Results 11  20
of
720
Elliptical slice sampling
 JMLR: W&CP
"... Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with multivariate Gaussian priors. Its key properties are: 1) it h ..."
Abstract

Cited by 60 (8 self)
 Add to MetaCart
Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with multivariate Gaussian priors. Its key properties are: 1) it has simple, generic code applicable to many models, 2) it has no free parameters, 3) it works well for a variety of Gaussian process based models. These properties make our method ideal for use while model building, removing the need to spend time deriving and tuning updates for more complex algorithms.
Learning Stable Nonlinear Dynamical Systems With Gaussian Mixture Models
"... Abstract—This paper presents a method to learn discrete robot motions from a set of demonstrations. We model a motion as a nonlinear autonomous (i.e., timeinvariant) dynamical system (DS) and define sufficient conditions to ensure global asymptotic stability at the target. We propose a learning met ..."
Abstract

Cited by 59 (17 self)
 Add to MetaCart
(Show Context)
Abstract—This paper presents a method to learn discrete robot motions from a set of demonstrations. We model a motion as a nonlinear autonomous (i.e., timeinvariant) dynamical system (DS) and define sufficient conditions to ensure global asymptotic stability at the target. We propose a learning method, which is called Stable Estimator of Dynamical Systems (SEDS), to learn the parameters of the DS to ensure that all motions closely follow the demonstrations while ultimately reaching and stopping at the target. Timeinvariance and global asymptotic stability at the target ensures that the system can respond immediately and appropriately to perturbations that are encountered during the motion. The method is evaluated through a set of robot experiments and on a library of human handwriting motions. Index Terms—Dynamical systems (DS), Gaussian mixture model, imitation learning, pointtopoint motions, stability analysis. I.
Slice sampling covariance hyperparameters of latent Gaussian models
 IN ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 23
, 2010
"... The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these hyperparameters considers different possible explanations fo ..."
Abstract

Cited by 56 (10 self)
 Add to MetaCart
The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these hyperparameters considers different possible explanations for the data when making predictions. This integration is often performed using Markov chain Monte Carlo (MCMC) sampling. However, with nonGaussian observations standard hyperparameter sampling approaches require careful tuning and may converge slowly. In this paper we present a slice sampling approach that requires little tuning while mixing well in both strong and weakdata regimes.
Beam Sampling for the Infinite Hidden Markov Model
"... The infinite hidden Markov model is a nonparametric extension of the widely used hidden Markov model. Our paper introduces a new inference algorithm for the infinite Hidden Markov model called beam sampling. Beam sampling combines slice sampling, which limits the number of states considered at each ..."
Abstract

Cited by 52 (8 self)
 Add to MetaCart
(Show Context)
The infinite hidden Markov model is a nonparametric extension of the widely used hidden Markov model. Our paper introduces a new inference algorithm for the infinite Hidden Markov model called beam sampling. Beam sampling combines slice sampling, which limits the number of states considered at each time step to a finite number, with dynamic programming, which samples whole state trajectories efficiently. Our algorithm typically outperforms the Gibbs sampler and is more robust. We present applications of iHMM inference using the beam sampler on changepoint detection and text prediction problems. 1.
Nonmyopic active learning of gaussian processes: An explorationexploitation approach
 IN ICML
, 2007
"... When monitoring spatial phenomena, such as the ecological condition of a river, deciding where to make observations is a challenging task. In these settings, a fundamental question is when an active learning, or sequential design, strategy, where locations are selected based on previous measurements ..."
Abstract

Cited by 51 (5 self)
 Add to MetaCart
(Show Context)
When monitoring spatial phenomena, such as the ecological condition of a river, deciding where to make observations is a challenging task. In these settings, a fundamental question is when an active learning, or sequential design, strategy, where locations are selected based on previous measurements, will perform significantly better than sensing at an a priori specified set of locations. For Gaussian Processes (GPs), which often accurately model spatial phenomena, we present an analysis and efficient algorithms that address this question. Central to our analysis is a theoretical bound which quantifies the performance difference between active and a priori design strategies. We consider GPs with unknown kernel parameters and present a nonmyopic approach for trading off exploration, i.e., decreasing uncertainty about the model parameters, and exploitation, i.e., nearoptimally selecting observations when the parameters are (approximately) known. We discuss several exploration strategies, and present logarithmic sample complexity bounds for the exploration phase. We then extend our algorithm to handle nonstationary GPs exploiting local structure in the model. A variational approach allows us to perform efficient inference in this class of nonstationary models. We also present extensive empirical evaluation on several realworld problems.
Relational learning with Gaussian processes
 In NIPS 19
, 2007
"... Correlation between instances is often modelled via a kernel function using input attributes of the instances. Relational knowledge can further reveal additional pairwise correlations between variables of interest. In this paper, we develop a class of models which incorporates both reciprocal relat ..."
Abstract

