Inference on Neuronal Networks using Temporal and Graphical Models

Abstract

This dissertation deals with modeling and analysis of multi-neuronal spike train data. Brain tissue is composed of many neurons which function and interact with each other by generating a time sequence of characteristic electrical pulses known as action potentials or spikes. These time sequences of spikes generated by a set of neurons are referred to as multi-neuronal spike train data. Analyzing such data to identify the spatio-temporal network structure of the functional connectivity of the neurons underlying a specific brain activity is one of the biggest challenges in neuroscience.

The dissertation makes three separate contributions. The first one considered computationally fast methods for detecting pairwise connections among a set of neurons. We focus on the notion of `non-overlapping' episodes and develop distribution theory for counts based on these episodes. The results are used to develop statistical procedures for testing functional connectivity above given thresholds as well screening out false connections that can arise. The usefulness of the results are demonstrated on simulated and real data sets.

The second contribution considers a class of models for analyzing the spike-train data from all the neurons and develops likelihood-based inference. Algorithms for estimating the connectivity matrix and the baseline firing rates are developed, associated inference methods are obtained, and their asymptotic properties are studied.

The final contribution uses a graphical modeling framework and develops a model selection algorithm. The approach uses iterative methods to estimate delay and connectivity strength matrices. The method is used to reconstruct the graphical structure of the functional connectivity among a group of neurons. We demonstrate the effectiveness of our method on simulated neuronal networks and also apply the method to discover the significant connections in spike train data from cultures of cortical neurons.