Real-Time Point Process Filter for Multidimensional Decoding Problems Using Mixture Models

There is an increasing demand for a computationally efficient and accurate point process filter solution for real-time decoding of population spiking activity in multidimensional spaces. Real-time tools for neural data analysis, specifically real-time neural decoding solutions open doors for developing experiments in a closed-loop setting and more versatile brain-machine interfaces. Over the past decade, the point process filter has been successfully applied in the decoding of behavioral and biological signals using spiking activity of an ensemble of cells; however, the filter solution is computationally expensive in multi-dimensional filtering problems. Here, we propose an approximate filter solution for a general point-process filter problem when the conditional intensity of a cell's spiking activity is characterized using a Mixture of Gaussians. We propose the filter solution for a broader class of point process observation called marked point-process, which encompasses both clustered - mainly, called sorted - and clusterless - generally called unsorted or raw- spiking activity. We assume that the posterior distribution on each filtering time-step can be approximated using a Gaussian Mixture Model and propose a computationally efficient algorithm to estimate the optimal number of mixture components and their corresponding weights, mean, and covariance estimates. This algorithm provides a real-time solution for multi-dimensional point-process filter problem and attains accuracy comparable to the exact solution. Our solution takes advantage of mixture dropping and merging algorithms, which collectively control the growth of mixture components on each filtering time-step. We apply this methodology in decoding a rat's position in both 1-D and 2-D spaces using clusterless spiking data of an ensemble of rat hippocampus place cells. The approximate solution in 1-D and 2-D decoding is more than 20 and 4,000 times faster than the exact solution, while their accuracy in decoding a rat position only drops by less than 9% and 4% in RMSE and 95% highest probability coverage area (HPD) performance metrics. Though the marked-point filter solution is better suited for real-time decoding problems, we discuss how the filter solution can be applied to sorted spike data to better reflect the proposed methodology versatility.