Gaussian Process Priors with Uncertain Inputs - Application to Multiple-Step Ahead Time Series Forecasting

By Agathe Girard, Carl E. Rasmussen, Joaquin Quiñonero Candela, Roderick Murray-Smith. 2002

497 citations recorded by the source corpus.

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “, Girard et al. (2002). A major drawback of previous studies is that they usually impose a strong parametric assumption on the form of probability distribution.”
Deep Factors for Forecasting (2019, background): “Gaussian Processes (Rasmussen & Williams, 2006; Seeger, 2004) (GPs) are another family of the models that have been applied to time series forecasting (Girard et al., 2003; Brahim-Belhouari & Bermak, 2004).”
Data-Efficient Reinforcement Learning with Probabilistic Model Predictive Control (2017, methodology): “MPC methods with deterministic models are useful only when model errors and system noise can be neglected in the problem [19, 12].”
Continual Multi-task Gaussian Processes (2019, methodology): “Similar uses of the predictive formula within the posterior distribution were analyzed in Girard et al. (2003) before the appearance of variational methods in the GP literature.”
Towards Real-Time Information Processing of Sensor Network Data Using Computationally Efficient Multi-output Gaussian Processes (2008, background): “Our approach has several advantages relative to sequential state-space models [8, 9], Firstly, these models require the discretisation of the time input, representing a discarding of potentially valuable information.”
GP-BayesFilters: Bayesian filtering using Gaussian process prediction and observation models (2008, methodology): “GPs have been applied successfully to the problem of learning predictive state models (Girard et al. 2005; Grimes et al. 2006; Ko et al. 2007b; Liu et al. 2005).”
Variational Gaussian Process Dynamical Systems (2011, methodology): “The model which employed an RBF covariance to govern the dynamics retained four dimensions, whereas the model that used the Matern kept only three.”
Deep Learning for Time Series Forecasting: Tutorial and Literature Survey (2020, methodology): “, via a Kalman filter, and Gaussian Processes (GPs) [27, 67, 149, 159].”
Empowerment for continuous agent—environment systems (2011, background): “In other words, it is ‘‘the best guess’’ where the agent should place itself in expectation of a yet unknown goal, assuming one wishes to minimize the number of steps to the goal.10 However, the performance in our scenarios is even better than that in that the natural goals that one would impose a…”
GluonTS: Probabilistic Time Series Models in Python (2019, background): “Further examples in this family include Gaussian Processes (Girard et al., 2003) and Deep Factor models (Maddix et al.”
Residential probabilistic load forecasting: A method using Gaussian process designed for electric load data (2018, methodology): “[43] used the recursive approach, however, they viewed the lagged values as random variables.”
Gaussian Process Training with Input Noise (2011, background): “[11] then gives the mean and variance of the posterior distribution, for a squared exponential kernel (equation 12), to be,”