The Experts below are selected from a list of 6588 Experts worldwide ranked by ideXlab platform
Sandra Hirche - One of the best experts on this subject based on the ideXlab platform.
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Learning stochastically stable Gaussian Process State–space models
IFAC Journal of Systems and Control, 2020Co-Authors: Jonas Umlauft, Sandra HircheAbstract:Abstract Control systems are increasingly applied in domains where an analytic description of the system dynamics does not exist or is difficult to obtain. Example applications include autonomous robots in unstructured environments, human behavior modeling for prediction and action recognition in human–machine-interaction, and chemical Process industry. In many of these cases, classical system identification is challenging, because a parametric model structure is unknown. Data-driven nonparametric models such as Gaussian Process State–space models (GPSSMs) offer a suitable alternative: GPSSMs are known for their data-efficiency and rely on Bayesian principles to include prior knowledge. However, properties like stability or boundedness are often known a priori, but rarely exploited during modeling. We therefore propose a novel approach for learning GPSSMs subject to stability constraints. Our approach enforces the convergence using control Lyapunov functions which are also obtained in a data-driven fashion. We analyze the resulting dynamics with respect to convergence radius and data collection. In simulation, we illustrate the precision of the identified model on a real-world dataset of goal-directed motions.
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Localized active learning of Gaussian Process State space models.
arXiv: Learning, 2020Co-Authors: Alexandre Capone, Thomas Beckers, Jonas Umlauft, Armin Lederer, Sandra HircheAbstract:The performance of learning-based control techniques crucially depends on how effectively the system is explored. While most exploration techniques aim to achieve a globally accurate model, such approaches are generally unsuited for systems with unbounded State spaces. Furthermore, a globally accurate model is not required to achieve good performance in many common control applications, e.g., local stabilization tasks. In this paper, we propose an active learning strategy for Gaussian Process State space models that aims to obtain an accurate model on a bounded subset of the State-action space. Our approach aims to maximize the mutual information of the exploration trajectories with respect to a discretization of the region of interest. By employing model predictive control, the proposed technique integrates information collected during exploration and adaptively improves its exploration strategy. To enable computational tractability, we decouple the choice of most informative data points from the model predictive control optimization step. This yields two optimization problems that can be solved in parallel. We apply the proposed method to explore the State space of various dynamical systems and compare our approach to a commonly used entropy-based exploration strategy. In all experiments, our method yields a better model within the region of interest than the entropy-based method.
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Uncertainty-based Human Motion Tracking with Stable Gaussian Process State Space Models
IFAC-PapersOnLine, 2019Co-Authors: Lukas Pohler, Jonas Umlauft, Sandra HircheAbstract:Abstract Data-driven approaches are well suited to represent human motion because arbitrary complex trajectories can be captured. Gaussian Process State space models allow to encode human motion while quantifying uncertainty due to missing data. Such human motion models are relevant for many application domains such as learning by demonstration and motion prediction in human-robot collaboration. For goal-directed tasks it is essential to impose stability constraints on the model representing the human motion. Motivated by learning by demonstration applications, this paper proposes an uncertainty-based control Lyapunov function approach for goal-directed path tracking. We exploit the model fidelity which is related to the location of the training and test data: Our approach actively strives into regions with more demonstration data and thus higher model certainty. This achieves accurate reproduction of the human motion independent of the initial condition and we show that generated trajectories are uniformly globally asymptotically stable. The approach is validated in a nonlinear learning by demonstration task where human-demonstrated motions are reproduced by the learned dynamical system, and higher precision than competitive State of the art methods is achieved.
