# A-NICE-MC: Adversarial Training for MCMC

arXiv: https://arxiv.org/abs/1706.07561 · HTML: https://mlsanity.com/paper/1706.07561/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2017.

## Built on by (most cited first, 30 of 38)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Versatile Diffusion: Text, Images and Variations All in One Diffusion Model](https://mlsanity.com/paper/2211.08332/) (2022)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamics](https://mlsanity.com/paper/2302.01170/) (2023)
- [Estimating High Order Gradients of the Data Distribution by Denoising](https://mlsanity.com/paper/2111.04726/) (2021)
- [Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint](https://mlsanity.com/paper/2109.11375/) (2021)
- [Aspects of scaling and scalability for flow-based sampling of lattice QCD](https://mlsanity.com/paper/2211.07541/) (2022)
- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [Local-Global MCMC kernels: the best of both worlds](https://mlsanity.com/paper/2111.02702/) (2021)
- [Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks](https://mlsanity.com/paper/2105.05650/) (2021)
- [Efficient Bayesian Sampling Using Normalizing Flows to Assist Markov Chain Monte Carlo Methods](https://mlsanity.com/paper/2107.08001/) (2021)
- [Applications of Machine Learning to Lattice Quantum Field Theory](https://mlsanity.com/paper/2202.05838/) (2022)
- [Optimal Preconditioning and Fisher Adaptive Langevin Sampling](https://mlsanity.com/paper/2305.14442/) (2023)
- [Energy-Guided Continuous Entropic Barycenter Estimation for General Costs](https://mlsanity.com/paper/2310.01105/) (2023)
- [LSB: Local Self-Balancing MCMC in Discrete Spaces](https://mlsanity.com/paper/2109.03867/) (2021)
- [Energy based diffusion generator for efficient sampling of Boltzmann distributions](https://mlsanity.com/paper/2401.02080/) (2024)
- [Modeling Unknown Stochastic Dynamical System Subject to External Excitation](https://mlsanity.com/paper/2406.15747/) (2024)
- [Zero-shot-Learning Cross-Modality Data Translation Through Mutual Information Guided Stochastic Diffusion](https://mlsanity.com/paper/2301.13743/) (2023)
- [Bootstrap Your Flow](https://mlsanity.com/paper/2111.11510/) (2021)
- [Quasi-Bayes meets Vines](https://mlsanity.com/paper/2406.12764/) (2024)
- [Hitchhiker's guide on the relation of Energy-Based Models with other generative models, sampling and statistical physics: a comprehensive review](https://mlsanity.com/paper/2406.13661/) (2024)
- [A Diffusion-based Method for Multi-turn Compositional Image Generation](https://mlsanity.com/paper/2304.02192/) (2023)
- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)
- [Self-Tuning Hamiltonian Monte Carlo for Accelerated Sampling](https://mlsanity.com/paper/2309.13593/) (2023)
- [Score-Based Metropolis-Hastings Algorithms](https://mlsanity.com/paper/2501.00467/) (2024)
- [Learning Non-linear Wavelet Transformation via Normalizing Flow](https://mlsanity.com/paper/2101.11306/) (2021)
- [Reparameterized Sampling for Generative Adversarial Networks](https://mlsanity.com/paper/2107.00352/) (2021)
- [Semi-Empirical Objective Functions for MCMC Proposal Optimization](https://mlsanity.com/paper/2106.02104/) (2021)
- [Probabilistic Regular Tree Priors for Scientific Symbolic Reasoning](https://mlsanity.com/paper/2306.08506/) (2023)

## Abstract (arXiv)

Existing Markov Chain Monte Carlo (MCMC) methods are either based on general-purpose and domain-agnostic schemes which can lead to slow convergence, or hand-crafting of problem-specific proposals by an expert. We propose A-NICE-MC, a novel method to train flexible parametric Markov chain kernels to produce samples with desired properties. First, we propose an efficient likelihood-free adversarial training method to train a Markov chain and mimic a given data distribution. Then, we leverage flexible volume preserving flows to obtain parametric kernels for MCMC. Using a bootstrap approach, we show how to train efficient Markov chains to sample from a prescribed posterior distribution by iteratively improving the quality of both the model and the samples. A-NICE-MC provides the first framework to automatically design efficient domain-specific MCMC proposals. Empirical results demonstrate that A-NICE-MC combines the strong guarantees of MCMC with the expressiveness of deep neural networks, and is able to significantly outperform competing methods such as Hamiltonian Monte Carlo.