Inferring unobserved neural field intensities from spiking observations

Edit: I am very happy to report that this work has now been published in PLoS Computational Biology.

I'll be presenting our ongoing work on merging neural field models with statistical inference at the Integrated Systems Neuroscience Workshop in Manchester, and at the Bernstein Conference in Göttingen. [get poster PDF]

What's exciting about this work is that it combines modelling principles from statistical physics and statistical inference. We start with a detailed microscopic model, and then construct a second-order neural field model, which is then used directly for statistical inference. Normally, neural field models are only treated as abstract, qualitative mathematical models, and are rarely integrated with data. 

Video: Simulation of 3-state Quiescent-Active-Refractory blue, red, green) neural field model of spontaneous retinal waves that occur during development. Waves are generated by the inner retina, and drive retinal ganglion cell spiking, which we can observe on a high-density multi-electrode array. [get original avi from Github]

Abstract:

High-density multi-electrode arrays have recently enabled detailed recording of large-scale spatiotemporal spiking activity. Neural field models for spatiotemporal activity can capture qualitative behaviors of such activity, but Bayesian approaches to state inference and model fitting are still needed. Bayesian spatiotemporal point-process filtering algorithms have recently been developed for applications in chemical reaction-diffusion systems and social dynamics. Such methods enable inference of latent intensity fields from point-process observations. We extend this work by developing a Bayesian spatiotemporal point-process filter for neural fields, based on a master equation formulation of the three-state "Quiescent-Activated-Refractory" neural field model, which corresponds to the well-studied "Susceptible-Infected-Recovered" reaction model from epidemiology. We demonstrate a state inference algorithm on a model of spontaneous retina waves in the developing mouse retina, which can approximate the posterior distribution for mean-field intensities and their spatial correlations. Overall, this work provides a practical demonstration for inference of latent spatiotemporal neural field dynamics from point-process observations, and lays the groundwork for merging spatiotemporal neural field equations with latent state-space point process models for neural dynamics.

Many thanks to Gerrit Hilgen, Evelyne Sernagor, David Schnoerr, Dimitris Milios, Botond Cseke, Guido Sanguinetti, and Matthias Hennig. 

To cite:

The posters are the same, although one has a different title. I brought an earlier iteration of poster to the 4th International Conference on Neural Field Theory in July, but there was an issue with the poster session and it wasn't really presented :P Depending on which poster you encounter(ed), you could cite it as one of; 

Rule, M., Schnoerr, D, Hennig, M. H., Sanguinetti, G. (2017) A Statistical Field Model of Spatiotemporal Neural Point-Processes Applied to Large-Scale Neuronal Recordings. [Poster] Bernstein Conference 2017, 13-15th September 2017, at Göttingen, Germany. 

Rule, M., Schnoerr, D, Hennig, M. H., Sanguinetti, G. (2017) Inference of Latent Neural Field Intensities from Spatiotemporal Point-Process Observations. [Poster] The second Integrated Systems Neuroscience Workshop, 7-8th September 2017, at The University of Manchester, Manchester, UK.

Rule, M., Schnoerr, D., Hennig, M., Sanguinetti, G. (2017) Inference of Latent Neural Field Intensities from Spatiotemporal Point-Process Observations. [Poster] 4th International Conference on Neural Field Theory (ICNFT) - The Interplay of Models and Data Assimilation, Reading UK.

Edit: this has now been published as

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.