2,508 research outputs found
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
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
Particle Learning and Smoothing
Particle learning (PL) provides state filtering, sequential parameter
learning and smoothing in a general class of state space models. Our approach
extends existing particle methods by incorporating the estimation of static
parameters via a fully-adapted filter that utilizes conditional sufficient
statistics for parameters and/or states as particles. State smoothing in the
presence of parameter uncertainty is also solved as a by-product of PL. In a
number of examples, we show that PL outperforms existing particle filtering
alternatives and proves to be a competitor to MCMC.Comment: Published in at http://dx.doi.org/10.1214/10-STS325 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
CAREER: motion capture from movies: video-based tracking and modeling of human motion
Issued as final reportNational Science Foundation (U.S.
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
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