Variational Inference for Nonlinear Regression Using Dimension Reduced Mixtures of Generalized Linear Models with Application to Neural Data

Variational Inference for Nonlinear Regression Using Dimension Reduced Mixtures of Generalized Linear Models with Application to Neural Data by Vivek Subramanian Department of Statistical Science Duke University Date: Approved: Sayan Mukherjee, Co-supervisor Jeffrey Beck, Co-supervisor Katherine Heller Miguel A. L. Nicolelis An abstract of a thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Statistical Science in the Graduate School of Duke University 2015 Copyright c © 2015 by Vivek Subramanian All rights reserved except the rights granted by the Creative Commons Attribution-Noncommercial Licence Abstract Brain-machine interfaces (BMIs) are devices that transform neural activity into commands executed by a robotic actuator. For paraplegics who have suffered spinal cord injury and for amputees, BMIs provide an avenue to regain lost limb mobility by providing a direct connection between the brain and an actuator. One of the most important aspects of a BMI is the decoding algorithm, which interprets patterns of neural activity and issues an appropriate kinematic action. The decoding algorithm relies heavily on a neural tuning function for each neuron which describes the response of that neuron to an external stimulus or upcoming motor action. Modern BMI decoders assume a simple parametric form for this tuning function such as cosine, linear, or quadratic, and fit parameters of the chosen function to a training data set. While this may be appropriate for some neurons, tuning curves for all neurons may not all take the same parametric form; hence, performance of BMI decoding may suffer because of an inappropriate mapping from firing rate to kinematic. In this work, we develop a non-parametric model for the identification of non-linear tuning curves with arbitrary shape. We also develop an associated variational Bayesian (VB) inference scheme which provides a fast, big data-friendly method to obtain approximate posterior distributions on model parameters. We demonstrate our model’s capabilities on both simulated and experimental datasets.Brain-machine interfaces (BMIs) are devices that transform neural activity into commands executed by a robotic actuator. For paraplegics who have suffered spinal cord injury and for amputees, BMIs provide an avenue to regain lost limb mobility by providing a direct connection between the brain and an actuator. One of the most important aspects of a BMI is the decoding algorithm, which interprets patterns of neural activity and issues an appropriate kinematic action. The decoding algorithm relies heavily on a neural tuning function for each neuron which describes the response of that neuron to an external stimulus or upcoming motor action. Modern BMI decoders assume a simple parametric form for this tuning function such as cosine, linear, or quadratic, and fit parameters of the chosen function to a training data set. While this may be appropriate for some neurons, tuning curves for all neurons may not all take the same parametric form; hence, performance of BMI decoding may suffer because of an inappropriate mapping from firing rate to kinematic. In this work, we develop a non-parametric model for the identification of non-linear tuning curves with arbitrary shape. We also develop an associated variational Bayesian (VB) inference scheme which provides a fast, big data-friendly method to obtain approximate posterior distributions on model parameters. We demonstrate our model’s capabilities on both simulated and experimental datasets.