Propagation of uncertainty in Bayesian kernel models - application to multiple-step ahead forecasting

By Joaquin Quiñonero Candela, Agathe Girard, J. Larsen, Carl E. Rasmussen. 2003

172 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

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Citations in the corpus

Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models (2018, methodology): “Multiple approaches to approximate uncertainty propagation can be found in the literature [Girard et al., 2002, Quiñonero-Candela et al., 2003].”
Learning to Control a Low-Cost Manipulator using Data-Efficient Reinforcement Learning (2011, background): “In the following, we assume that these test inputs are Gaussian distributed and extend the results from [17, 6, 7] to long-term planning in stochastic systems with control inputs.”
Gaussian Processes for Data-Efficient Learning in Robotics and Control (2015, background): “For uncertain inputs, the target dimensions covary [44], see also Sec.”
Probabilistic Differential Dynamic Programming (2014, methodology): “However, the predictive distribution can be approximated by a Gaussian p(dxk) ∼ N (dμk,dΣk) [16].”
Data-Efficient Reinforcement Learning in Continuous State-Action Gaussian-POMDPs (2017, background): “[1] generalised to hierarchically-uncertain inputs detailed in Appendix E.”
Gaussian Process Priors with Uncertain Inputs - Application to Multiple-Step Ahead Time Series Forecasting (2002, methodology): “In [8], we derived the exact expressions of the first and second moments.”
Probabilistic model-based imitation learning (2013, background): “, p(xT ), therefore, requires to predict with Gaussian processes at uncertain inputs [32].”
Expectation Propagation in Gaussian Process Dynamical Systems (2012, methodology): “However, the mean and covariance of a Gaussian approximation Z̃M to ZM can be computed analytically: either using exact moment matching [14, 3], or approximately by expected linearization of the posterior GP [8]; details are given in [4].”
State-Space Inference and Learning with Gaussian Processes (2010, methodology): “Once the pseudo training set, α and β, is determined , predicting x t from x t−1 is a GP prediction using GP f (Deisenroth et al., 2009; Quiñonero-Candela et al., 2003).”
Analytic moment-based Gaussian process filtering (2009, methodology): “Furthermore, we approximate the predictive distribution by a Gaussian with the exact mean and the exact covariance matrix, which can be computed analytically using results from (Quiñonero-Candela et al., 2003).”
PILCO: A Model-Based and Data-Efficient Approach to Policy Search (2011, methodology): “In the following, we assume that these test inputs are Gaussian distributed and extend the results from Quiñonero-Candela et al. (2003) to the multivariate case and the incorporation of controls.”
Stability of Controllers for Gaussian Process Forward Models (2016, methodology): “, via moment matching (Quiñonero-Candela et al., 2003) or linearization (Ko & Fox, 2008), can be computed.”