P153 Efficient estimation of mutual-information rates from spiking data by maximum-entropy models
Tobias Kühn*1, Gabriel Mahuas1, Ulisse Ferrari1
1Institut de la Vision, Sorbonne Université, CNRS, INSERM, Paris, France
*Email: tkuehn@posteo.de
Introduction
Neurons in sensory systems encode stimulus information into their stochastic spiking response. This is quantified by the mutual-information rate (MIR), given by the ratio of the mutual information between the activity of a spiking neuron and a (dynamical) stimulus and time. The computation of the MIR is challenging, because it requires the estimation of entropies, in particular the ones conditional on the stimulus. However, this is difficult in the realm of correlated, poorly sampled data, for which estimates are prone to biases.
Methods
We here present moment-based the mutual-information-rate approximation (Moba-MIRA), a computational method to estimate the MIR. It is based on the idea of taking into account the statistics of the activity single time bins exactly and consider the correlations of the activity between them by employing a statistical model featuring pairwise interactions, similar to the Ising model of statistical physics. This is similar to other maximum-entropy approaches employed in neuroscience, however, we do not restrict our spike counts to be binary, allowing the use of relatively large time bins. To achieve the estimate of the entropies, we use a (Feynman) diagrammatic expansion in the covariances between the activities of all time bins [1,2,3].
ResultsWe test our method on artificial data from a generalized linear model mimicking the activity of retinal ganglion cells and demonstrate that we approximate the exact result in the well-sampled regime in a satisfactory way. Importantly, our method introduces only a limited bias even in case of a number of samples attainable in experiments, about 60 to 100, allowing it to use it for to real data. Applying it to ex-vivo electrophysiological recordings from rat retinal-ganglion cells (on and off), stimulated by black-and-white checkerboards or bars moving in a random way, we obtain information rates of about 2 to 20 bits/s for every neuron, consistent with values from the literature.
DiscussionTested on artificial data, Moba-MIRA outperforms the state-of-the-art method [4] - depending on the variant clearly in speed, with comparable precision, or in precision, with comparable speed, compare figure. We therefore believe that it can serve as a efficient and simple tool for the analysis of spiking data. In particular, extending it to be applicable to populations of neurons is easy, so that it will allow the study of collective effects in addition to the effects coming about by neuronal dynamics.
Figure 1. a) Estimate of the MIR for artificial, retina-like data with state-of-the-art method by Strong et al. (histogram) and our approach. In the latter, we estimate the entropy conditional on the stimulus by a maximum-entropy model, for which we show the compute time in panel b.
Acknowledgements
We acknowledge ANR for financial support.
References
[1] Tobias Kühn and Moritz Helias. Expansion of the effective action around non-gaussian theories. Journal of Physics A: Mathematical and Theoretical, 51(37):375004, Aug 2018.
[2] Tobias Kühn and Frédéric van Wijland. Diagrammatics for the inverse problem in spin systems and simple liquids. Journal of Physics A: Mathematical and Theoretical, 56(11):115001, Feb 2023.
[3] Gabriel Mahuas, Olivier Marre, Thierry Mora, and Ulisse Ferrari. Small-correlation expansion to quantify information in noisy sensory systems. Phys. Rev. E, 108:024406, Aug 2023.
