Table 5. Alternative models explored.

Most are linear models, using either the Ridge or ElasticNet regularization. In some cases, we add an additional term to the cost function which penalizes errors in the temporal derivative of model output (which, for velocity models, corresponds to the error in the predicted acceleration). For features, we use either the neural activities alone, or the neural activities together with their temporal derivatives. We also explore two nonlinear models: MARS Friedman, 1991, and a shallow decision tree which chooses between two linear models.

Model	Penalty	Features	Number of parameters
Linear	Ridge	$F$ and $dF/dt$	$2N_n+1$
Linear	Ridge	$F$	$N_n+1$
Linear	Ridge + Acceleration Penalty	$F$ and $dF/dt$	$2N_n+1$
Linear	Ridge + Acceleration Penalty	$F$	$N_n+1$
Linear	ElasticNet	$F$ and $dF/dt$	$2N_n+1$
Linear	ElasticNet	$F$	$N_n+1$
MARS (nonlinear)	MARS	$F$ and $dF/dt$	variable
Linear with Decision Tree (nonlinear)	Ridge	$F$ and $dF/dt$	$4N_n+9$