Neural Decoding: A Predictive Viewpoint

Abstract

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.

Computationally efficient model selection for joint spikes and waveforms decoding

“…Our goal in this paper is to identify minimum or low risk OLE and Bayesian decoding models, which consists of identifying which observation equations to include in eq. 4 (Todorova and Ventura, 2017). To avoid overfitting, we score each model by calculating a cross-validated estimate of the prediction risk in a training set, with prediction risk taken to be the mean squared error (MSE), and we report the prediction risks evaluated on a separate testing set in our figures and comments.…”

“…Model space At present, the model space is composed of all subsets of the observation equations in Eqs.2 and 3. The lag τ between neural activity and kinematics is often taken to be the same across all electrodes or all neurons, but Wu et al (2006) and Todorova and Ventura (2017) show that using different lags can improve decoding performance. We therefore consider that option, allowing temporal lags between neural data and kinematics to be different across electrodes, from τ = 0 to 12 time bins, where τ = 12 corresponds to 192 ms with the 16 ms wide bins we use in the results section.…”

“…Next, the assumed parametric models in Eqs.2 and 3 are biased since they cannot match exactly the true models, and this in turn biases kinematic predictions. Following (Todorova and Ventura, 2017), we augment the model space with alternative conditional expectation (ACE, Breiman and Friedman (1985)) response transformation models:…”

“…tetrodes) that have different tuning curves contain substantial information that is unlikely to be fully captured by a single waveform feature (indeed Kloosterman et al (2014) observed an efficiency bump of 26% from using two of the tetrode amplitudes instead of one, and a further 14% bump from using four instead of two), and that conversely, waveforms provide no information in addition to the information in spike trains, for electrodes that record only one neuron or several neurons that are similarly modulated by the kinematics. Yet, including waveforms in the decoding model injects noise in the predicted kinematics since their models are estimated from training data, and bias when parametric models are used (Todorova and Ventura, 2017). Hence, there is a tradeoff between the amount of information provided by the waveforms and the amount of additional variability and bias they induce.…”

“…Model selection is straightforward for forward filters that predict kinematics as functions of neural covariates, using stepwise regression or penalized approaches like LASSO or ridge regression, and can improve decoding accuracy very substantially. Model selection for OLE and Bayesian models can also rip substantial rewards, but a major hurdle is the computational burden of recomputing the prediction risk for each candidate model, which prevents stepwise, let alone exhaustive searches (Todorova and Ventura, 2017). In their stepwise search, Ventura and Todorova (2015) and Todorova and Ventura (2017) selected waveform features using an added variable test (AVT) that prevented highly correlated observation equations from entering the joint model, which had the advantage of speed but was not particularly effective to reduce the prediction risk.…”