# The Fundamental Incompatibility of Hamiltonian Monte Carlo and Data Subsampling

arXiv: https://arxiv.org/abs/1502.01510 · HTML: https://mlsanity.com/paper/1502.01510/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2015.

## Built on by (most cited first, 7 of 7)

- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Bayesian inference via sparse Hamiltonian flows](https://mlsanity.com/paper/2203.05723/) (2022)
- [Fast Bayesian Coresets via Subsampling and Quasi-Newton Refinement](https://mlsanity.com/paper/2203.09675/) (2022)
- [Decentralized Bayesian Learning with Metropolis-Adjusted Hamiltonian Monte Carlo](https://mlsanity.com/paper/2107.07211/) (2021)
- [Variational Inference with Locally Enhanced Bounds for Hierarchical Models](https://mlsanity.com/paper/2203.04432/) (2022)
- [Bayesian Pseudo-Coresets via Contrastive Divergence](https://mlsanity.com/paper/2303.11278/) (2023)
- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)

## Abstract (arXiv)

Leveraging the coherent exploration of Hamiltonian flow, Hamiltonian Monte Carlo produces computationally efficient Monte Carlo estimators, even with respect to complex and high-dimensional target distributions. When confronted with data-intensive applications, however, the algorithm may be too expensive to implement, leaving us to consider the utility of approximations such as data subsampling. In this paper I demonstrate how data subsampling fundamentally compromises the efficient exploration of Hamiltonian flow and hence the scalable performance of Hamiltonian Monte Carlo itself.