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Computational Issues when Modeling Neural Coding Schemes Albert E. Parker Center for Computational Biology Department of Mathematical Sciences Montana State University Collaborators: Alexander Dimitrov John P. Miller Zane Aldworth Thomas Gedeon Brendan Mumey
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Modeling Neural Coding Schemes
Albert E. Parker
Center for Computational Biology
Department of Mathematical Sciences
Montana State University
John P. Miller
Zane Aldworth Thomas Gedeon
Goal: Determine a coding scheme: How does neural ensemble activity represent information about sensory stimuli?
Major Problem: The search for a coding scheme requires large amounts of data
Idea: Model a part of a neural system as a communication channel using Information Theory. This model enables us to:
A quantizer or encoder, Q, relates the environmental stimulus, X, to the neural response, Y, through a process called quantization. In general, Q is a stochastic map
The Reproduction space Y is a quantization of X. This can be repeated: Let Yf be a reproduction of Y. So there is a quantizer
Use Mutual information to measure the degree of dependence between X and Yf.
Use Conditional Entropy to measure the self-information of Yfgiven Y
distinguishable classes of stimulus/response pairs
Stimulus and Response Classes
Problem: To determine a coding scheme between X and Y requires large amounts of data
Idea: Determine the coding scheme between X and Yf, a squashing (reproduction) of Y, such that: Yf preserves as much information (mutual information) with X as possible and the self-information (entropy) of Yf |Y is maximized. That is, we are searching for an optimal mapping (quantizer):
that satisfies these conditions.
Justification: Jayne's maximum entropy principle, which states that
of all the quantizers that satisfy a given set of constraints, choose
the one that maximizes the entropy.
maximize I(X,Yf ) over vertices of constraint space
Modeling the cricket cercal sensory system as a communication channel
Wind Stimulus and Neural Response in the cricket cercal systemNeural Responses (over a 30 minute recording) caused by white noise wind stimulus.
Time in ms. A t T=0, the first spike occurs
Some of the air current stimuli preceding one of the neural responses
Neural Responses (these are all doublets) for a 12 ms window
Quantization:A quantizer is any map f: Y -> Yf from Y to a reproduction space Yf with finitely many elements. Quantizers can be
To recover such a coding scheme, we