Inference in Hybrid Systems with Applications in Neural Prosthetics

This thesis develops new hybrid system models and associated inference algorithms to create a “supervisory decoder” for cortical neural prosthetic devices that aim to help the severely handicapped. These devices are a brain-machine interface, consisting of surgically implanted electrode arrays and associated computer decoding algorithms, that enable a human to control external electromechanical devices, such as artificial limbs, by thought alone. Hybrid systems are characterized by discrete switching between sets of continuous dynamical activity. New hybrid models, which are flexible enough to model neurological activity, are created that incorporate both duration and dynamical state based switching paradigms. Combining generalized linear models with nonstationary and semi-Markov chains gives rise to three new hybrid systems: generalized linear hidden Markov models (GLHMM), hidden semi-Markov models (HSMM) with generalized linear model dynamics, and hidden regressor dependent Markov models (HRDMM). Bayesian inference methods, including variational Bayes and Gibbs sampling, are derived for the identification of existing and developed hybrid models. The developed inference algorithms provide advances over the current hybrid system identification literature by providing a principled way to incorporate prior knowledge and select between alternative model classes and orders, including the number of discrete system states. Future neuroprostheses that seek to provide a facile interface for the paralyzed patient will require a supervisory decoder that classifies, in real time, the discrete cognitive, behavioral, or planning state of the brain. The developed hybrid models and inference algorithms provide a framework for supervisory decoding, where first, a hybrid-state neurological activity model is identified from data, and then used to estimate the discrete state in real time. The electrical activity of multiple neurons from a cortical area in the brain associated with motor planning (the parietal reach region), and multiple signal types, including both spike arrival times and local field potentials, are fused to give more accurate results. The model structure, including the number of discrete cognitive states, can also be estimated from the data, resulting in significantly improved decoding performance compared to existing methods. Additional demonstrated applications include the automated segmentation of honey bee motion into discrete primitives, and generating mechanical system models for a pick-and-place machine.