Title: Inference of functional neural connectivity and convergence acceleration methods
Description: The knowledge of the maps of neuronal interactions is key for system neuroscience, but at the moment we possess relatively little of it . The recent development of experimental methods which allow a simultaneous recording of the spiking activity, but not the intracellular voltage, of thousands of neurons gives us an opportunity to start filling that gap. In Chapter 2, I present a method for the inference of the parameters of the leaky integrate-and-fire (LIF) model featuring time-dependent currents and conductances based only on the extracellular recording of spiking in the network. The fitted parameters can describe the functional connections in the network, as well as the internal properties of the cells. The method can also be used to determine whether a single-compartment model of a neuron should include conductance- or current-based synapses, or their mixture. In addition, because the same mathematical model describes some of the flavors of the Drift Diffusion Model (DDM), popular in the studies of decision making process, the presented method can be readily used to fit their parameters.

Making the proposed inference procedure -- based on the expectation-maximization (EM) algorithm -- accurate and robust, necessitated a development of a new numerical adaptive-grid (AG) method for the forward-backward (FB) propagation of the probability density, which is required in the computation of the sufficient statistic in the EM algorithm. These topics are covered in Chapter 3. Another issue which had to be addressed in order to obtain a usable inference algorithm is the well known slow convergence of the EM algorithm in the flat regions of the loglikelihood. Two complementary approaches to this issue are presented in this dissertation. In Chapter 4, I present a new framework for the acceleration of convergence of iterative algorithms (not limited to the EM) which unifies all previously known methods and allows us to construct a new method demonstrating the best performance of them all. To make the computations even faster, I wrote a Matlab package which allows them to be done in parallel on several machines and clusters.

As one can see, all the aforementioned projects were sprouted up from one "head" project on the inference of the LIF model parameters. At the end of the dissertation, I briefly describe a disconnected project which is devoted to the development of a flexible experimental setup (software and hardware) for behavioral experiments, with a specific application to a particular type of the virtual Morris water maze experiment (VMWM).