---
title: "Variational autoencoder (ELBO): formula and papers"
description: "Variational autoencoder (ELBO) was mentioned in 18 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #47 of the 104 equations and models mentioned."
url: https://scholar4ai.com/equations/variational-autoencoder-elbo
markdown_url: https://scholar4ai.com/equations/variational-autoencoder-elbo.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
share_text: "Variational autoencoder (ELBO) was mentioned in 18 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #47 of the 104 equations and models mentioned."
data_url: https://scholar4ai.com/data/rankings.json
updated: 2026-10-26T14:32:25+09:00
window: 2026-09-27 to 2026-10-26
source: OpenAlex (CC0)
---

# Variational autoencoder (ELBO)

$$
\log p_\theta(x) \ge E_{q_\phi(z \mid x)}\big[\log p_\theta(x \mid z)\big] - D_{\mathrm{KL}}\big(q_\phi(z \mid x) \parallel p(z)\big)
$$

Generative model trained by maximizing the evidence lower bound on the data likelihood.

- area: Machine learning
- 2 papers in the last 7 days
- Names searched for: variational autoencoder, variational auto-encoder, evidence lower bound, ELBO, VAE

Back to the ranking: https://scholar4ai.com/rankings/equations.md

## Key findings

- Variational autoencoder (ELBO) was mentioned in 18 papers in the last 30 days (2026-09-27 to 2026-10-26), ranking #47 of the 104 equations and models mentioned.
- By journal category: AI (13), Operations Research (4) and Finance (1).
- Most of them appeared in Machine Learning (4), Pattern Recognition (2) and Artificial Intelligence (2).
- Often mentioned together with Generative adversarial network (GAN) (9), Convolutional neural network (CNN) (7) and Logistic regression (logit) (6).
- Datasets named in the same papers: CIFAR-10 / CIFAR-100 (3), UCI Machine Learning Repository (2) and ImageNet (2).
- From Oct 2023 to Sep 2026, 309 archived papers mentioned Variational autoencoder (ELBO) in their title, abstract or keywords, most of them in Jan 2025 (27).

## Mentions over 36 months

*Papers mentioning it by publication month, Oct 2023 to Sep 2026 (titles, abstracts and keywords)*

| Trend | Oct 23–Sep 24 | Oct 24–Sep 25 | Oct 25–Sep 26 | 36 months |
|---|---:|---:|---:|---:|
|  | 102 | 164 | 43 | 309 |

