# Joint Stochastic Approximation learning of Helmholtz Machines

arXiv: https://arxiv.org/abs/1603.06170 · HTML: https://mlsanity.com/paper/1603.06170/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2016.

## Built on by (most cited first, 5 of 5)

- [Advancing Semi-Supervised Task Oriented Dialog Systems by JSA Learning of Discrete Latent Variable Models](https://mlsanity.com/paper/2207.12235/) (2022)
- [Pronunciation-Lexicon Free Training for Phoneme-based Crosslingual ASR via Joint Stochastic Approximation](https://mlsanity.com/paper/2507.06249/) (2025)
- [Improving End-to-End Training of Retrieval-Augmented Generation Models via Joint Stochastic Approximation](https://mlsanity.com/paper/2508.18168/) (2025)
- [Joint-stochastic-approximation Autoencoders with Application to Semi-supervised Learning](https://mlsanity.com/paper/2505.18558/) (2025)
- [Joint-stochastic-approximation Random Fields with Application to Semi-supervised Learning](https://mlsanity.com/paper/2505.20330/) (2025)

## Abstract (arXiv)

Though with progress, model learning and performing posterior inference still remains a common challenge for using deep generative models, especially for handling discrete hidden variables. This paper is mainly concerned with algorithms for learning Helmholz machines, which is characterized by pairing the generative model with an auxiliary inference model. A common drawback of previous learning algorithms is that they indirectly optimize some bounds of the targeted marginal log-likelihood. In contrast, we successfully develop a new class of algorithms, based on stochastic approximation (SA) theory of the Robbins-Monro type, to directly optimize the marginal log-likelihood and simultaneously minimize the inclusive KL-divergence. The resulting learning algorithm is thus called joint SA (JSA). Moreover, we construct an effective MCMC operator for JSA. Our results on the MNIST datasets demonstrate that the JSA's performance is consistently superior to that of competing algorithms like RWS, for learning a range of difficult models.