# Entropy-based adaptive Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/2110.14625 · HTML: https://mlsanity.com/paper/2110.14625/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 62 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [Understanding and Mitigating Exploding Inverses in Invertible Neural Networks](https://mlsanity.com/paper/2006.09347/) (2020)
- [Generalizing Hamiltonian Monte Carlo with Neural Networks](https://mlsanity.com/paper/1711.09268/) (2017)
- [Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradients](https://mlsanity.com/paper/1905.12247/) (2019)
- [Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributions](https://mlsanity.com/paper/1905.02313/) (2019)
- [Geometric integrators and the Hamiltonian Monte Carlo method](https://mlsanity.com/paper/1711.05337/) (2017)
- [On the Geometric Ergodicity of Hamiltonian Monte Carlo](https://mlsanity.com/paper/1601.08057/) (2016)
- [On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods](https://mlsanity.com/paper/1306.4032/) (2013)
- [Gradient-based Adaptive Markov Chain Monte Carlo](https://mlsanity.com/paper/1911.01373/) (2019)
- [Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributions](https://mlsanity.com/paper/1708.07114/) (2017)
- [A Neural Network MCMC sampler that maximizes Proposal Entropy](https://mlsanity.com/paper/2010.03587/) (2020)
- [Leave Pima Indians alone: binary regression as a benchmark for Bayesian computation](https://mlsanity.com/paper/1506.08640/) (2015)
- [Banded Matrix Operators for Gaussian Markov Models in the Automatic Differentiation Era](https://mlsanity.com/paper/1902.10078/) (2019)
- [Hamiltonian Monte Carlo Without Detailed Balance](https://mlsanity.com/paper/1409.5191/) (2014)
- [tfp.mcmc: Modern Markov Chain Monte Carlo Tools Built for Modern Hardware](https://mlsanity.com/paper/2002.01184/) (2020)
- [A general perspective on the Metropolis-Hastings kernel](https://mlsanity.com/paper/2012.14881/) (2020)
- [Couplings for Multinomial Hamiltonian Monte Carlo](https://mlsanity.com/paper/2104.05134/) (2021)
- [Stochastic Chebyshev Gradient Descent for Spectral Optimization](https://mlsanity.com/paper/1802.06355/) (2018)
- [A Condition Number for Hamiltonian Monte Carlo](https://mlsanity.com/paper/1905.09813/) (2019)
- [Markov chain Monte Carlo algorithms with sequential proposals](https://mlsanity.com/paper/1907.06544/) (2019)
- [Semi-Empirical Objective Functions for MCMC Proposal Optimization](https://mlsanity.com/paper/2106.02104/) (2021)

## Built on by (most cited first, 5 of 5)

- [Optimal Scaling for Locally Balanced Proposals in Discrete Spaces](https://mlsanity.com/paper/2209.08183/) (2022)
- [Accelerating Hamiltonian Monte Carlo via Chebyshev Integration Time](https://mlsanity.com/paper/2207.02189/) (2022)
- [Score-Based Metropolis-Hastings Algorithms](https://mlsanity.com/paper/2501.00467/) (2024)
- [Ai-Sampler: Adversarial Learning of Markov kernels with involutive maps](https://mlsanity.com/paper/2406.02490/) (2024)
- [Learning variational autoencoders via MCMC speed measures](https://mlsanity.com/paper/2308.13731/) (2023)

## Abstract (arXiv)

Hamiltonian Monte Carlo (HMC) is a popular Markov Chain Monte Carlo (MCMC) algorithm to sample from an unnormalized probability distribution. A leapfrog integrator is commonly used to implement HMC in practice, but its performance can be sensitive to the choice of mass matrix used therein. We develop a gradient-based algorithm that allows for the adaptation of the mass matrix by encouraging the leapfrog integrator to have high acceptance rates while also exploring all dimensions jointly. In contrast to previous work that adapt the hyperparameters of HMC using some form of expected squared jumping distance, the adaptation strategy suggested here aims to increase sampling efficiency by maximizing an approximation of the proposal entropy. We illustrate that using multiple gradients in the HMC proposal can be beneficial compared to a single gradient-step in Metropolis-adjusted Langevin proposals. Empirical evidence suggests that the adaptation method can outperform different versions of HMC schemes by adjusting the mass matrix to the geometry of the target distribution and by providing some control on the integration time.