# Limitations to Estimating Mutual Information in Large Neural Populations

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## Abstract

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## 1. Introduction

## 2. Results

#### 2.1. Analysis of a Computational Model of Sensory Processing Regarding Estimating Information Theoretic Quantities

#### 2.2. Computing the Probability of a Finite Number of Independent and Identically Distributed Random Variables being Mutually Different

## 3. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**A computational model of sensory processing. We consider a population of N neurons, illustrated irrespective of the physical location as points in the plane on the left-hand side that is exposed to the presentation of a stimulus, which is modelled by a random variable S. The (measured) activity of this population, illustrated as spiking activity on the right-hand side over the presentation of two different values of the stimulus, is modelled by a vector-valued random variable $X\equiv {\u2a02}_{n=1}^{N}{X}^{\left(n\right)}$. For every stimulus value s, we assume there exists a subset of the population, ${U}_{s}$, depicted as circular regions on the plane, such that, intuitively, the neurons within this subpopulation are receptive to the particular stimulus value. Conversely, the neurons in the complement of that set in $\left\{1,\dots N\right\}$, ${U}_{\u2aebs}$, are assumed to be not receptive to that stimulus value and to activate independently according to a common noise profile. As an example, the sets for stimulus values s and ${s}^{\prime}$ are highlighted. Neurons from any of the two sets are shown to have an increased spiking activity during the presentation of the corresponding stimulus value. In contrast to this activity, others are shown to be rather sporadically active.

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Mölter, J.; Goodhill, G.J. Limitations to Estimating Mutual Information in Large Neural Populations. *Entropy* **2020**, *22*, 490.
https://doi.org/10.3390/e22040490

**AMA Style**

Mölter J, Goodhill GJ. Limitations to Estimating Mutual Information in Large Neural Populations. *Entropy*. 2020; 22(4):490.
https://doi.org/10.3390/e22040490

**Chicago/Turabian Style**

Mölter, Jan, and Geoffrey J. Goodhill. 2020. "Limitations to Estimating Mutual Information in Large Neural Populations" *Entropy* 22, no. 4: 490.
https://doi.org/10.3390/e22040490