Switching state-space modeling of neural signal dynamics
Fig 3
Simulation results: Segmentation performance when true parameters are unknown.
(a) Histograms of segmentation accuracy across 200 repetitions of sequences of 200 time points. Since the true parameters were not known, they were estimated using an instance of EM algorithm for VI-A and VI-I inference starting from a random initialization. Static switching and IMM treated those random initialization as true model parameters. The mean segmentation accuracy for each method is displayed and marked by the dashed red line. The mean accuracy previously obtained using true parameters is shown in gray. Random = random segmentation with a Bernoulli process; Static = static switching method; IMM = interacting multiple models method; VI-A EM = variational EM learning with deterministic annealing (orange color); VI-I EM = variational EM learning with interpolated densities (blue color). (b) Swarm plots showing the distributions of model parameters learned by the variational learning algorithms for sequences of 200 time points. Uniform distributions used to sample initial parameters are marked in bold fonts on the y-axes, as well as using solid black lines (true values) and dotted gray lines (upper and lower bounds of the ranges). (c) Changes of mean segmentation accuracy over sequences of varying data lengths. Shaded bounds denote the standard error of the mean around the average accuracy values. (d) Mean parameter estimation errors from the true values across 10 EM iterations for two different data lengths. For transition matrix F and state noise variance Q, normalized error is defined as abs(estimated—true)/true, and averaged across the two switching models. Absolute error is defined as abs(estimated—true). Shaded bounds denote the standard error of the mean around the average error values.