On Kernel-based Variational Autoencoder

• URL: http://arxiv.org/abs/2405.12783v2
• Date: Mon, 12 May 2025 15:43:11 GMT
• Title: On Kernel-based Variational Autoencoder
• Authors: Tian Qin, Wei-Min Huang,
• Abstract summary: We bridge Variational Autoencoders (VAEs) and kernel density estimations (KDEs)<n>We deriving an upper bound of the Kullback-Leibler (KL) divergence in the evidence lower bound (ELBO)<n>We show that the Epanechnikov kernel is the optimal choice in minimizing the derived upper bound of KL-divergenceally.
• Score: 7.262815775303641
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• A New Formulation of Lipschitz Constrained With Functional Gradient Learning for GANs [52.55025869932486]
  This paper introduces a promising alternative method for training Generative Adversarial Networks (GANs) on large-scale datasets with clear theoretical guarantees. We propose a novel Lipschitz-constrained Functional Gradient GANs learning (Li-CFG) method to stabilize the training of GAN. We demonstrate that the neighborhood size of the latent vector can be reduced by increasing the norm of the discriminator gradient.
  arXiv  Detail & Related papers  (2025-01-20T02:48:07Z)
• MIK: Modified Isolation Kernel for Biological Sequence Visualization, Classification, and Clustering [3.9146761527401424]
  This research proposes a novel approach called the Modified Isolation Kernel (MIK) as an alternative to the Gaussian kernel. MIK uses adaptive density estimation to capture local structures more accurately and integrates robustness measures. It exhibits improved preservation of the local and global structure and enables better visualization of clusters and subclusters in the embedded space.
  arXiv  Detail & Related papers  (2024-10-21T06:57:09Z)
• Improved Anomaly Detection through Conditional Latent Space VAE Ensembles [49.1574468325115]
  Conditional Latent space Variational Autoencoder (CL-VAE) improved pre-processing for anomaly detection on data with known inlier classes and unknown outlier classes. Model shows increased accuracy in anomaly detection, achieving an AUC of 97.4% on the MNIST dataset. In addition, the CL-VAE shows increased benefits from ensembling, a more interpretable latent space, and an increased ability to learn patterns in complex data with limited model sizes.
  arXiv  Detail & Related papers  (2024-10-16T07:48:53Z)
• Kernel Semi-Implicit Variational Inference [27.61976547543748]
  Semi-implicit variational inference (SIVI) extends traditional variational families with semi-implicit distributions defined in a hierarchical manner. A recent advancement in SIVI, named SIVI-SM, utilizes an alternative score matching objective made tractable via a minimax formulation. We propose kernel SIVI (KSIVI), a variant of SIVI-SM that eliminates the need for lower-level optimization through kernel tricks.
  arXiv  Detail & Related papers  (2024-05-29T11:21:25Z)
• Self-Attention through Kernel-Eigen Pair Sparse Variational Gaussian Processes [20.023544206079304]
  We propose Kernel-Eigen Pair Sparse Variational Gaussian Processes (KEP-SVGP) for building uncertainty-aware self-attention. Experiments verify our excellent performances and efficiency on in-distribution, distribution-shift and out-of-distribution benchmarks.
  arXiv  Detail & Related papers  (2024-02-02T15:05:13Z)
• Matching aggregate posteriors in the variational autoencoder [0.5759862457142761]
  The variational autoencoder (VAE) is a well-studied, deep, latent-variable model (DLVM) This paper addresses shortcomings in VAEs by reformulating the objective function associated with VAEs in order to match the aggregate/marginal posterior distribution to the prior. The proposed method is named the emphaggregate variational autoencoder (AVAE) and is built on the theoretical framework of the VAE.
  arXiv  Detail & Related papers  (2023-11-13T19:22:37Z)
• The Schr\"odinger Bridge between Gaussian Measures has a Closed Form [101.79851806388699]
  We focus on the dynamic formulation of OT, also known as the Schr"odinger bridge (SB) problem. In this paper, we provide closed-form expressions for SBs between Gaussian measures.
  arXiv  Detail & Related papers  (2022-02-11T15:59:01Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• Flow-based Kernel Prior with Application to Blind Super-Resolution [143.21527713002354]
  Kernel estimation is generally one of the key problems for blind image super-resolution (SR) This paper proposes a normalizing flow-based kernel prior (FKP) for kernel modeling. Experiments on synthetic and real-world images demonstrate that the proposed FKP can significantly improve the kernel estimation accuracy.
  arXiv  Detail & Related papers  (2021-03-29T22:37:06Z)
• Neighbor Embedding Variational Autoencoder [14.08587678497785]
  We propose a novel model, neighbor embedding VAE(NE-VAE), which explicitly constraints the encoder to encode inputs close in the input space to be close in the latent space. In our experiments, NE-VAE can produce qualitatively different latent representations with majority of the latent dimensions remained active.
  arXiv  Detail & Related papers  (2021-03-21T09:49:12Z)
• Cauchy-Schwarz Regularized Autoencoder [68.80569889599434]
  Variational autoencoders (VAE) are a powerful and widely-used class of generative models. We introduce a new constrained objective based on the Cauchy-Schwarz divergence, which can be computed analytically for GMMs. Our objective improves upon variational auto-encoding models in density estimation, unsupervised clustering, semi-supervised learning, and face analysis.
  arXiv  Detail & Related papers  (2021-01-06T17:36:26Z)
• Unbiased Gradient Estimation for Variational Auto-Encoders using Coupled Markov Chains [34.77971292478243]
  The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture. We develop a training scheme for VAEs by introducing unbiased estimators of the log-likelihood gradient. We show experimentally that VAEs fitted with unbiased estimators exhibit better predictive performance.
  arXiv  Detail & Related papers  (2020-10-05T08:11:55Z)
• Preventing Posterior Collapse with Levenshtein Variational Autoencoder [61.30283661804425]
  We propose to replace the evidence lower bound (ELBO) with a new objective which is simple to optimize and prevents posterior collapse. We show that Levenstein VAE produces more informative latent representations than alternative approaches to preventing posterior collapse.
  arXiv  Detail & Related papers  (2020-04-30T13:27:26Z)
• Stochastic Normalizing Flows [52.92110730286403]
  We introduce normalizing flows for maximum likelihood estimation and variational inference (VI) using differential equations (SDEs) Using the theory of rough paths, the underlying Brownian motion is treated as a latent variable and approximated, enabling efficient training of neural SDEs. These SDEs can be used for constructing efficient chains to sample from the underlying distribution of a given dataset.
  arXiv  Detail & Related papers  (2020-02-21T20:47:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.