*Papers mentioning Variational autoencoder (ELBO), newest first.*

| Date | Title | Journal | Authors | Affiliations |
|---|---|---|---|---|
| 2026-10-23 | [Towards minute-level pedestrian trajectory prediction in crowded traffic scenarios](https://doi.org/10.1016/j.patcog.2026.115198) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Yonghao Dong, Sanping Zhou, Gang Hua et al. | Xi'an Jiaotong University; Amazon (United States) |
| 2026-10-20 | [Central description length (CDL) clustering validation index](https://doi.org/10.1016/j.artint.2026.104644) | [Artificial Intelligence](https://scholar4ai.com/journals/artificial-intelligence.md) | Mahdi Shamsi, Soosan Beheshti | McGill University |
| 2026-10-17 | [Beyond Likelihood Ratio Bias: Nested Multi-time Scale Stochastic Approximation for Likelihood-Free Parameter Estimation](https://doi.org/10.1007/s10994-026-07175-y) | [Machine Learning](https://scholar4ai.com/journals/machine-learning.md) | Zehao Li, Zhouchen Lin, Yijie Peng | Peking University; Nanjing University |
| 2026-10-16 | [Generative deep learning for class imbalance in credit risk modeling: comparative evaluation of synthetic oversampling methods and an elastic oversampling extension](https://doi.org/10.1186/s40854-026-00970-5) | [Financial Innovation](https://scholar4ai.com/journals/financial-innovation.md) | Tae Yeon Kwon | Hankuk University of Foreign Studies |
| 2026-10-16 | [The Challenges of Hyperparameter Tuning for Accurate Causal Effect Estimation](https://doi.org/10.1007/s10994-026-07140-9) | [Machine Learning](https://scholar4ai.com/journals/machine-learning.md) | Damian Machlanski, Spyridon Samothrakis, Paul Clarke | University of Edinburgh; University of Essex; Institute for Social and Economic Research |
| 2026-10-15 | [Metropolis-scale resilient and trustworthy traffic flow inference using multi-source data](https://doi.org/10.1016/j.trc.2026.106083) | [Transportation Research Part C Emerging Technologies](https://scholar4ai.com/journals/transportation-research-part-c-emerging-technologies.md) | Qishen Zhou, Yifan Zhang, Michail Makridis et al. | Jilin University; City University of Hong Kong; City University of Hong Kong (Dongguan); … |
| 2026-10-06 | [Anomaly detection in SAP S/4HANA using hybrid deep learning for multivariate time series data](https://doi.org/10.1186/s40537-026-01572-9) | [Journal Of Big Data](https://scholar4ai.com/journals/journal-of-big-data.md) | Ram Reddy Jonnalagadda, B. P. Joshi, Kiran Kumar Reddy et al. | Osmania University; Graphic Era Hill University; Graphic Era University; … |
| 2026-10-06 | [Optimization modeling in business and government: in honor of Professor John M. Mulvey on his 80th birthday](https://doi.org/10.1007/s10479-026-07445-x) | [Annals of Operations Research](https://scholar4ai.com/journals/annals-of-operations-research.md) | David A. Saunders, Stavros A. Zenios | University of Waterloo; Durham University; University of Cyprus |
| 2026-10-03 | [Uncertainty quantification for trustworthy deep learning: Methods and measures](https://doi.org/10.1016/j.neunet.2026.109699) | [Neural Networks](https://scholar4ai.com/journals/neural-networks.md) | H. Martin Gillis, Thomas P. Trappenberg | Dalhousie University |
| 2026-10-01 | [Unbounded stick-breaking-assisted generalized Dirichlet variational autoencoder](https://doi.org/10.1016/j.patcog.2026.115130) | [Pattern Recognition](https://scholar4ai.com/journals/pattern-recognition.md) | Akinlolu Oluwabusayo Ojo, Nizar Bouguila |  |
| 2026-10-01 | [Addressing Methodological Challenges in Time Series Anomaly Detection](https://doi.org/10.1007/s10994-026-07183-y) | [Machine Learning](https://scholar4ai.com/journals/machine-learning.md) | Nancy Xu, Henrik Boström |  |
| 2026-10-01 | [Blurring Modal Boundaries: A Unified Survey from Single- to Multi-modal Person Re-ldentification](https://doi.org/10.1007/s11263-026-03069-7) | [International Journal of Computer Vision](https://scholar4ai.com/journals/international-journal-of-computer-vision.md) | Xiao Wang, Bing Wang, B Yang et al. | Wuhan University of Science and Technology; Wuhan University; Anhui University |
| 2026-10-01 | [Optimization under uncertainty for energy infrastructure planning: A synthesis of methods, tools, and open challenges](https://doi.org/10.1016/j.ejor.2026.10.008) | [European Journal of Operational Research](https://scholar4ai.com/journals/european-journal-of-operational-research.md) | Rahman Khorramfar, Aron Brenner, Lara Booth et al. | Massachusetts Institute of Technology |
| 2026-10-01 | [Privacy Leakage on DNNs: A Survey of Model Inversion Attacks and Defenses](https://doi.org/10.1007/s11263-026-03049-x) | [International Journal of Computer Vision](https://scholar4ai.com/journals/international-journal-of-computer-vision.md) | Hao Fang, Yixiang Qiu, Hongyao Yu et al. | Tsinghua Shenzhen International Graduate School; Tsinghua University; Harbin Institute of Technology; … |
| 2026-09-30 | [Sample-based approaches for monitoring ordinal time series in production environments](https://doi.org/10.1016/j.cie.2026.112411) | [Computers & Industrial Engineering](https://scholar4ai.com/journals/computers-industrial-engineering.md) | Osama Swidan, Christian H. Weiß, Murat Caner Testik | Helmut Schmidt University; Hacettepe University |
| 2026-09-30 | [P2Mark: Plug-and-play parameter-level watermarking for neural speech generation](https://doi.org/10.1016/j.artint.2026.104627) | [Artificial Intelligence](https://scholar4ai.com/journals/artificial-intelligence.md) | Yong Sheng Ren, Jiangyan Yi, Tao Wang et al. | Chinese Academy of Sciences; Institute of Automation; University of Chinese Academy of Sciences; … |
| 2026-09-28 | [CausalCACTUS: A Causally Consistent and Context-Aware Framework for Counterfactual Explanations](https://doi.org/10.1007/s10994-026-07155-2) | [Machine Learning](https://scholar4ai.com/journals/machine-learning.md) | Zhendong Wang, Diego García, José María Enguita et al. | KTH Royal Institute of Technology; Universidad de Oviedo |
| 2026-09-28 | [DAMEL: Dual-axis multi-expert learning for class-imbalanced learning](https://doi.org/10.1016/j.knosys.2026.117115) | [Knowledge-Based Systems](https://scholar4ai.com/journals/knowledge-based-systems.md) | Hyuck Lee, Taemin Park, Heeyoung Kim | Korea Advanced Institute of Science and Technology |

## Cite this page

Scholar4AI. (2026). Variational autoencoder (ELBO). Journal Research Rankings. Retrieved October 26, 2026, from https://scholar4ai.com/equations/variational-autoencoder-elbo

```bibtex
@misc{scholar4ai-equations-variational-autoencoder-elbo,
  author = {{Scholar4AI}},
  title = {Variational autoencoder (ELBO)},
  year = {2026},
  howpublished = {\url{https://scholar4ai.com/equations/variational-autoencoder-elbo}},
  urldate = {2026-10-26},
  note = {Journal Research Rankings; data from OpenAlex (CC0); licensed CC BY-NC 4.0}
}
```

License: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/).