# Semi-Empirical Objective Functions for MCMC Proposal Optimization

arXiv: https://arxiv.org/abs/2106.02104 · HTML: https://mlsanity.com/paper/2106.02104/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 3 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [Generalizing Hamiltonian Monte Carlo with Neural Networks](https://mlsanity.com/paper/1711.09268/) (2017)
- [A-NICE-MC: Adversarial Training for MCMC](https://mlsanity.com/paper/1706.07561/) (2017)
- [Gradient-based Adaptive Markov Chain Monte Carlo](https://mlsanity.com/paper/1911.01373/) (2019)
- [A Neural Network MCMC sampler that maximizes Proposal Entropy](https://mlsanity.com/paper/2010.03587/) (2020)
- [Introducing an Explicit Symplectic Integration Scheme for Riemannian Manifold Hamiltonian Monte Carlo](https://mlsanity.com/paper/1910.06243/) (2019)
- [Variational MCMC](https://mlsanity.com/paper/1301.2266/) (2013)
- [Metropolis-Hastings view on variational inference and adversarial training](https://mlsanity.com/paper/1810.07151/) (2018)
- [Kernel Adaptive Metropolis-Hastings](https://mlsanity.com/paper/1307.5302/) (2013)
- [Deep Involutive Generative Models for Neural MCMC](https://mlsanity.com/paper/2006.15167/) (2020)

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

- [Entropy-based adaptive Hamiltonian Monte Carlo](https://mlsanity.com/paper/2110.14625/) (2021)

## Abstract (arXiv)

Current objective functions used for training neural MCMC proposal distributions implicitly rely on architectural restrictions to yield sensible optimization results, which hampers the development of highly expressive neural MCMC proposal architectures. In this work, we introduce and demonstrate a semi-empirical procedure for determining approximate objective functions suitable for optimizing arbitrarily parameterized proposal distributions in MCMC methods. Our proposed Ab Initio objective functions consist of the weighted combination of functions following constraints on their global optima and transformation invariances that we argue should be upheld by general measures of MCMC efficiency for use in proposal optimization. Our experimental results demonstrate that Ab Initio objective functions maintain favorable performance and preferable optimization behavior compared to existing objective functions for neural MCMC optimization. We find that Ab Initio objective functions are sufficiently robust to enable the confident optimization of neural proposal distributions parameterized by deep generative networks extending beyond the regimes of traditional MCMC schemes