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

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.