3,306 research outputs found
Bayesian nonparametric learning of complex dynamical phenomena
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 257-270).The complexity of many dynamical phenomena precludes the use of linear models for which exact analytic techniques are available. However, inference on standard nonlinear models quickly becomes intractable. In some cases, Markov switching processes, with switches between a set of simpler models, are employed to describe the observed dynamics. Such models typically rely on pre-specifying the number of Markov modes. In this thesis, we instead take a Bayesian nonparametric approach in defining a prior on the model parameters that allows for flexibility in the complexity of the learned model and for development of efficient inference algorithms. We start by considering dynamical phenomena that can be well-modeled as a hidden discrete Markov process, but in which there is uncertainty about the cardinality of the state space. The standard finite state hidden Markov model (HMM) has been widely applied in speech recognition, digital communications, and bioinformatics, amongst other fields. Through the use of the hierarchical Dirichlet process (HDP), one can examine an HMM with an unbounded number of possible states. We revisit this HDPHMM and develop a generalization of the model, the sticky HDP-HMM, that allows more robust learning of smoothly varying state dynamics through a learned bias towards self-transitions. We show that this sticky HDP-HMM not only better segments data according to the underlying state sequence, but also improves the predictive performance of the learned model. Additionally, the sticky HDP-HMM enables learning more complex, multimodal emission distributions.(cont.) We demonstrate the utility of the sticky HDP-HMM on the NIST speaker diarization database, segmenting audio files into speaker labels while simultaneously identifying the number of speakers present. Although the HDP-HMM and its sticky extension are very flexible time series models, they make a strong Markovian assumption that observations are conditionally independent given the discrete HMM state. This assumption is often insufficient for capturing the temporal dependencies of the observations in real data. To address this issue, we develop extensions of the sticky HDP-HMM for learning two classes of switching dynamical processes: the switching linear dynamical system (SLDS) and the switching vector autoregressive (SVAR) process. These conditionally linear dynamical models can describe a wide range of complex dynamical phenomena from the stochastic volatility of financial time series to the dance of honey bees, two examples we use to show the power and flexibility of our Bayesian nonparametric approach. For all of the presented models, we develop efficient Gibbs sampling algorithms employing a truncated approximation to the HDP that allows incorporation of dynamic programming techniques, greatly improving mixing rates. In many applications, one would like to discover and model dynamical behaviors which are shared among several related time series. By jointly modeling such sequences, we may more robustly estimate representative dynamic models, and also uncover interesting relationships among activities.(cont.) In the latter part of this thesis, we consider a Bayesian nonparametric approach to this problem by harnessing the beta process to allow each time series to have infinitely many potential behaviors, while encouraging sharing of behaviors amongst the time series. For this model, we develop an efficient and exact Markov chain Monte Carlo (MCMC) inference algorithm. In particular, we exploit the finite dynamical system induced by a fixed set of behaviors to efficiently compute acceptance probabilities, and reversible jump birth and death proposals to explore new behaviors. We present results on unsupervised segmentation of data from the CMU motion capture database.by Emily B. Fox.Ph.D
Robot Introspection with Bayesian Nonparametric Vector Autoregressive Hidden Markov Models
Robot introspection, as opposed to anomaly detection typical in process
monitoring, helps a robot understand what it is doing at all times. A robot
should be able to identify its actions not only when failure or novelty occurs,
but also as it executes any number of sub-tasks. As robots continue their quest
of functioning in unstructured environments, it is imperative they understand
what is it that they are actually doing to render them more robust. This work
investigates the modeling ability of Bayesian nonparametric techniques on
Markov Switching Process to learn complex dynamics typical in robot contact
tasks. We study whether the Markov switching process, together with Bayesian
priors can outperform the modeling ability of its counterparts: an HMM with
Bayesian priors and without. The work was tested in a snap assembly task
characterized by high elastic forces. The task consists of an insertion subtask
with very complex dynamics. Our approach showed a stronger ability to
generalize and was able to better model the subtask with complex dynamics in a
computationally efficient way. The modeling technique is also used to learn a
growing library of robot skills, one that when integrated with low-level
control allows for robot online decision making.Comment: final version submitted to humanoids 201
Bayesian Nonparametric Inference of Switching Linear Dynamical Systems
Many complex dynamical phenomena can be effectively modeled by a system that
switches among a set of conditionally linear dynamical modes. We consider two
such models: the switching linear dynamical system (SLDS) and the switching
vector autoregressive (VAR) process. Our Bayesian nonparametric approach
utilizes a hierarchical Dirichlet process prior to learn an unknown number of
persistent, smooth dynamical modes. We additionally employ automatic relevance
determination to infer a sparse set of dynamic dependencies allowing us to
learn SLDS with varying state dimension or switching VAR processes with varying
autoregressive order. We develop a sampling algorithm that combines a truncated
approximation to the Dirichlet process with efficient joint sampling of the
mode and state sequences. The utility and flexibility of our model are
demonstrated on synthetic data, sequences of dancing honey bees, the IBOVESPA
stock index, and a maneuvering target tracking application.Comment: 50 pages, 7 figure
Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments
Optical microscopy provides rich spatio-temporal information characterizing
in vivo molecular motion. However, effective forces and other parameters used
to summarize molecular motion change over time in live cells due to latent
state changes, e.g., changes induced by dynamic micro-environments,
photobleaching, and other heterogeneity inherent in biological processes. This
study focuses on techniques for analyzing Single Particle Tracking (SPT) data
experiencing abrupt state changes. We demonstrate the approach on GFP tagged
chromatids experiencing metaphase in yeast cells and probe the effective forces
resulting from dynamic interactions that reflect the sum of a number of
physical phenomena. State changes are induced by factors such as microtubule
dynamics exerting force through the centromere, thermal polymer fluctuations,
etc. Simulations are used to demonstrate the relevance of the approach in more
general SPT data analyses. Refined force estimates are obtained by adopting and
modifying a nonparametric Bayesian modeling technique, the Hierarchical
Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT
applications. The HDP-SLDS method shows promise in systematically identifying
dynamical regime changes induced by unobserved state changes when the number of
underlying states is unknown in advance (a common problem in SPT applications).
We expand on the relevance of the HDP-SLDS approach, review the relevant
background of Hierarchical Dirichlet Processes, show how to map discrete time
HDP-SLDS models to classic SPT models, and discuss limitations of the approach.
In addition, we demonstrate new computational techniques for tuning
hyperparameters and for checking the statistical consistency of model
assumptions directly against individual experimental trajectories; the
techniques circumvent the need for "ground-truth" and subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One
publication available freely as an open-access article at
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763
Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation
The control of nonlinear dynamical systems remains a major challenge for
autonomous agents. Current trends in reinforcement learning (RL) focus on
complex representations of dynamics and policies, which have yielded impressive
results in solving a variety of hard control tasks. However, this new
sophistication and extremely over-parameterized models have come with the cost
of an overall reduction in our ability to interpret the resulting policies. In
this paper, we take inspiration from the control community and apply the
principles of hybrid switching systems in order to break down complex dynamics
into simpler components. We exploit the rich representational power of
probabilistic graphical models and derive an expectation-maximization (EM)
algorithm for learning a sequence model to capture the temporal structure of
the data and automatically decompose nonlinear dynamics into stochastic
switching linear dynamical systems. Moreover, we show how this framework of
switching models enables extracting hierarchies of Markovian and
auto-regressive locally linear controllers from nonlinear experts in an
imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro
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