Learning and inference algorithms for dynamical system models of dextrous motion

High dimensional time series data such as video sequences, spectral trajectories of a speech signal or the kinematic measurements of skilled human activity are encountered in several engineering applications, and computational models of such data hold considerable interest, particularly models that capture the inherent stochastic variability in the signal. Of particular interest in this dissertation are kinematic measurements of manipulator and tool motion in robot-assisted minimally invasive surgery (RMIS). A set of gesture labelled RMIS data is initially assumed to be given. The primary goal is to develop statistical models for gesture recognition for new RMIS trials from kinematic data, for eventually supporting automatic skill evaluation and surgeon training. The goal of automatically discovering the structure of dextrous motion in an unsupervised manner is also addressed, when an inventory of gestures is not known, or gesture-labeled data are not provided.;A number of statistical models to address these problems have been investigated, including hidden Markov models (HMM) with linear discriminant analysis, factor-analyzed hidden Markov models and linear dynamical systems with time varying parameters. Gesture recognition accuracies for three RMIS training tasks—suturing, knot-tying and needle-passing—are shown to improve significantly with increasing model complexity, justifying the concomitant increase in the computation required to estimate model parameters from gesture-labeled data or to perform recognition.;Algorithms for unsupervised structure induction have been investigated for discovering gestures used in skilled dexterous motion directly from kinematic data when gesture-labeled data are not available. An improved algorithm based on successive state splitting is presented for discovering the state-topology of a hidden Markov model. The algorithm efficiently explores an enormous space of possible topologies and yields models with a high goodness-of-fit to the RMIS kinematic data.;Technical contributions of this dissertations include novel, efficient algorithms for probabilistic principal component analysis, for switching linear dynamical system parameter estimation, and for hidden Markov model topology induction. Other techniques for improving gesture recognition accuracy beyond those mentioned above are also investigated by incorporating ideas such as user-adaptation of the models.