# Deep Latent Dirichlet Allocation with Topic-Layer-Adaptive Stochastic Gradient Riemannian MCMC

arXiv: https://arxiv.org/abs/1706.01724 · HTML: https://mlsanity.com/paper/1706.01724/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2017.

## Built on by (most cited first, 9 of 9)

- [Sawtooth Factorial Topic Embeddings Guided Gamma Belief Network](https://mlsanity.com/paper/2107.02757/) (2021)
- [TopicNet: Semantic Graph-Guided Topic Discovery](https://mlsanity.com/paper/2110.14286/) (2021)
- [A Unifying and Canonical Description of Measure-Preserving Diffusions](https://mlsanity.com/paper/2105.02845/) (2021)
- [A Non-negative VAE:the Generalized Gamma Belief Network](https://mlsanity.com/paper/2408.03388/) (2024)
- [Matching Visual Features to Hierarchical Semantic Topics for Image Paragraph Captioning](https://mlsanity.com/paper/2105.04143/) (2021)
- [Scalable Weibull Graph Attention Autoencoder for Modeling Document Networks](https://mlsanity.com/paper/2410.09696/) (2024)
- [Scaling up Dynamic Edge Partition Models via Stochastic Gradient MCMC](https://mlsanity.com/paper/2403.00044/) (2024)
- [Embedded Topic Models Enhanced by Wikification](https://mlsanity.com/paper/2410.02441/) (2024)
- [Meta-probabilistic Modeling](https://mlsanity.com/paper/2601.04462/) (2026)

## Abstract (arXiv)

It is challenging to develop stochastic gradient based scalable inference for deep discrete latent variable models (LVMs), due to the difficulties in not only computing the gradients, but also adapting the step sizes to different latent factors and hidden layers. For the Poisson gamma belief network (PGBN), a recently proposed deep discrete LVM, we derive an alternative representation that is referred to as deep latent Dirichlet allocation (DLDA). Exploiting data augmentation and marginalization techniques, we derive a block-diagonal Fisher information matrix and its inverse for the simplex-constrained global model parameters of DLDA. Exploiting that Fisher information matrix with stochastic gradient MCMC, we present topic-layer-adaptive stochastic gradient Riemannian (TLASGR) MCMC that jointly learns simplex-constrained global parameters across all layers and topics, with topic and layer specific learning rates. State-of-the-art results are demonstrated on big data sets.