Title: Statistical Machine Learning & Deep Neural Networks Applied to Neural Data Analysis
Description: Computational neuroscience seeks to discover the underlying mechanisms by which neural activity is generated. With the recent advancement in neural data acquisition methods, the bottleneck of this pursuit is the analysis of ever-growing volume of neural data acquired in numerous labs from various experiments. These analyses can be broadly divided into two categories. First, extraction of high quality neuronal signals from noisy large scale recordings. Second, inference for statistical models aimed at explaining the neuronal signals and underlying processes that give rise to them. Conventionally, majority of the methodologies employed for this effort are based on statistics and signal processing. However, in recent years recruiting Artificial Neural Networks (ANN) for neural data analysis is gaining traction. This is due to their immense success in computer vision and natural language processing, and the stellar track record of ANN architectures generalizing to a wide variety of problems.

In this work we investigate and improve upon statistical and ANN machine learning methods applied to multi-electrode array recordings and inference for dynamical systems that play critical roles in computational neuroscience. In the first and second part of this thesis, we focus on spike sorting problem. The analysis of large-scale multi-neuronal spike train data is crucial for current and future of neuroscience research. However, this type of data is not available directly from recordings and require further processing to be converted into spike trains. Dense multi-electrode arrays (MEA) are standard methods for collecting such recordings. The processing needed to extract spike trains from these raw electrical signals is carried out by ``spike sorting'' algorithms. We introduce a robust and scalable MEA spike sorting pipeline YASS (Yet Another Spike Sorter) to address many challenges that are inherent to this task. We primarily pay attention to MEA data collected from the primate retina for important reasons such as the unique challenges and available side information that ultimately assist us in scoring different spike sorting pipelines.

We also introduce a Neural Network architecture and an accompanying training scheme specifically devised to address the challenging task of deconvolution in MEA recordings. In the last part, we shift our attention to inference for non-linear dynamics. Dynamical systems are the governing force behind many real world phenomena and temporally correlated data. Recently, a number of neural network architectures have been proposed to address inference for nonlinear dynamical systems. We introduce two different methods based on normalizing flows for posterior inference in latent non-linear dynamical systems. We also present gradient-based amortized posterior inference approaches using the auto-encoding variational Bayes framework that can be applied to a wide range of generative models with nonlinear dynamics. We call our method 𝘍𝘪𝘭𝘵𝘦𝘳𝘪𝘯𝘨 𝘕𝘰𝘳𝘮𝘢𝘭𝘪𝘻𝘪𝘯𝘨 𝘍𝘭𝘰𝘸𝘴 (FNF). FNF performs favorably against state-of-the-art inference methods in terms of accuracy of predictions and quality of uncovered codes and dynamics on synthetic data.