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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
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