Bayesian Monte Carlo

By Carl E. Rasmussen, Zoubin Ghahramani. 2002

322 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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In Probabilistic & Bayesian Methods

Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “There are some recent studies on high-dimensional analysis of MMD and related tests: see Reddi et al. (2015), Ramdas et al.”
On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions (2015, methodology): “For these problems, techniques based on positive definite kernels have emerged as having the potential to efficiently deal with these situations, and to improve over plain Monte-Carlo integration (O’Hagan, 1991; Rasmussen and Ghahramani, 2003; Huszár and Duvenaud, 2012; Oates and Girolami, 2015).”
Control functionals for Monte Carlo integration (2014, methodology): “These include (a) importance sampling and its extensions (Cornuet et al., 2012; Li et al., 2013), (b) stratified sampling and related techniques (Rubinstein and Kroese, 2011), (c) antithetic variables (Green and Han, 1992) and more generally (randomized) quasi- Monte-Carlo (RQMC) sampling (Dick and ”
Quasi-Monte Carlo Feature Maps for Shift-Invariant Kernels (2014, methodology): “(17) Selecting the weights in such a way is closely connected to the so-called Bayesian Monte Carlo (BMC) method, originally suggested by Ghahramani and Rasmussen (2003). In BMC, a Bayesian approach is utilized in which the function is a assumed to be random with a prior that is a Gaussian Process.”
Super-Samples from Kernel Herding (2010, methodology): “ This is illustrated in Figure 1 for a mixture of Gaussians. Similar ideas are the basis for methods such as Quasi Monte Carlo sampling, Quadrature integration and more recently Bayesian integration [Rasmussen and Ghahramani, 2002]. For kernel herding one needs to be able to convolve the density p w”
Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature (2014, methodology): “When a GP prior is placed directly on the integrand in this manner, the posterior mean and variance of the integral can be derived analytically through the use of Gaussian identities, as in [10].”
Towards Real-Time Information Processing of Sensor Network Data Using Computationally Efficient Multi-output Gaussian Processes (2008, methodology): “To this end, we apply Bayesian Monte Carlo, and thus, assign a second GP prior to these functions [17].”
Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees (2015, methodology): “To facilitate the experiments in this paper we followed [1, 2, 11, 18] and employed an exponentiatedquadratic (EQ) kernel k(x, x′) := λ(2) exp(−1/2σ2‖x − x‖(2)2).”
Gaussian Processes for Prediction (2007, background): “But what do we assign to our prior p( q(·) | I )? Bayesian Monte Carlo [Rasmussen and Ghahramani, 2003], née Bayes-Hermite Quadrature [O’Hagan, 1991] chooses a GP, p( q | I ) = N(q; 0, K).”