# NEO: Non Equilibrium Sampling on the Orbit of a Deterministic Transform

arXiv: https://arxiv.org/abs/2103.10943 · HTML: https://mlsanity.com/paper/2103.10943/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 51 references that are in the map.
- First posted on arXiv 17 Mar 2021.

## Builds on (most cited first, 19 of 19)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Sampling](https://mlsanity.com/paper/2003.06060/) (2020)
- [Targeted free energy estimation via learned mappings](https://mlsanity.com/paper/2002.04913/) (2020)
- [Generalizing Hamiltonian Monte Carlo with Neural Networks](https://mlsanity.com/paper/1711.09268/) (2017)
- [Metropolis-Hastings Generative Adversarial Networks](https://mlsanity.com/paper/1811.11357/) (2018)
- [On the Quantitative Analysis of Decoder-Based Generative Models](https://mlsanity.com/paper/1611.04273/) (2016)
- [Reinterpreting Importance-Weighted Autoencoders](https://mlsanity.com/paper/1704.02916/) (2017)
- [Conformal Symplectic and Relativistic Optimization](https://mlsanity.com/paper/1903.04100/) (2019)
- [Convergence rates for optimised adaptive importance samplers](https://mlsanity.com/paper/1903.12044/) (2019)
- [Energy-Inspired Models: Learning with Sampler-Induced Distributions](https://mlsanity.com/paper/1910.14265/) (2019)
- [Learning Deep Generative Models with Annealed Importance Sampling](https://mlsanity.com/paper/1906.04904/) (2019)
- [Unbiased Gradient Estimation for Variational Auto-Encoders using Coupled Markov Chains](https://mlsanity.com/paper/2010.01845/) (2020)
- [Normalizing Constant Estimation with Gaussianized Bridge Sampling](https://mlsanity.com/paper/1912.06073/) (2019)

## Built on by (most cited first, 1 of 1)

- [MixFlows: principled variational inference via mixed flows](https://mlsanity.com/paper/2205.07475/) (2022)

## Abstract (arXiv)

Sampling from a complex distribution π and approximating its intractable normalizing constant Z are challenging problems. In this paper, a novel family of importance samplers (IS) and Markov chain Monte Carlo (MCMC) samplers is derived. Given an invertible map T, these schemes combine (with weights) elements from the forward and backward Orbits through points sampled from a proposal distribution ρ. The map T does not leave the target π invariant, hence the name NEO, standing for Non-Equilibrium Orbits. NEO-IS provides unbiased estimators of the normalizing constant and self-normalized IS estimators of expectations under π while NEO-MCMC combines multiple NEO-IS estimates of the normalizing constant and an iterated sampling-importance resampling mechanism to sample from π. For T chosen as a discrete-time integrator of a conformal Hamiltonian system, NEO-IS achieves state-of-the art performance on difficult benchmarks and NEO-MCMC is able to explore highly multimodal targets. Additionally, we provide detailed theoretical results for both methods. In particular, we show that NEO-MCMC is uniformly geometrically ergodic and establish explicit mixing time estimates under mild conditions.