Gaussian Process Approximations of Stochastic Differential Equations

By Cédric Archambeau, Dan Cornford, Manfred Opper, John Shawe-Taylor. 2007

176 citations recorded by the source corpus.

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Citations in the corpus

Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges (2021, background): “…Gaussian processes for approximating solutions to PDEs, these Gaussianprocess solutions often rely on discrete (finite-difference) approximations for the original PDEs (see Zhao et al., 2011), or they could be non-differentiable at times where there are observations (see Archambeau et al., 2007).”
Variational Inference: A Review for Statisticians (2016, background): “…Dunson 2011; Armagan and Dunson 2011; Neville, Ormerod, and Wand 2014), general time-series models (Roberts et al. 2004; Barber and Chiappa 2006; Archambeau et al. 2007a, 2007b; Johnson and Willsky 2014; Foti et al. 2014), robust models (Tipping and Lawrence 2005; Wang and Blei 2015), and…”
Explaining Variational Approximations (2010, background): “Examples where it has appeared are the works by Barber and Bishop (1998), Seeger (2000, 2004), Honkela and Valpola (2005), and Archambeau et al.”
AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs (2019, methodology): “S¨arkk¨a et al. (2015) investigate different approximation methods based on Kalman ﬁltering, while Archambeau et al. (2007) and Vrettas et al. (2015) use a variational Gaussian Process-based approximation.”
Learning Stationary Time Series using Gaussian Processes with Nonparametric Kernels (2015, background): “In this way, the prior over h(t) implicitly defines a prior over the coefficients of linear differential equations of potentially infinite order [13].”
Applied Stochastic Differential Equations (2019, methodology): “274 Stochastic Differential Equations in Machine Learning The variational Gaussian process approximation to the smoothing problem can thus be given in the form of the following algorithm (Archambeau et al., 2007).”
DEM: A variational treatment of dynamic systems (2008, methodology): “Archambeau et al. (2007)motivate the importance of this inference for models based on stochastic differential equations and presents a clever approach based on Gaussian process approximations.”
Hierarchical Models in the Brain (2008, background): “Perhaps the work of Archambeau et al. [75] is formally the closest to one presented in this paper.”
Semiparametric Mean Field Variational Bayes: General Principles and Numerical Issues (2016, methodology): “Gaussian Q families have also been used by Lappalainen and Honkela (2000), Archambeau et al. (2007), Raiko et al. (2007), Nickisch and Rasmussen (2008), Honkela and Valpola (2005), Honkela et al. (2007), Honkela et al. (2008) and Opper and Archambeau (2009). The recent contribution by Challis and Ba”