# Learning Proposals for Probabilistic Programs with Inference Combinators

arXiv: https://arxiv.org/abs/2103.00668 · HTML: https://mlsanity.com/paper/2103.00668/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 76 references that are in the map.
- First posted on arXiv 1 Mar 2021.

## Builds on (most cited first, 30 of 40)

- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Gradient Estimation Using Stochastic Computation Graphs](https://mlsanity.com/paper/1506.05254/) (2015)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Tighter Variational Bounds are Not Necessarily Better](https://mlsanity.com/paper/1802.04537/) (2018)
- [Learning Disentangled Representations with Semi-Supervised Deep Generative Models](https://mlsanity.com/paper/1706.00400/) (2017)
- [Reweighted Wake-Sleep](https://mlsanity.com/paper/1406.2751/) (2014)
- [Auto-Encoding Sequential Monte Carlo](https://mlsanity.com/paper/1705.10306/) (2017)
- [Elements of Sequential Monte Carlo](https://mlsanity.com/paper/1903.04797/) (2019)
- [An Introduction to Probabilistic Programming](https://mlsanity.com/paper/1809.10756/) (2018)
- [Hamiltonian Variational Auto-Encoder](https://mlsanity.com/paper/1805.11328/) (2018)
- [Doubly Reparameterized Gradient Estimators for Monte Carlo Objectives](https://mlsanity.com/paper/1810.04152/) (2018)
- [Automated Variational Inference in Probabilistic Programming](https://mlsanity.com/paper/1301.1299/) (2013)
- [Edward: A library for probabilistic modeling, inference, and criticism](https://mlsanity.com/paper/1610.09787/) (2016)
- [The Thermodynamic Variational Objective](https://mlsanity.com/paper/1907.00031/) (2019)
- [Improving Explorability in Variational Inference with Annealed Variational Objectives](https://mlsanity.com/paper/1809.01818/) (2018)
- [Deep Amortized Inference for Probabilistic Programs](https://mlsanity.com/paper/1610.05735/) (2016)
- [Approximate Inference with Amortised MCMC](https://mlsanity.com/paper/1702.08343/) (2017)
- [A New Approach to Probabilistic Programming Inference](https://mlsanity.com/paper/1507.00996/) (2015)
- [Venture: a higher-order probabilistic programming platform with programmable inference](https://mlsanity.com/paper/1404.0099/) (2014)
- [Nested Sequential Monte Carlo Methods](https://mlsanity.com/paper/1502.02536/) (2015)
- [Simple, Distributed, and Accelerated Probabilistic Programming](https://mlsanity.com/paper/1811.02091/) (2018)
- [Etalumis: Bringing Probabilistic Programming to Scientific Simulators at Scale](https://mlsanity.com/paper/1907.03382/) (2019)
- [Design and Implementation of Probabilistic Programming Language Anglican](https://mlsanity.com/paper/1608.05263/) (2016)
- [A Convenient Category for Higher-Order Probability Theory](https://mlsanity.com/paper/1701.02547/) (2017)
- [Automated learning with a probabilistic programming language: Birch](https://mlsanity.com/paper/1810.01539/) (2018)

## Built on by (most cited first, 6 of 6)

- [Nested Variational Inference](https://mlsanity.com/paper/2106.11302/) (2021)
- [Recursive Monte Carlo and Variational Inference with Auxiliary Variables](https://mlsanity.com/paper/2203.02836/) (2022)
- [Variational Marginal Particle Filters](https://mlsanity.com/paper/2109.15134/) (2021)
- [Probabilistic Programming with Programmable Variational Inference](https://mlsanity.com/paper/2406.15742/) (2024)
- [Divide-and-Conquer Predictive Coding: a structured Bayesian inference algorithm](https://mlsanity.com/paper/2408.05834/) (2024)
- [VISA: Variational Inference with Sequential Sample-Average Approximations](https://mlsanity.com/paper/2403.09429/) (2024)

## Abstract (arXiv)

We develop operators for construction of proposals in probabilistic programs, which we refer to as inference combinators. Inference combinators define a grammar over importance samplers that compose primitive operations such as application of a transition kernel and importance resampling. Proposals in these samplers can be parameterized using neural networks, which in turn can be trained by optimizing variational objectives. The result is a framework for user-programmable variational methods that are correct by construction and can be tailored to specific models. We demonstrate the flexibility of this framework by implementing advanced variational methods based on amortized Gibbs sampling and annealing.