Efficient Decoding of Multi-Dimensional Signals From Population Spiking Activity Using a Gaussian Mixture Particle Filter.

New recording technologies and the potential for closed-loop experiments have led to an increasing demand for computationally efficient and accurate algorithms to decode population spiking activity in multi-dimensional spaces. Exact point process filters can accurately decode low-dimensional signals, but are computationally intractable for high-dimensional signals. Approximate Gaussian filters are computationally efficient, but are inaccurate when the signals have complex distributions and nonlinear dynamics. Even particle filter methods tend to become inefficient and inaccurate when the filter distribution has multiple peaks. Here, we develop a new point process filter algorithm that combines the computational efficiency of approximate Gaussian methods with a numerical accuracy that exceeds standard particle filters. We use a mixture of Gaussian model for the posterior at each time step, allowing for an analytic solution to the computationally expensive filter integration step. During non-spike intervals, the filter needs only to update the mean, covariance, and mixture weight of each component. At spike times, a sampling procedure is used to update the filtering distribution and find the number of Gaussian mixture components necessary to maintain an accurate approximation. We illustrate the application of this algorithm to the problem of decoding a rat's position and velocity in a maze from hippocampal place cell data using both 2-D and 4-D decoders.