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Limitations to Estimating Mutual Information in Large Neural Populations
Jan Mölter1, Geoffrey J Goodhill1
1Queensland Brain Institute & School of Mathematics and Physics, The University of Queensland, St. Lucia, QLD 4072, Australia.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
Estimating information theory metrics like mutual information from neural population data is challenging. For large populations, direct estimation leads to maximal bias, suggesting new methods are needed for accurate sensory processing analysis.
Area of Science:
- Computational neuroscience
- Information theory
- Systems neuroscience
Background:
- Information theory quantifies sensory stimulus representation in neural activity.
- Estimating information-theoretic quantities (entropy, mutual information) from finite neural data samples is difficult and prone to bias.
- Bias is particularly severe in large neural populations.
Purpose of the Study:
- To investigate the impact of large neural populations on information-theoretic analyses.
- To demonstrate a combinatorial argument explaining the bias in direct estimation methods.
- To highlight the need for alternative analytical approaches in computational neuroscience.
Main Methods:
- Analysis of a simple sensory processing model.
- Application of a combinatorial argument to neural population activity.
- Evaluation of direct estimation of mutual information using empirical histograms.
Main Results:
- For large neural populations, finite samples of neural activity are likely to be mutually distinct.
- Direct estimation of mutual information from empirical histograms equals stimulus entropy, indicating maximal bias.
- This bias is independent of the specific stimulus-neural activity relationship.
Conclusions:
- Direct estimation of information-theoretic quantities is unreliable for large neural populations due to maximal bias.
- Current methods are insufficient for accurate analysis of sensory coding in complex neural systems.
- Development of alternative, bias-corrected methods is crucial for advancing information theory applications in neuroscience.

