# Dirichlet Variational Autoencoder

arXiv: https://arxiv.org/abs/1901.02739 · HTML: https://mlsanity.com/paper/1901.02739/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2019.

## Built on by (most cited first, 30 of 43)

- [Is Automated Topic Model Evaluation Broken?: The Incoherence of Coherence](https://mlsanity.com/paper/2107.02173/) (2021)
- [Topic Modelling Meets Deep Neural Networks: A Survey](https://mlsanity.com/paper/2103.00498/) (2021)
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- [From Noisy Prediction to True Label: Noisy Prediction Calibration via Generative Model](https://mlsanity.com/paper/2205.00690/) (2022)
- [Better Latent Spaces for Better Autoencoders](https://mlsanity.com/paper/2104.08291/) (2021)
- [Benchmarking Constraint Inference in Inverse Reinforcement Learning](https://mlsanity.com/paper/2206.09670/) (2022)
- [t3-Variational Autoencoder: Learning Heavy-tailed Data with Student's t and Power Divergence](https://mlsanity.com/paper/2312.01133/) (2023)
- [A Survey on Neural Topic Models: Methods, Applications, and Challenges](https://mlsanity.com/paper/2401.15351/) (2024)
- [SCALE: Online Self-Supervised Lifelong Learning without Prior Knowledge](https://mlsanity.com/paper/2208.11266/) (2022)
- [Pathologies in priors and inference for Bayesian transformers](https://mlsanity.com/paper/2110.04020/) (2021)
- [Advancing Graph Generation through Beta Diffusion](https://mlsanity.com/paper/2406.09357/) (2024)
- [DyGen: Learning from Noisy Labels via Dynamics-Enhanced Generative Modeling](https://mlsanity.com/paper/2305.19395/) (2023)
- [A Comprehensive Survey on Inverse Constrained Reinforcement Learning: Definitions, Progress and Challenges](https://mlsanity.com/paper/2409.07569/) (2024)
- [Generating Multivariate Load States Using a Conditional Variational Autoencoder](https://mlsanity.com/paper/2110.11435/) (2021)
- [Coupled Variational Autoencoder](https://mlsanity.com/paper/2306.02565/) (2023)
- [Hyperspectral Pixel Unmixing with Latent Dirichlet Variational Autoencoder](https://mlsanity.com/paper/2203.01327/) (2022)
- [Online Unsupervised Learning of Visual Representations and Categories](https://mlsanity.com/paper/2109.05675/) (2021)
- [A Prescriptive Dirichlet Power Allocation Policy with Deep Reinforcement Learning](https://mlsanity.com/paper/2201.08445/) (2022)
- [Physics-informed Variational Autoencoders for Improved Robustness to Environmental Factors of Variation](https://mlsanity.com/paper/2210.10418/) (2022)
- [Learning Latent Graph Structures and their Uncertainty](https://mlsanity.com/paper/2405.19933/) (2024)
- [A Non-negative VAE:the Generalized Gamma Belief Network](https://mlsanity.com/paper/2408.03388/) (2024)
- [Calibrating Pre-trained Language Classifiers on LLM-generated Noisy Labels via Iterative Refinement](https://mlsanity.com/paper/2505.19675/) (2025)
- [Hierarchical Variational Auto-Encoding for Unsupervised Domain Generalization](https://mlsanity.com/paper/2101.09436/) (2021)
- [Data-driven Nonlinear Parametric Model Order Reduction Framework using Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2307.06816/) (2023)
- [XTRA: Cross-Lingual Topic Modeling with Topic and Representation Alignments](https://mlsanity.com/paper/2510.02788/) (2025)
- [A Framework for Overparameterized Learning](https://mlsanity.com/paper/2205.13507/) (2022)
- [Diff-PCC: Diffusion-based Neural Compression for 3D Point Clouds](https://mlsanity.com/paper/2408.10543/) (2024)
- [BN-Pool: Bayesian Nonparametric Pooling for Graphs](https://mlsanity.com/paper/2501.09821/) (2025)
- [Learning Reduced Representations for Quantum Classifiers](https://mlsanity.com/paper/2512.01509/) (2025)
- [Unsupervised Image Generation with Infinite Generative Adversarial Networks](https://mlsanity.com/paper/2108.07975/) (2021)

## Abstract (arXiv)

This paper proposes Dirichlet Variational Autoencoder (DirVAE) using a Dirichlet prior for a continuous latent variable that exhibits the characteristic of the categorical probabilities. To infer the parameters of DirVAE, we utilize the stochastic gradient method by approximating the Gamma distribution, which is a component of the Dirichlet distribution, with the inverse Gamma CDF approximation. Additionally, we reshape the component collapsing issue by investigating two problem sources, which are decoder weight collapsing and latent value collapsing, and we show that DirVAE has no component collapsing; while Gaussian VAE exhibits the decoder weight collapsing and Stick-Breaking VAE shows the latent value collapsing. The experimental results show that 1) DirVAE models the latent representation result with the best log-likelihood compared to the baselines; and 2) DirVAE produces more interpretable latent values with no collapsing issues which the baseline models suffer from. Also, we show that the learned latent representation from the DirVAE achieves the best classification accuracy in the semi-supervised and the supervised classification tasks on MNIST, OMNIGLOT, and SVHN compared to the baseline VAEs. Finally, we demonstrated that the DirVAE augmented topic models show better performances in most cases.