# Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families

@inproceedings{Strathmann2015GradientfreeHM, title={Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families}, author={Heiko Strathmann and D. Sejdinovic and Samuel Livingstone and Zolt{\'a}n Szab{\'o} and Arthur Gretton}, booktitle={NIPS}, year={2015} }

We propose Kernel Hamiltonian Monte Carlo (KMC), a gradient-free adaptive MCMC algorithm based on Hamiltonian Monte Carlo (HMC). On target densities where classical HMC is not an option due to intractable gradients, KMC adaptively learns the target's gradient structure by fitting an exponential family model in a Reproducing Kernel Hilbert Space. Computational costs are reduced by two novel efficient approximations to this gradient. While being asymptotically exact, KMC mimics HMC in terms of…

## 68 Citations

### Modified Hamiltonian Monte Carlo for Bayesian inference

- Computer ScienceStat. Comput.
- 2020

It is shown that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible part of the dynamics into a chain, and is called Mix & Match Hamiltonian Monte Carlo (MMHMC).

### Maximum Conditional Entropy Hamiltonian Monte Carlo Sampler

- Computer ScienceSIAM J. Sci. Comput.
- 2021

A Kolmogorov-Sinai entropy (KSE) based design criterion is proposed to optimize algorithm parameters, which can avoid some potential issues in the often used jumping-distance based measures.

### Hamiltonian Monte Carlo Acceleration Using Neural Network Surrogate functions

- Computer Science
- 2015

An efficient and scalable computational technique for a state-of-the-art Markov Chain Monte Carlo methods, namely, Hamiltonian Monte Carlo (HMC), to explore and exploit the regularity in parameter space for the underlying probabilistic model to construct an effective approximation of the collective geometric and statistical properties of the whole observed data.

### Kernel Sequential Monte Carlo

- Computer ScienceECML/PKDD
- 2017

Kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities, is proposed, which combines the strengths of sequental Monte Carlo and kernel methods and the emulator’s ability to represent targets that exhibit high degrees of nonlinearity.

### Kernel Sequential Monte

- Computer Science
- 2017

Kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities, is proposed, which combines the strengths of sequental Monte Carlo and kernel methods and the emulator’s ability to represent targets that exhibit high degrees of nonlinearity.

### Pseudo-Marginal Hamiltonian Monte Carlo

- Computer ScienceJ. Mach. Learn. Res.
- 2021

An original MCMC algorithm, termed pseudo-marginal HMC, is proposed, which approximates the HMC algorithm targeting the marginal posterior of the parameters and can outperform significantly both standard HMC and pseudo- Marginal MH schemes.

### Slice Sampling on Hamiltonian Trajectories

- Mathematics, PhysicsICML
- 2016

Hamiltonian slice sampling is presented, which allows slice sampling to be carried out along Hamiltonian trajectories, or transformations thereof, and offers advantages over Hamiltonian Monte Carlo, in that it has fewer tunable hyperparameters and does not require gradient information.

### SpHMC: Spectral Hamiltonian Monte Carlo

- Computer ScienceAAAI
- 2019

This piece of work proposed a novel SGHMC sampler, namely Spectral Hamiltonian Monte Carlo (SpHMC), that produces the high dimensional sparse representations of given datasets through sparse sensing and S GHMC.

### Scalable Hamiltonian Monte Carlo via Surrogate Methods

- Computer Science
- 2016

A random network surrogate architecture is proposed which can effectively capture the collective properties of large data sets or complex models with scalability, flexibility and efficiency and an approximate inference framework that combines the advantages of both variational Bayes and Markov chain Monte Carlo methods is proposed.

### Mix & Match Hamiltonian Monte Carlo

- Computer Science
- 2017

It is shown that performance of HMC can be dramatically improved by incorporating importance sampling and an irreversible part of the dynamics into the chain, and the resulting generalized HMC importance sampler is called Mix & Match Hamiltonian Monte Carlo.

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