6,840 research outputs found
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
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
A Bayesian Nonparametric Markovian Model for Nonstationary Time Series
Stationary time series models built from parametric distributions are, in
general, limited in scope due to the assumptions imposed on the residual
distribution and autoregression relationship. We present a modeling approach
for univariate time series data, which makes no assumptions of stationarity,
and can accommodate complex dynamics and capture nonstandard distributions. The
model for the transition density arises from the conditional distribution
implied by a Bayesian nonparametric mixture of bivariate normals. This implies
a flexible autoregressive form for the conditional transition density, defining
a time-homogeneous, nonstationary, Markovian model for real-valued data indexed
in discrete-time. To obtain a more computationally tractable algorithm for
posterior inference, we utilize a square-root-free Cholesky decomposition of
the mixture kernel covariance matrix. Results from simulated data suggest the
model is able to recover challenging transition and predictive densities. We
also illustrate the model on time intervals between eruptions of the Old
Faithful geyser. Extensions to accommodate higher order structure and to
develop a state-space model are also discussed
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
A flexible approach to parametric inference in nonlinear time series models
Many structural break and regime-switching models have been used with macroeconomic and ā¦nancial data. In this paper, we develop an extremely flexible parametric model which can accommodate virtually any of these speciā¦cations and does so in a simple way which allows for straightforward Bayesian inference. The basic idea underlying our model is that it adds two simple concepts to a standard state space framework. These ideas are ordering and distance. By ordering the data in various ways, we can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the state equation variances to depend on the distance between observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). We show how our model will (approximately) nest virtually every popular model in the regime-switching and structural break literatures. Bayesian econometric methods for inference in this model are developed. Because we stay within a state space framework, these methods are relatively straightforward, drawing on the existing literature. We use artiā¦cial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth
Online Discrimination of Nonlinear Dynamics with Switching Differential Equations
How to recognise whether an observed person walks or runs? We consider a
dynamic environment where observations (e.g. the posture of a person) are
caused by different dynamic processes (walking or running) which are active one
at a time and which may transition from one to another at any time. For this
setup, switching dynamic models have been suggested previously, mostly, for
linear and nonlinear dynamics in discrete time. Motivated by basic principles
of computations in the brain (dynamic, internal models) we suggest a model for
switching nonlinear differential equations. The switching process in the model
is implemented by a Hopfield network and we use parametric dynamic movement
primitives to represent arbitrary rhythmic motions. The model generates
observed dynamics by linearly interpolating the primitives weighted by the
switching variables and it is constructed such that standard filtering
algorithms can be applied. In two experiments with synthetic planar motion and
a human motion capture data set we show that inference with the unscented
Kalman filter can successfully discriminate several dynamic processes online
A flexible approach to parametric inference in nonlinear and time varying time series models
Many structural break and regime-switching models have been used with macroeconomic and ā¦nancial data. In this paper, we develop an extremely flexible parametric model which can accommodate virtually any of these speciā¦cations and does so in a simple way which allows for straightforward Bayesian inference. The basic idea underlying our model is that it adds two simple concepts to a standard state space framework. These ideas are ordering and distance. By ordering the data in various ways, we can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the state equation variances to depend on the distance between observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). We show how our model will (approximately) nest virtually every popular model in the regime-switching and structural break literatures. Bayesian econometric methods for inference in this model are developed. Because we stay within a state space framework, these methods are relatively straightforward, drawing on the existing literature. We use artiā¦cial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth
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