Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI
Fig 7
Decoding task conditions from model trajectories.
A. Relative LDA classification error on different task phases based on the inferred states (top) and freely generated states (bottom) from the PLRNN-BOLD-SSM (solid lines) and LDS-BOLD-SSM (dashed lines), for models including (blue) or excluding (red) stimulus inputs. Black lines indicate classification results for random state permutations. Except for M = 2, the classification error for the PLRNN-BOLD-SSM based on generated states, drawn from the prior model pgen(Z), is significantly lower than for the permutation bootstraps (all p < .01), indicating that the prior dynamics contains task-related information. In contrast, the LDS-BOLD-SSM produced substantially higher discrimination errors for the generated trajectories (which were close to chance level when stimulus information was excluded), and even on the inferred trajectories. Globally unstable system estimates were removed from analysis. B. Typical example of inferred (left) and generated (right) state space trajectories from a PLRNN-BOLD-SSM, projected down to the first 3 principle components for visualization purposes, color-coded according to task phases (see legend). C. Same as in B for example from trained LDS-BOLD-SSM. The simulated (generated) states usually converged to a fixed point in this case.