Fig 3. The calibration algorithm accurately computes the steady-state error covariance and convergence time as a function of learning rate for continuous signals.
(A) The analytically-computed and the true error covariance and convergence time of the encoding model parameters (baseline, ηx, and ηy in (1)) for different learning rates s, across a wide range of s. The top left panel shows the relation between the three quantities. The other three panels are projections of this plot to three planes, showing each of the three pair-wise relationships. All axes are in log scale. True quantities are computed from BMI simulations with periodic center-out-and-back training datasets. The analytically-computed values are obtained by the calibration algorithm according to Eqs (7) and (8). The analytically-computed and true values match tightly across a wide range of learning rates, showing that the calibration algorithm can accurately compute the learning rate for a desired trade-off between steady-state error and convergence time. (B) Adaptive estimation of the unknown observation noise variance using (11) under different learning rates s. The bottom three panels are zoomed-in versions of the top panels to show the transient behavior of the estimated noise variance, which converges to its true value in all cases.