Cited by 45 (10 self)
 Add to MetaCart
(Show Context)
Correlation between instances is often modelled via a kernel function using input attributes of the instances. Relational knowledge can further reveal additional pairwise correlations between variables of interest. In this paper, we develop a class of models which incorporates both reciprocal relational information and input attributes using Gaussian process techniques. This approach provides a novel nonparametric Bayesian framework with a datadependent covariance function for supervised learning tasks. We also apply this framework to semisupervised learning. Experimental results on several real world data sets verify the usefulness of this algorithm. 1
Most likely heteroscedastic gaussian process regression
 In International Conference on Machine Learning (ICML
, 2007
"... This paper presents a novel Gaussian process (GP) approach to regression with inputdependent noise rates. We follow Goldberg et al.’s approach and model the noise variance using a second GP in addition to the GP governing the noisefree output value. In contrast to Goldberg et al., however, we do ..."
Abstract

Cited by 44 (3 self)
 Add to MetaCart
(Show Context)
This paper presents a novel Gaussian process (GP) approach to regression with inputdependent noise rates. We follow Goldberg et al.’s approach and model the noise variance using a second GP in addition to the GP governing the noisefree output value. In contrast to Goldberg et al., however, we do not use a Markov chain Monte Carlo method to approximate the posterior noise variance but a most likely noise approach. The resulting model is easy to implement and can directly be used in combination with various existing extensions of the standard GPs such as sparse approximations. Extensive experiments on both synthetic and realworld data, including a challenging perception problem in robotics, show the effectiveness of most likely heteroscedastic GP regression. 1.
A tutorial on Bayesian nonparametric models.
 Journal of Mathematical Psychology,
, 2012
"... Abstract A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number of clusters in mixture models or the number of factors in factor analysis. In this tutorial ..."
Abstract

Cited by 42 (9 self)
 Add to MetaCart
Abstract A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number of clusters in mixture models or the number of factors in factor analysis. In this tutorial we describe Bayesian nonparametric methods, a class of methods that sidesteps this issue by allowing the data to determine the complexity of the model. This tutorial is a highlevel introduction to Bayesian nonparametric methods and contains several examples of their application.
Gaussian processes and reinforcement learning for identification and control of an autonomous blimp
 in IEEE Intl. Conf. on Robotics and Automation (ICRA
, 2007
"... Abstract — Blimps are a promising platform for aerial robotics and have been studied extensively for this purpose. Unlike other aerial vehicles, blimps are relatively safe and also possess the ability to loiter for long periods. These advantages, however, have been difficult to exploit because blimp ..."
Abstract

Cited by 40 (8 self)
 Add to MetaCart
(Show Context)
Abstract — Blimps are a promising platform for aerial robotics and have been studied extensively for this purpose. Unlike other aerial vehicles, blimps are relatively safe and also possess the ability to loiter for long periods. These advantages, however, have been difficult to exploit because blimp dynamics are complex and inherently nonlinear. The classical approach to system modeling represents the system as an ordinary differential equation (ODE) based on Newtonian principles. A more recent modeling approach is based on representing state transitions as a Gaussian process (GP). In this paper, we present a general technique for system identification that combines these two modeling approaches into a single formulation. This is done by training a Gaussian process on the residual between the nonlinear model and ground truth training data. The result is a GPenhanced model that provides an estimate of uncertainty in addition to giving better state predictions than either ODE or GP alone. We show how the GPenhanced model can be used in conjunction with reinforcement learning to generate a blimp controller that is superior to those learned with ODE or GP models alone. I.