Predictive information in a sensory population
Summary
The challenge for prediction lies in the fact that not all features in the past are predictive about the future. Therefore, intuitively, it would be more efficient for the retina to retain only the information that has predictive power about the future. In this paper, the authors show that in a group of retinal cells, nearly every cell participates in different sub-groups where their total predictive information is close to the limit set by the statistical properties of the input.
Predictive Power
The activity of N neurons can form a binary word Wt. Wt will be maximally informative about the position of the object at some time in the past due to delays. What’s important is that it also provides information about the future. We observe that:
1) The window over which predictions can be made is consistent with the correlations in the stimulus (Fig.1 B, C).
2) The information per spike decreases as the number of neuron increases, however crossover occurs for a certain time into the future (Fig.1 B).
The challenge for prediction lies in the fact that not all features in the past are predictive about the future. Therefore, intuitively, it would be more efficient for the retina to retain only the information that has predictive power about the future. In this paper, the authors show that in a group of retinal cells, nearly every cell participates in different sub-groups where their total predictive information is close to the limit set by the statistical properties of the input.
Predictive Power
The activity of N neurons can form a binary word Wt. Wt will be maximally informative about the position of the object at some time in the past due to delays. What’s important is that it also provides information about the future. We observe that:
1) The window over which predictions can be made is consistent with the correlations in the stimulus (Fig.1 B, C).
2) The information per spike decreases as the number of neuron increases, however crossover occurs for a certain time into the future (Fig.1 B).
Bounds on Predictability
The predictive power is limited by the information the past provides about the future (on the structure of the world). If we want to have a certain amount of predictive power in the future, we must provide at least some lower bound of information regarding the past. Similarly, if we have some amount of information about the past, there is a limit to the predictive power we can have. This is an example of the information bottleneck problem.
We may know the position and velocity to a certain range, for example the error ellipses. In the next time step, these ellipses evolve (purple and green points in Fig.2). Depending on the orientation of the ellipses, even if they have the same size, the information to keep so that we can have maximum predictive power is different (position yields more predictive information in this case).
Writer: Belle Liu
Disclaimer: These pictures are from the original paper linked down below.
Original Paper: Predictive information in a sensory population. Stephanie E. Palmer, Olivier Marre, Michael J. Berry, William Bialek. Proceedings of the National Academy of Sciences Jun 2015, 112 (22) 6908-6913; DOI:10.1073/pnas.1506855112
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