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Scenario-based Optimal Control for Gaussian Process State Space Models
2018 European Control Conference (ECC), 2018Co-Authors: Jonas Umlauft, Thomas Beckers, Sandra HircheAbstract:Data-driven approaches from machine learning provide powerful tools to identify dynamical systems with limited prior knowledge of the model structure. More particular, the Gaussian Process State space model, a Bayesian nonparametric approach, is increasingly utilized in control. Its probabilistic nature is interpreted differently in the control literature, but so far, it is not considered as a distribution over dynamical system which allows a scenario-based control design. This paper introduces how scenarios are sampled from a Gaussian Process and utilizes them in a differential dynamic programming approach to solve an optimal control problem. For the linear-quadratic case, we derive probabilistic performance guarantees using results from robust convex optimization. The proposed methods are evaluated numerically for the nonlinear and linear case.
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ECC - Scenario-based Optimal Control for Gaussian Process State Space Models
2018 European Control Conference (ECC), 2018Co-Authors: Jonas Umlauft, Thomas Beckers, Sandra HircheAbstract:Data-driven approaches from machine learning provide powerful tools to identify dynamical systems with limited prior knowledge of the model structure. More particular, the Gaussian Process State space model, a Bayesian nonparametric approach, is increasingly utilized in control. Its probabilistic nature is interpreted differently in the control literature, but so far, it is not considered as a distribution over dynamical system which allows a scenario-based control design. This paper introduces how scenarios are sampled from a Gaussian Process and utilizes them in a differential dynamic programming approach to solve an optimal control problem. For the linear-quadratic case, we derive probabilistic performance guarantees using results from robust convex optimization. The proposed methods are evaluated numerically for the nonlinear and linear case.
Carl Edward Rasmussen - One of the best experts on this subject based on the ideXlab platform.
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Closed-form Inference and Prediction in Gaussian Process State-Space Models.
arXiv: Machine Learning, 2018Co-Authors: Alessandro Davide Ialongo, Mark Van Der Wilk, Carl Edward RasmussenAbstract:We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the system States and the transition function. We exploit Markov structure in the true posterior, as well as an inducing point approximation to achieve linear time complexity in the length of the time series. Contrary to previous approaches, no Monte Carlo sampling is required: inference is cast as a deterministic optimisation problem. In a number of experiments, we demonstrate the ability to model non-linear dynamics in the presence of both Process and observation noise as well as to impute missing information (e.g. velocities from raw positions through time), to de-noise, and to estimate the underlying dimensionality of the system. Finally, we also introduce a closed-form method for multi-step prediction, and a novel criterion for assessing the quality of our approximate posterior.
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variational gaussian Process State space models
Neural Information Processing Systems, 2014Co-Authors: Roger Frigola, Yutian Chen, Carl Edward RasmussenAbstract:State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear State-space models based on sparse Gaussian Processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo. We also present stochastic variational inference and online learning approaches for fast learning with long time series.
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NIPS - Variational Gaussian Process State-Space Models
2014Co-Authors: Roger Frigola, Yutian Chen, Carl Edward RasmussenAbstract:State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear State-space models based on sparse Gaussian Processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo. We also present stochastic variational inference and online learning approaches for fast learning with long time series.
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identification of gaussian Process State space models with particle stochastic approximation em
IFAC Proceedings Volumes, 2014Co-Authors: Roger Frigola, Thomas B. Schön, Fredrik Lindsten, Carl Edward RasmussenAbstract:Abstract Gaussian Process State-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism enables systematic reasoning about the uncertainty in the system dynamics. We present an approach to maximum likelihood identification of the parameters in GP-SSMs, while retaining the full nonparametric description of the dynamics. The method is based on a stochastic approximation version of the EM algorithm that employs recent developments in particle Markov chain Monte Carlo for efficient identification.
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bayesian inference and learning in gaussian Process State space models with particle mcmc
arXiv: Machine Learning, 2013Co-Authors: Roger Frigola, Thomas B. Schön, Fredrik Lindsten, Carl Edward RasmussenAbstract:State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. State estimation and system identification) in nonlinear nonparametric State-space models. We place a Gaussian Process prior over the State transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the State transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian Processes to greatly reduce computational complexity.
