Neural spike train denoising by point process re-weighted iterative smoothing

An important problem in computational neuro-science is to design algorithms that can capture robustly abrupt changes in the conditional intensity function (CIF) of a stochastic point process model of neural spiking data. Towards this end, we advocate the use of a point process analogue of the total variation denoising algorithm, which trades off the point process likelihood with a total variation prior on the parameters of a log-linear model of the CIF. We propose an iteratively re-weighted least squares (IRLS) algorithm, termed Point process Re-weighted Iterative SMoothing (PRISM), to solve the point process total variation denoising (PPTVD) problem. PRISM can be implemented using well-established point process smoothing algorithms, which are point process analogues of the Kalman smoother. We use a connection between the Expectation-Maximization (EM) algorithm and IRLS to prove that the sequence generated by PRISM converges and that its limit point coincides with the unique stationary point of the PPTVD problem. We apply PRISM to 123 and 41 neuronal units acquired from two separate epileptic patients during general anesthesia induced using the drug propofol. The PRISM algorithm is able to capture robustly the onset of loss of consciousness at the millisecond time scale.