# Hybrid Memoised Wake-Sleep: Approximate Inference at the Discrete-Continuous Interface

arXiv: https://arxiv.org/abs/2107.06393 · HTML: https://mlsanity.com/paper/2107.06393/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 4 Jul 2021.

## Builds on (most cited first, 23 of 23)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Attend, Infer, Repeat: Fast Scene Understanding with Generative Models](https://mlsanity.com/paper/1603.08575/) (2016)
- [DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning](https://mlsanity.com/paper/2006.08381/) (2020)
- [Gradient Estimation Using Stochastic Computation Graphs](https://mlsanity.com/paper/1506.05254/) (2015)
- [Neural Variational Inference and Learning in Belief Networks](https://mlsanity.com/paper/1402.0030/) (2014)
- [Backpropagation through the Void: Optimizing control variates for black-box gradient estimation](https://mlsanity.com/paper/1711.00123/) (2017)
- [Structure Discovery in Nonparametric Regression through Compositional Kernel Search](https://mlsanity.com/paper/1302.4922/) (2013)
- [Variational inference for Monte Carlo objectives](https://mlsanity.com/paper/1602.06725/) (2016)
- [Computer-Aided Design as Language](https://mlsanity.com/paper/2105.02769/) (2021)
- [REBAR: Low-variance, unbiased gradient estimates for discrete latent variable models](https://mlsanity.com/paper/1703.07370/) (2017)
- [Reweighted Wake-Sleep](https://mlsanity.com/paper/1406.2751/) (2014)
- [Mining gold from implicit models to improve likelihood-free inference](https://mlsanity.com/paper/1805.12244/) (2018)
- [HOUDINI: Lifelong Learning as Program Synthesis](https://mlsanity.com/paper/1804.00218/) (2018)
- [Learning Differentiable Programs with Admissible Neural Heuristics](https://mlsanity.com/paper/2007.12101/) (2020)
- [Learning to learn generative programs with Memoised Wake-Sleep](https://mlsanity.com/paper/2007.03132/) (2020)
- [Variational Particle Approximations](https://mlsanity.com/paper/1402.5715/) (2014)
- [Amortised Learning by Wake-Sleep](https://mlsanity.com/paper/2002.09737/) (2020)

## Built on by (most cited first, 3 of 3)

- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [Delta-AI: Local objectives for amortized inference in sparse graphical models](https://mlsanity.com/paper/2310.02423/) (2023)
- [Natural Evolution Strategies as a Black Box Estimator for Stochastic Variational Inference](https://mlsanity.com/paper/2308.08053/) (2023)

## Abstract (arXiv)

Modeling complex phenomena typically involves the use of both discrete and continuous variables. Such a setting applies across a wide range of problems, from identifying trends in time-series data to performing effective compositional scene understanding in images. Here, we propose Hybrid Memoised Wake-Sleep (HMWS), an algorithm for effective inference in such hybrid discrete-continuous models. Prior approaches to learning suffer as they need to perform repeated expensive inner-loop discrete inference. We build on a recent approach, Memoised Wake-Sleep (MWS), which alleviates part of the problem by memoising discrete variables, and extend it to allow for a principled and effective way to handle continuous variables by learning a separate recognition model used for importance-sampling based approximate inference and marginalization. We evaluate HMWS in the GP-kernel learning and 3D scene understanding domains, and show that it outperforms current state-of-the-art inference methods.