Decoding in the context of brain-machine interface is a prediction problem, with the aim of retrieving the most accurate kinematic predictions attainable from the available neural signals. While selecting models that reduce the prediction error is done to various degrees, decoding has not received the attention that the fields of statistics and machine learning have lavished on the prediction problem in the past two decades. Here, we take a more systematic approach to the decoding prediction problem and search for risk-optimized reverse regression, optimal linear estimation (OLE), and Kalman filter models within a large model space composed of several nonlinear transformations of neural spike counts at multiple temporal lags. The reverse regression decoding framework is a standard prediction problem, where penalized methods such as ridge regression or Lasso are routinely used to find minimum risk models. We argue that minimum risk reverse regression is always more efficient than OLE and also happens to be 44% more efficient than a standard Kalman filter in a particular application of offline reconstruction of arm reaches of a rhesus macaque monkey. Yet model selection for tuning curves–based decoding models such as OLE and Kalman filtering is not a standard statistical prediction problem, and no efficient method exists to identify minimum risk models. We apply several methods to build low-risk models and show that in our application, a Kalman filter that includes multiple carefully chosen observation equations per neural unit is 67% more efficient than a standard Kalman filter, but with the drawback that finding such a model is computationally very costly.

Spike-based brain-computer interfaces (BCIs) have the potential to restore motor ability to people with paralysis and amputation, and have shown impressive performance in the lab. To transition BCI devices from the lab to the clinic, decoding must proceed automatically and in real time, which prohibits the use of algorithms that are computationally intensive or require manual tweaking. A common choice is to avoid spike sorting and treat the signal on each electrode as if it came from a single neuron, which is fast, easy, and therefore desirable for clinical use. But this approach ignores the kinematic information provided by individual neurons recorded on the same electrode. The contribution of this letter is a linear decoding model that extracts kinematic information from individual neurons without spike-sorting the electrode signals. The method relies on modeling sample averages of waveform features as functions of kinematics, which is automatic and requires minimal data storage and computation. In offline reconstruction of arm trajectories of a nonhuman primate performing reaching tasks, the proposed method performs as well as decoders based on expertly manually and automatically sorted spikes.