Xiao-ping Zhang - One of the best experts on this subject based on the ideXlab platform.
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Gaussian Process Regression Stochastic Volatility Model for Financial Time Series
IEEE Journal of Selected Topics in Signal Processing, 2016Co-Authors: Xiao-ping Zhang, Fang WangAbstract:Traditional economic models have rigid-form transition functions when modeling time-varying volatility of financial time series data and cannot capture other time-varying dynamics in the financial market. In this paper, combining the Gaussian Process State-space model framework and the stochastic volatility (SV) model, we introduce a new Gaussian Process regression stochastic volatility (GPRSV) model building procedures for financial time series data analysis and time-varying volatility modeling. The GPRSV extends the SV model. The flexible stochastic nature of the Gaussian Process State description allows the model to capture more time-varying dynamics of the financial market. We also present the model estimation methods for the GPRSV model. We demonstrate the superior volatility prediction performance of our model with both simulated and empirical financial data.
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GlobalSIP - Financial time series volatility analysis using Gaussian Process State-space models
2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2015Co-Authors: Xiao-ping ZhangAbstract:In this paper, we propose a novel nonparametric modeling framework for financial time series data analysis, and apply it to the problem of time varying volatility modeling. Existing parametric models have a rigid-form transition function and they often have over-fitting problems when model parameters are estimated using maximum likelihood methods. These drawbacks effect the models' prediction performance. To solve this problem, we take Bayesian nonparametric modeling approach. By adding Gaussian Process prior to the hidden State transition Process, we extend the standard State-space model to a Gaussian Process State-space model. We introduce the Gaussian Process regression stochastic volatility (GPRSV) model and instead of using maximum likelihood methods, we use Monte Carlo inference algorithms. We demonstrate performance of our model and inference methods with both simulated and empirical financial data.
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Financial time series volatility analysis using Gaussian Process State-space models
2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2015Co-Authors: Xiao-ping ZhangAbstract:In this paper, we propose a novel nonparametric modeling framework for financial time series data analysis, and apply it to the problem of time varying volatility modeling. Existing parametric models have a rigid-form transition function and they often have over-fitting problems when model parameters are estimated using maximum likelihood methods. These drawbacks effect the models' prediction performance. To solve this problem, we take Bayesian nonparametric modeling approach. By adding Gaussian Process prior to the hidden State transition Process, we extend the standard State-space model to a Gaussian Process State-space model. We introduce the Gaussian Process regression stochastic volatility (GPRSV) model and instead of using maximum likelihood methods, we use Monte Carlo inference algorithms. We demonstrate performance of our model and inference methods with both simulated and empirical financial data.
Roger Frigola - One of the best experts on this subject based on the ideXlab platform.
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NIPS - Variational Gaussian Process State-Space Models
2014Co-Authors: Roger Frigola, Yutian Chen, Carl Edward RasmussenAbstract:State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear State-space models based on sparse Gaussian Processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo. We also present stochastic variational inference and online learning approaches for fast learning with long time series.
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variational gaussian Process State space models
Neural Information Processing Systems, 2014Co-Authors: Roger Frigola, Yutian Chen, Carl Edward RasmussenAbstract:State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear State-space models based on sparse Gaussian Processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo. We also present stochastic variational inference and online learning approaches for fast learning with long time series.
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identification of gaussian Process State space models with particle stochastic approximation em
IFAC Proceedings Volumes, 2014Co-Authors: Roger Frigola, Thomas B. Schön, Fredrik Lindsten, Carl Edward RasmussenAbstract:Abstract Gaussian Process State-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism enables systematic reasoning about the uncertainty in the system dynamics. We present an approach to maximum likelihood identification of the parameters in GP-SSMs, while retaining the full nonparametric description of the dynamics. The method is based on a stochastic approximation version of the EM algorithm that employs recent developments in particle Markov chain Monte Carlo for efficient identification.
