mlsanityData to 7 Oct 2026

An Introduction to Variational Inference

arXiv 2108.13083 ↗First posted 30 Aug 2021cs.LG cs.AI stat.MLcited by 11

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Abstract (arXiv)

Approximating complex probability densities is a core problem in modern statistics. In this paper, we introduce the concept of Variational Inference (VI), a popular method in machine learning that uses optimization techniques to estimate complex probability densities. This property allows VI to converge faster than classical methods, such as, Markov Chain Monte Carlo sampling. Conceptually, VI works by choosing a family of probability density functions and then finding the one closest to the actual probability density -- often using the Kullback-Leibler (KL) divergence as the optimization metric. We introduce the Evidence Lower Bound to tractably compute the approximated probability density and we review the ideas behind mean-field variational inference. Finally, we discuss the applications of VI to variational auto-encoders (VAE) and VAE-Generative Adversarial Network (VAE-GAN). With this paper, we aim to explain the concept of VI and assist in future research with this approach.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 22 of its 51 references that are in the map. First posted on arXiv 30 Aug 2021.

Builds on

22 of 51 references.

References · 22

  1. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  2. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  3. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  4. 2013Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Mapscited by 2,348
  5. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  6. 2016Variational Inference: A Review for Statisticianscited by 1,466
  7. 2016InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Netscited by 858
  8. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 635
  9. 2015Autoencoding beyond pixels using a learned similarity metriccited by 407
  10. 2016Tutorial on Variational Autoencoderscited by 404
  11. 2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 375
  12. 2018Understanding disentangling in β-VAEcited by 332
10 more
  1. 2013Black Box Variational Inferencecited by 317
  2. 2019Monte Carlo Gradient Estimation in Machine Learningcited by 281
  3. 2017Advances in Variational Inferencecited by 236
  4. 2020Adversarial Latent Autoencoderscited by 155
  5. 2017Improved Variational Autoencoders for Text Modeling using Dilated Convolutionscited by 81
  6. 2020Anomaly Detection With Conditional Variational Autoencoderscited by 46
  7. 2018Amortized Inference Regularizationcited by 30
  8. 2019The capacity of feedforward neural networkscited by 14
  9. 2015Celeste: Variational inference for a generative model of astronomical imagescited by 7
  10. 2017Variational Inference for Stochastic Block Models from Sampled Datacited by 7

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 2; 2024: 1; 2025: 2; 2026: 3.

11 papers.

  1. 2023InfoPrompt: Information-Theoretic Soft Prompt Tuning for Natural Language Understandingcited by 29
  2. 2022Amortized Variational Inference: A Systematic Reviewcited by 16
  3. 2024BioDiffusion: A Versatile Diffusion Model for Biomedical Signal Synthesiscited by 9
  4. 2022Quasi Black-Box Variational Inference with Natural Gradients for Bayesian Learningcited by 3
  5. 2023Disposable Transfer Learning for Selective Source Task Unlearningcited by 2
  6. 2022Manifold Gaussian Variational Bayes on the Precision Matrixcited by 1
  7. 2025BanglaFake: Constructing and Evaluating a Specialized Bengali Deepfake Audio Datasetcited by 1
  8. 2025Guided Data Generation for Understanding Model Behaviorcited by 0
  9. 2026Monte Carlo Stochastic Depth for Uncertainty Estimation in Deep Learningcited by 0
  10. 2026Revisiting Neural Activation Coverage for Uncertainty Estimationcited by 0
  11. 2026From Static Personal Values to Contextualized Personalization: Bayesian Personalized Value Alignment for LLMscited by 0