Modulation depth estimation and variable selection in state-space models for neural interfaces
Wasim Q. Malik, Leigh R. Hochberg, John P. Donoghue, Emery N. Brown, Massachusetts General Hospital, Harvard Medical School, Brown University, Massachusetts Institute of Technology, Department of Veterans Affairs, Volume 62, Issue 2, Page:570-581
Multichannel signal acquisition in biomedical engineering and other applications can result in high-dimensional signal sets, but often the information is concentrated in a small subset of those signals. We present a method for dimensionality reduction by variable subset selection based on quantification and ranking of the information content of observed signals. We develop a theoretical framework to represent a multivariate Gauss-Markov system and derive expressions for estimating task-related modulation depth of an observed variable under various system configurations. We analyze generalized continuous- and discrete-time state-space models, and consider special cases involving steady-state and time-variant dynamical systems, colored measurement noise, and uncorrelated states. We consider the practical problem of selecting the optimal subset of human motor cortical single-neurons in a neural interface on the basis of their tuning to intended movement kinematics in an open-loop motor imagery task. We show that a small number of optimally chosen single-neurons are adequate for reconstructing intended movement. We show that for selecting, for instance, 5 of 39 available channels, our method’s computational complexity is several orders of magnitude lower than that of the commonly used greedy search algorithm, while the neural decoding performance is virtually identical. Such a large improvement in the performance-complexity tradeoff has important practical implications both for offline analyses of neural data and for real-time neural interface control. The methods we develop can be applied various types of neural signals including single-unit and multiunit spike-rates, local field potentials, electrocorticograms and electroencephalograms. The modulation depth estimation approach can also be used for improved identification responsive voxels in functional imaging data, or quantification of stimulus-evoked vs. stimulus-free neural response in neural coding studies. Our methods apply to any system that can be cast as a state-space model with a set of latent states and observations, which underlines the broad applicability of this approach.
Keywords: Brain-machine interface, brain-computer interface, feature selection, modulation depth, neural decoding, signal-to-noise ratio, state-space model, variable selection.