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bayesian inference and learning in gaussian Process State space models with particle mcmc
arXiv: Machine Learning, 2013Co-Authors: Roger Frigola, Thomas B. Schön, Fredrik Lindsten, Carl Edward RasmussenAbstract:State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. State estimation and system identification) in nonlinear nonparametric State-space models. We place a Gaussian Process prior over the State transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the State transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian Processes to greatly reduce computational complexity.
Karl Berntorp - One of the best experts on this subject based on the ideXlab platform.
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Recursive Bayesian Inference and Learning of Gaussian-Process State-Space Models
2019 18th European Control Conference (ECC), 2019Co-Authors: Karl BerntorpAbstract:Gaussian Processes in combination with sequential Monte-Carlo methods have emerged as promising tools for offline nonlinear system identification. However, sometimes the dynamical system evolves in such a way that online learning is preferable. This paper addresses the online joint State estimation and learning problem for nonlinear dynamical systems. We leverage a recently developed reduced-rank formulation of Gaussian-Process State-space models (GP-SSMs), and develop a recursive formulation for updating the sufficient statistics associated with the GP-SSM by exploiting marginalization and conjugate priors. The results indicate that our method efficiently learns the system jointly with estimating the State, and that the approach for certain scenarios gives similar performance as more computation-heavy offline approaches.
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Bayesian Tire-Friction Learning by Gaussian-Process State-Space Models
2019 18th European Control Conference (ECC), 2019Co-Authors: Karl BerntorpAbstract:This paper addresses learning of the tire-friction curve for road vehicles, using a batch of wheel-speed and inertial measurements. We formulate a Bayesian approach based on recent advances in particle filtering and Markov chain Monte-Carlo methods. The unknown function mapping the wheel slip to tire friction is modeled as a Gaussian Process (GP) that is included in a dynamic vehicle model relating the GP to the vehicle State. The approach is nonparametric and learns the probability density function of the tire friction, from which explicit estimates can be extracted. One benefit of the method is that it is not subject to overfitting issues. We illustrate the efficacy of the method for a set of simulated step-steer maneuvers. The results show that the method can accurately identify the nonlinear tire-friction curves, even for a limited amount of data.
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ECC - Recursive Bayesian Inference and Learning of Gaussian-Process State-Space Models
2019 18th European Control Conference (ECC), 2019Co-Authors: Karl BerntorpAbstract:Gaussian Processes in combination with sequential Monte-Carlo methods have emerged as promising tools for offline nonlinear system identification. However, sometimes the dynamical system evolves in such a way that online learning is preferable. This paper addresses the online joint State estimation and learning problem for nonlinear dynamical systems. We leverage a recently developed reduced-rank formulation of Gaussian-Process State-space models (GP-SSMs), and develop a recursive formulation for updating the sufficient statistics associated with the GP-SSM by exploiting marginalization and conjugate priors. The results indicate that our method efficiently learns the system jointly with estimating the State, and that the approach for certain scenarios gives similar performance as more computation-heavy offline approaches.
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Bayesian Learning of Tire Friction with Automotive-Grade Sensors by Gaussian-Process State-Space Models
2019 IEEE 58th Conference on Decision and Control (CDC), 2019Co-Authors: Karl Berntorp, Kitano HiroakiAbstract:The friction dependence between tire and road is highly nonlinear and varies heavily between different surfaces. Knowledge of the tire friction is important for real-time vehicle control, but difficult to estimate with automotive-grade sensors. Based on recent advances in particle filtering and Markov chain Monte-Carlo methods, we propose a batch method for identifying the tire friction as a function of the wheel slip. The unknown function mapping the wheel slip to tire friction is modeled as a Gaussian Process (GP) that is included in a dynamic vehicle model relating the GP to the vehicle State. The method is able to efficiently learn the tire friction using only wheel-speed, steering-wheel angle, and inertial automotive-grade sensors. We illustrate the efficacy of the method using several experimental data sets obtained on a snow-covered road.