# On Kernel-based Variational Autoencoder

arXiv: https://arxiv.org/abs/2405.12783 · HTML: https://mlsanity.com/paper/2405.12783/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 21 May 2024.

## Builds on (most cited first, 14 of 14)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [von Mises-Fisher Mixture Model-based Deep learning: Application to Face Verification](https://mlsanity.com/paper/1706.04264/) (2017)
- [Stick-Breaking Variational Autoencoders](https://mlsanity.com/paper/1605.06197/) (2016)
- [On Implicit Regularization in β-VAEs](https://mlsanity.com/paper/2002.00041/) (2020)
- [t3-Variational Autoencoder: Learning Heavy-tailed Data with Student's t and Power Divergence](https://mlsanity.com/paper/2312.01133/) (2023)
- [Coupled Variational Autoencoder](https://mlsanity.com/paper/2306.02565/) (2023)
- [Matching aggregate posteriors in the variational autoencoder](https://mlsanity.com/paper/2311.07693/) (2023)

## Built on by (most cited first, 2 of 2)

- [Scaling Image Tokenizers with Grouped Spherical Quantization](https://mlsanity.com/paper/2412.02632/) (2024)
- [Fenchel-Young Variational Learning](https://mlsanity.com/paper/2502.10295/) (2025)

## Abstract (arXiv)

In this paper, we bridge Variational Autoencoders (VAEs) and kernel density estimations (KDEs) by approximating the posterior by KDEs and deriving an upper bound of the Kullback-Leibler (KL) divergence in the evidence lower bound (ELBO). The flexibility of KDEs makes the optimization of posteriors in VAEs possible, which not only addresses the limitations of Gaussian latent space in vanilla VAE but also provides a new perspective of estimating the KL-divergence in ELBO. Under appropriate conditions, we show that the Epanechnikov kernel is the optimal choice in minimizing the derived upper bound of KL-divergence asymptotically. Compared with Gaussian kernel, Epanechnikov kernel has compact support which should make the generated sample less noisy and blurry. The implementation of Epanechnikov kernel in ELBO is straightforward as it lies in the "location-scale" family of distributions where the reparametrization tricks can be directly employed. A series of experiments on benchmark datasets such as MNIST, Fashion-MNIST, CIFAR-10 and CelebA further demonstrate the superiority of Epanechnikov Variational Autoenocoder (EVAE) over vanilla VAE in the quality of reconstructed images, as measured by the FID score and Sharpness.