EFFICIENT APPROXIMATION OF NEURAL POPULATION STRUCTURE AND CORRELATIONS WITH PROBABILISTIC CIRCUITS

Abstract

We present a computationally efficient framework to model a wide range of population structures with high order correlations and a large number of neurons. Our method is based on a special type of Bayesian network that has linear inference time and is founded upon the concept of contextual independence. Our framework is both fast and accurate in approximating neural population structures. Furthermore, our approach enables us to reliably quantify higher order neural correlations. We test our method on simulated neural populations commonly used to generate higher order correlations, as well as on publicly available large-scale neural recordings from the Allen Brain Observatory. Our approach significantly outperforms other models both in terms of statistical measures and alignment with experimental evidence.

1. INTRODUCTION

With the rise and fast growth of simultaneous neural population recording, modeling population structures and measuring correlations has become a focus of computational neuroscience (Abbott & Dayan, 1999; Averbeck et al., 2006; Azeredo da Silveira & Rieke, 2021; Urai et al., 2022) . Theoretical and Experimental works have demonstrated the necessity of measuring population correlations to investigate information coding (Moreno-Bote et al., 2014; Averbeck et al., 2006) , functional connectivity (Dunn et al., 2015) , learning (Ganmor et al., 2011), and arousal (Vinck et al., 2015; Doiron et al., 2016) . Despite significant progress in recent years, research on measurement and analysis of population correlations still faces significant challenges (Kohn et al., 2016) . Exact measurement of population correlations is an NP-hard problem in the general case since it requires computing every form of dependency among spiking neurons. As a result, researchers have tried to come up with computationally efficient ways of approximation or indirect measurement of neural correlations. Existing approaches are energy-based models rooted in statistical mechanics where the energy function incorporates couplings between subsets of variables (here neurons) (Roudi et al., 2009c; Tkačik et al., 2006; Sohl-Dickstein et al., 2011; Aurell & Ekeberg, 2012) . However, these methods often carry auxiliary (and even unrealistic) assumptions about the neural dynamics and do not scale up for large populations (Roudi et al., 2009b) . Notably, generative models commonly used in other domains such as latent variable methods are often not applicable to neural populations as spiking neural data is discrete and sparse (Zhao et al., 2020) . Furthermore, various parameters such as behavioural and emotional state of the animal affect firing patterns of neurons even in sensory cortex (Urai et al., 2022) . As a result, a recording long enough to train these models contains many external variable changes and confounding factors that make drawing scientific conclusions difficult.

