Gaussian Processes to Speed up Hybrid Monte Carlo for Expensive Bayesian Integrals

By Carl E. Rasmussen, J. Bernardo, Maria J. Bayarri, James O. Berger, A. P. Dawid, David E. Heckerman, Adrian F. M. Smith, Matthew West. 2003

206 citations recorded by the source corpus.

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Citations in the corpus

Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families (2015, methodology): “Gaussian Processes (GP) were also used in [16] as an emulator of the target density in order to speed up HMC, however, this requires access to the target in closed form, to provide training points for the GP.”
Handbook of Markov Chain Monte Carlo (2011, neutral): “Rasmussen (2003) has proposed approximating the potential energy by modeling it as a Gaussian process, that is inferred from values of the potential energy at positions selected during an initial exploratory phase.”
Gaussian Processes for Prediction (2007, methodology): “The study of other noise models forms an active area of research, see Rasmussen and Williams [2006].”
Efficient Acquisition Rules for Model-Based Approximate Bayesian Computation (2017, methodology): “Rasmussen (2003) used GP regression to accelerate Hybrid Monte Carlo but did not consider the setting of ABC.”
Bayesian Optimization in a Billion Dimensions via Random Embeddings (2013, methodology): “In recent years, the machine learning community has increasingly used Bayesian optimization (Rasmussen, 2003; Brochu et al., 2007; Martinez-Cantin et al., 2007; Lizotte et al., 2007; Frazier et al., 2009; Azimi et al., 2010; Hamze et al., 2011; Azimi et al., 2011; Bergstra et al., 2011; Gramacy &…”
GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation (2014, methodology): “For example, in [17] a Hamiltonian Monte Carlo run on the GP surface is used to generate independent proposals.”
Gaussian Processes for Regression and Optimisation (2007, methodology): “Interesting machine learning applications include Gaussian processes for reinforcement learning [60], the incorporation of derivative observations into Gaussian process models [73], Gaussian processes to speed up the evaluation of Bayesian integrals [58], and Gaussian process models of dynamical sys”
Neural Network Renormalization Group (2018, background): “Training such proposal policy is different from the previous attempts of training surrogate functions [57, 58, 62, 63] or”
Portfolio Allocation for Bayesian Optimization (2010, background): “Examples can be found in robot gait design [23], online path planning [24, 25], intelligent user interfaces for animation [6, 4], algorithm conﬁguration [17], eﬃcient MCMC [28], sensor placement [31, 27], and reinforcement learning [5].”
Hamiltonian Monte Carlo Acceleration Using Neural Network Surrogate functions (2015, methodology): “Following [14], we propose to run our method, henceforth cal led neural network surrogate Hamiltonian Monte Carlo (NNS-HMC, see Algorithm 3), in two phases: explo ration phase and exploitation phase.”
Hamiltonian ABC (2015, background): “However, previous work in Bayesian inference has shown the usefulness of HMC-based proposals based on Gaussian process of loglikelihood surfaces [18].”
Adaptive MCMC with Bayesian Optimization (2012, background): “…the strategy in the complex setting of sampling from constrained, discrete and densely connected probabilistic graphical models where, for each variation of the problem, one needs to adjust the parameters of the proposal mechanism automatically to ensure efficient mixing of the Markov chains.”
Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models (2015, methodology): “Our approach is related to the work by Rasmussen (2003) and the two recent papers by Wilkinson (2014) and Meeds and Welling (2014) (which became only available after we first proposed our approach at “ABC in Rome” in 2013): Rasmussen (2003) used a Gaussian process to model the logarithm of the…”
Adaptive Gaussian Process Approximation for Bayesian Inference with Expensive Likelihood Functions (2017, methodology): “rocess (GP) model [33]. The idea of using the GP model to approximate the posterior or the likelihood function dates back to the the so-called Bayesian quadrature (or Bayesian Monte Carlo) approaches [22, 27, 26, 10], which were designed to perform numerical integrations in a Bayesian fashion (for e”
MCMC Using Hamiltonian Dynamics (2011, background): “eal, 1998; Rasmussen and Williams, 2006), for which computation time scales as the cube of the number of data points, so that even a small reduction in the number of points produces a useful speedup. Rasmussen (2003) has proposed approximating the potential energy by modeling it as a Gaussian proces”
Many-Body Coarse-Grained Interactions Using Gaussian Approximation Potentials. (2016, unknown): “We can also train the Gaussian process from derivative observations [122, 123].”