Moment-closure approaches to statistical mechanics and inference in models of neural dynamics

At the upcoming SAND meeting in Pittsburgh, I'll be presenting our recent work on using moment closures to combine theoretical models with statistical inference. This work has already been published, but this poster provides a quick summary. 

In my postdoc at Edinburgh, I worked on methods to combine neural field modelling and statistical inference. Neural field models capture how microscopic actions of single neurons combine to create emergent collective dynamics. Statistical modelling of spiking data commonly uses Poisson point-process models. These projects combined the two in an interesting way. 

In "autoregressive point-processes as latent state-space models" [PDF], we convert a popular statistical model for spike-train data into a neural field model. This neural field model is a bit unusual: it extends over time rather than space, and describes correlations as well as mean firing rates. This may lead to new tricks for inference and coarse-graining on these types of models. 

In "neural field models for latent state inference", we use a microscopic model of retinal waves to specify a second-order neural field model that doubles as a latent state-space model for spiking observations. This advances methods for developing data-driven neural field models.

[download poster PDF]

Abstract: 

Integrating large-scale neuronal recordings with models of emergent collective dynamics remains a central problem in statistical neuroscience. We illustrate a moment-closure approach to relate mechanistic descriptions of neural spiking to state-space models amenable to recursive Bayesian estimation. We focus on two classes of models common in computational neuroscince: autoregressive point-processes, which are commonly used to model spiking populations, and neural field models, which are popular analytically-tractable models of spatiotemporal dynamics. Inspired by recent advances in modelling of chemical reaction systems, the moment-closure approach yields tractable low-order approximations of the evolving population state distributions. These approximations capture how fluctuations and correlations interact with nonlinearities, and can be interpreted as latent state-space models of neural spiking activity. In the case of autoregressive point-process models, moment-closure provides a coarse-graned description of the system that captures nonlinear and stochastic effects on the slow dynamics. In the case of neural field models, moment-closure provides a model of both the mean-field and two-point correlation functions, and accounts for finite-size effects and correlations. Overall, moment closure methods provide a tractable route to low-dimensional approximations of population dynamics, and suggest a promising route forward for model coarse-graining that can be integrated with experimental datasets. 

Many thanks again to Gerrit Hilgen, Evelyne Sernagor, David Schnoerr, Dimitris Milios, Botond Cseke, Guido Sanguinetti, and Matthias Hennig. The papers described in this poster can be cited as:

Rule, M. and Sanguinetti, G., 2018. Autoregressive point processes as latent state-space models: A moment-closure approach to fluctuations and autocorrelations. Neural Computation, 30(10), pp.2757-2780.

Rule, M.E., Schnoerr, D., Hennig, M.H. and Sanguinetti, G., 2019. Neural field models for latent state inference: Application to large-scale neuronal recordings. PLoS computational biology, 15(11), p.e1007442.