Bayesian Learning Methods for Neural Coding

Dedicated to the memory of my mother Acknowledgments I would like to express my sincere appreciation to my adviser, Prof. Jonathan W. Pillow for his support and friendship throughout my Ph.D.. His enthusiasm deeply motivated me to push myself hard to become a competent research scientist. I would also like to thank my co-adviser, Prof. Alan C. I would also like to thank my family and my best friends in Korea for their support throughout my life. To Marcel, you made the tough times easier. To my small group at Gateway church Austin, thanks for your constant prayer support. Finally, to every corner on UT campus, where I stood alone and thought hard to overcome frustrations, I am going to miss you! v A primary goal in systems neuroscience is to understand how neural spike responses encode information about the external world. A popular approach to this problem is to build an explicit probabilistic model that characterizes the encoding relationship in terms of a cascade of stages: (1) linear dimensionality reduction of a high-dimensional stimulus space using a bank of filters or receptive fields (RFs); (2) a nonlinear function from filter outputs to spike rate; and (3) a stochastic spiking process with recurrent feedback. These models have described single-and multi-neuron spike responses in a wide variety of brain areas. This dissertation addresses Bayesian methods to efficiently estimate the linear and non-linear stages of the cascade encoding model. In the first part, the dissertation describes a novel Bayesian receptive field estimator based on a hierarchical prior that flexibly incorporates knowledge about the shapes of vi neural receptive fields. This estimator achieves error rates several times lower than existing methods, and can be applied to a variety of other neural inference problems such as extracting structure in fMRI data. The dissertation also presents active learning frameworks developed for receptive field estimation incorporating a hierarchical prior in real-time neurophysiology experiments. In addition, the dissertation describes a novel low-rank model for the high dimensional receptive field, combined with a hierarchical prior for more efficient receptive field estimation. In the second part, the dissertation describes new models for neural nonlinearities using Gaussian processes (GPs) and Bayesian active learning algorithms in closed-loop neurophysiology experiments to rapidly estimate neural nonlinearities. The dissertation also presents several stimulus selection criteria and compare their performance in neural nonlinearity estimation. Furthermore, the dissertation presents a variation of the new models by …