Kernel Adaptive Metropolis-Hastings

By Dino Sejdinovic, Heiko Strathmann, M. Garcia, Christophe Andrieu, Arthur Gretton. 2013

47 citations recorded by the source corpus.

A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the choice of proposal. The procedure is computationally efficient and straightforward to implement, since the RKHS moves can be integrated out analytically: our proposal distribution in the original space is a normal distribution whose mean and covariance depend on where the current sample lies in the support of the target distribution, and adapts to its local covariance structure. Furthermore, the procedure requires neither gradients nor any other higher order information about the target, making it particularly attractive for contexts such as Pseudo-Marginal MCMC. Kernel Adaptive Metropolis-Hastings outperforms competing fixed and adaptive samplers on multivariate, highly nonlinear target distributions, arising in both real-world and synthetic examples.

Subfields: Artificial Intelligence, Statistics and Probability, Optimization & Training, Probabilistic & Bayesian Methods

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

In Optimization & Training

In Probabilistic & Bayesian Methods

Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “MCMC is a classical technique for estimating the expectations in approximate Bayesian inference (Robert and Casella 2005, Neal 1993).”
Kernel Sequential Monte Carlo (2015, methodology): “Sejdinovic et al. [20] showed that it is possible to integrate out the RKHS proposal analytically, which elegantly results in a closed form Gaussian proposal density in the input space.”
Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families (2015, methodology): “We are interested in constructing a Markov chain x 1 → x 2 → . . . such that lim t →∞ x t ∼ π .”
K2-ABC: Approximate Bayesian Computation with Infinite Dimensional Summary Statistics via Kernel Embeddings (2015, methodology): “Embeddings of probability measures into RKHSs (Berlinet & Thomas-Agnan, 2004; Smola et al., 2007; Sriperumbudur et al., 2010) offer a flexible representation of probability measures and have been used in nonparametric hypothesis testing (Gretton et al., 2012), inference in graphical models (Song et ”
A Spectral Approach to Gradient Estimation for Implicit Distributions (2018, background): “As mentioned in Section 4, kernel adaptive Metropolis samplers (Sejdinovic et al., 2014) were developed and then extended to kernel HMC (KMC) (Strath-mann et al., 2015).”
Generalizing Hamiltonian Monte Carlo with Neural Networks (2017, methodology): “Kernel methods have been used both for learning a proposal distribution (Sejdinovic et al., 2014) and for approximating the gradient of the energy (Strathmann et al.”
Gradient Importance Sampling (2015, unknown): “We can still have =1 p t →∞ as N → ∞ , i.e. inﬁnite overall adaptation (as in [15]).”