Scalable Bayesian Inference for Excitatory Point Process Networks

TL;DR

This paper introduces a scalable Bayesian inference method for discovering latent networks from activity data modeled as Hawkes processes, using a discrete-time formulation and stochastic variational inference to handle long sequences.

Contribution

It extends previous Bayesian approaches by developing a discrete-time model and an efficient SVI algorithm for large-scale neural activity data analysis.

Findings

Successfully applied to calcium imaging data from neural connectomics

Achieved scalable inference for long activity sequences

Improved computational efficiency over previous methods

Abstract

Networks capture our intuition about relationships in the world. They describe the friendships between Facebook users, interactions in financial markets, and synapses connecting neurons in the brain. These networks are richly structured with cliques of friends, sectors of stocks, and a smorgasbord of cell types that govern how neurons connect. Some networks, like social network friendships, can be directly observed, but in many cases we only have an indirect view of the network through the actions of its constituents and an understanding of how the network mediates that activity. In this work, we focus on the problem of latent network discovery in the case where the observable activity takes the form of a mutually-excitatory point process known as a Hawkes process. We build on previous work that has taken a Bayesian approach to this problem, specifying prior distributions over the latent network structure and a likelihood of observed activity given this network. We extend this work by proposing a discrete-time formulation and developing a computationally efficient stochastic variational inference (SVI) algorithm that allows us to scale the approach to long sequences of observations. We demonstrate our algorithm on the calcium imaging data used in the Chalearn neural connectomics challenge.