# Reweighted Wake-Sleep

arXiv: https://arxiv.org/abs/1406.2751 · HTML: https://mlsanity.com/paper/1406.2751/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2014.

## Built on by (most cited first, 30 of 66)

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- [Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows](https://mlsanity.com/paper/2207.08219/) (2022)
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- [Nearest Neighbour Score Estimators for Diffusion Generative Models](https://mlsanity.com/paper/2402.08018/) (2024)
- [Coupled Gradient Estimators for Discrete Latent Variables](https://mlsanity.com/paper/2106.08056/) (2021)
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- [Bridge the Inference Gaps of Neural Processes via Expectation Maximization](https://mlsanity.com/paper/2501.03264/) (2025)
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- [Sequential Monte Carlo for Inclusive KL Minimization in Amortized Variational Inference](https://mlsanity.com/paper/2403.10610/) (2024)
- [Learning Proposals for Probabilistic Programs with Inference Combinators](https://mlsanity.com/paper/2103.00668/) (2021)
- [Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradients](https://mlsanity.com/paper/2206.06295/) (2022)
- [Variational Inference for Deblending Crowded Starfields](https://mlsanity.com/paper/2102.02409/) (2021)
- [Variational Inference with Coverage Guarantees in Simulation-Based Inference](https://mlsanity.com/paper/2305.14275/) (2023)
- [NAS-X: Neural Adaptive Smoothing via Twisting](https://mlsanity.com/paper/2308.14864/) (2023)
- [Wake-Sleep Consolidated Learning](https://mlsanity.com/paper/2401.08623/) (2023)
- [Probabilistic Programming with Programmable Variational Inference](https://mlsanity.com/paper/2406.15742/) (2024)
- [Multi-level Reliability Interface for Semantic Communications over Wireless Networks](https://mlsanity.com/paper/2407.05487/) (2024)

## Abstract (arXiv)

Training deep directed graphical models with many hidden variables and performing inference remains a major challenge. Helmholtz machines and deep belief networks are such models, and the wake-sleep algorithm has been proposed to train them. The wake-sleep algorithm relies on training not just the directed generative model but also a conditional generative model (the inference network) that runs backward from visible to latent, estimating the posterior distribution of latent given visible. We propose a novel interpretation of the wake-sleep algorithm which suggests that better estimators of the gradient can be obtained by sampling latent variables multiple times from the inference network. This view is based on importance sampling as an estimator of the likelihood, with the approximate inference network as a proposal distribution. This interpretation is confirmed experimentally, showing that better likelihood can be achieved with this reweighted wake-sleep procedure. Based on this interpretation, we propose that a sigmoidal belief network is not sufficiently powerful for the layers of the inference network in order to recover a good estimator of the posterior distribution of latent variables. Our experiments show that using a more powerful layer model, such as NADE, yields substantially better generative models.