# Nonparametric Involutive Markov Chain Monte Carlo

arXiv: https://arxiv.org/abs/2211.01100 · HTML: https://mlsanity.com/paper/2211.01100/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 12 of 12)

- [A New Approach to Probabilistic Programming Inference](https://mlsanity.com/paper/1507.00996/) (2015)
- [Involutive MCMC: a Unifying Framework](https://mlsanity.com/paper/2006.16653/) (2020)
- [A Lambda-Calculus Foundation for Universal Probabilistic Programming](https://mlsanity.com/paper/1512.08990/) (2015)
- [Semantics for probabilistic programming: higher-order functions, continuous distributions, and soft constraints](https://mlsanity.com/paper/1601.04943/) (2016)
- [Divide, Conquer, and Combine: a New Inference Strategy for Probabilistic Programs with Stochastic Support](https://mlsanity.com/paper/1910.13324/) (2019)
- [Hamiltonian Monte Carlo Without Detailed Balance](https://mlsanity.com/paper/1409.5191/) (2014)
- [Denotational validation of higher-order Bayesian inference](https://mlsanity.com/paper/1711.03219/) (2017)
- [A Domain Theory for Statistical Probabilistic Programming](https://mlsanity.com/paper/1811.04196/) (2018)
- [Densities of Almost Surely Terminating Probabilistic Programs are Differentiable Almost Everywhere](https://mlsanity.com/paper/2004.03924/) (2020)
- [Nonparametric Hamiltonian Monte Carlo](https://mlsanity.com/paper/2106.10238/) (2021)
- [Measurable Cones and Stable, Measurable Functions](https://mlsanity.com/paper/1711.09640/) (2017)
- [Contextual Equivalence for a Probabilistic Language with Continuous Random Variables and Recursion](https://mlsanity.com/paper/1807.02809/) (2018)

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

- [Automatically Marginalized MCMC in Probabilistic Programming](https://mlsanity.com/paper/2302.00564/) (2023)

## Abstract (arXiv)

A challenging problem in probabilistic programming is to develop inference algorithms that work for arbitrary programs in a universal probabilistic programming language (PPL). We present the nonparametric involutive Markov chain Monte Carlo (NP-iMCMC) algorithm as a method for constructing MCMC inference algorithms for nonparametric models expressible in universal PPLs. Building on the unifying involutive MCMC framework, and by providing a general procedure for driving state movement between dimensions, we show that NP-iMCMC can generalise numerous existing iMCMC algorithms to work on nonparametric models. We prove the correctness of the NP-iMCMC sampler. Our empirical study shows that the existing strengths of several iMCMC algorithms carry over to their nonparametric extensions. Applying our method to the recently proposed Nonparametric HMC, an instance of (Multiple Step) NP-iMCMC, we have constructed several nonparametric extensions (all of which new) that exhibit significant performance improvements.