– Noise entropy– Mutual information, KL divergence

• Maximizing information transfer yields biological receptive fields– Factorial codes– Equalization– Whitening

• Spike train mutual information