Wei Wu (1), David Mumford (1), Michael J. Black (2), Yun Gao (1), Elie Bienenstock (1,3), John P. Donoghue (3)(1) Division of Applied Mathematics,
(2) Department of Computer Science,
(3) Department of Neuroscience,
Brown University, Providence, RI 02912
Recently we developed a control-theoretic, Kalman filter, model which outperforms previous methods in the decoding of hand movement from multi-cell recordings in the primary motor cortex of a macaque monkey. Central to the method is a generative model that assumes the firing rate of neurons in MI are normally distributed with the mean given by a linear function of hand kinematics (position, velocity, and acceleration). Here we relax this assumption and model firing rates using a probabilistic mixture of Gaussians. To train the model, we record 2D hand kinematics along with the activity of 42 cells using an implanted microelectrode array (firing rates are computed in 70ms time bins). The Gaussian Mixture Model (GMM) assumes that the probability density of observing the firing rates of the cells at a particular time instant is a mixture (weighted sum) of several Gaussians in which the mean of each Gaussian is a linear function of the hand kinematics. The Expectation-Maximization algorithm is used to the fit this Gaussian Mixture Model (GMM) to training data. We also present a probabilistic decoding algorithm for estimating hand kinematics from the firing rates of a population of cells. In particular we use a particle filter which is a stochastic Bayesian inference method that can cope with general (non-Gaussian) probabilistic models. Quantitative results show that the GMM outperforms the simple linear Gaussian model for both encoding (in terms of likelihood of firing rate conditioned on hand kinematics) and decoding (in terms of mean squared error in hand trajectory reconstructed from firing rates). We also analyze how the number of mixture components affects encoding and decoding accuracy. These results suggest that the GMM may be an effective method for modeling and decoding the population activity of cells in primary motor cortex.
Acknowledgments: This work was supported in part by: the DARPA Brain Machine Interface Program, NINDS Neural Prosthetics Program and Grant #NS25074, and the National Science Foundation (ITR Program award #0113679). We thank M. Serruya, A. Shaikhouni, J. Dushanova, C. Vargas, L. Lennox, and M. Fellows for their assistance.