A variational bayes approach to inferring neuronal network connectivity

Abstract

Uncovering a neuronal circuit's structure is an important step toward developing a mechanistic understanding of that circuit's function. In this thesis, we develop an algorithm which can accurately reconstruct an integrate-and-fire neuronal network's connectivity from observations of its spike-train data. Our network reconstruction algorithm is designed to achieve two primary goals: efficiently recover network connectivity given minimal observed data, and quantify our uncertainty about each connection in the network. Pursuant to our first goal, we define a novel Bayesian statistical model for neuronal spike train data, uniquely structured around empirically observed characteristics of spike-trains from conductance based integrate-and-fire neuronal networks. In particular, the model directly accounts for the spike-reset-refractory-period dynamics characteristic of spiking neurons; additionally, the model's dimensionality is reduced by flexibly encoding the typical response a neuron has to presynaptic spikes. We show that building a model which accounts for the structure inherent in neuronal network spiking dynamics makes recovering network connectivity more data-efficient, especially for large networks. Furthermore, our Bayesian model has parameters which directly correspond to structural properties of the observed neuronal circuit. Most importantly, the model contains a connection-type parameter for each pair of observed neurons $(c \leftarrow j)$, which indicates if neuron $j$ is excitatorily presynaptic, inhibitorily presynaptic to, or disconnected from neuron $c$. Thus, the posterior distribution over these parameters facilitates direct inference of the network's connectivity, direct inference of the connection type (excitatory or inhibitory) between each connected pair, and local, pairwise estimates of our uncertainty about each inferred connection. An approximation to the Bayesian model's posterior distribution is derived using a variational Bayes algorithm which is carefully designed to retain meaningful probabilities over the model's connection type parameters.