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The Variational Auto-Encoder (VAE) is a simple, efficient, and popular deep maximum likelihood model. Though usage of VAEs is widespread, the derivation of the VAE is not as widely understood. In this tutorial, we will provide an overview…

Machine Learning · Computer Science 2020-07-02 Ronald Yu

Variational Autoencoders (VAEs) are well-established as a principled approach to probabilistic unsupervised learning with neural networks. Typically, an encoder network defines the parameters of a Gaussian distributed latent space from…

Machine Learning · Computer Science 2025-05-16 Alan Jeffares , Liyuan Liu

Accurate analysis of microscopy images is hindered by the presence of noise. This noise is usually signal-dependent and often additionally correlated along rows or columns of pixels. Current self- and unsupervised denoisers can address…

Image and Video Processing · Electrical Eng. & Systems 2025-04-09 Benjamin Salmon , Alexander Krull

Aiming at exploiting the rich information in user behaviour sequences, sequential recommendation has been widely adopted in real-world recommender systems. However, current methods suffer from the following issues: 1) sparsity of user-item…

Information Retrieval · Computer Science 2022-12-06 Yu Wang , Hengrui Zhang , Zhiwei Liu , Liangwei Yang , Philip S. Yu

In this paper we present a new implementation of a Variational Autoencoder (VAE) for the calibration of sensors. We propose that the VAE can be used to calibrate sensor data by training the latent space as a calibration output. We discuss…

Machine Learning · Computer Science 2025-11-04 Travis Barrett , Amit Kumar Mishra , Joyce Mwangama

Estimation of the value-at-risk (VaR) of a large portfolio of assets is an important task for financial institutions. As the joint log-returns of asset prices can often be projected to a latent space of a much smaller dimension, the use of…

Machine Learning · Computer Science 2021-12-06 Robert Sicks , Stefanie Grimm , Ralf Korn , Ivo Richert

Variational autoencoders (VAEs) are one class of generative probabilistic latent-variable models designed for inference based on known data. They balance reconstruction and regularizer terms. A variational approximation produces an evidence…

Machine Learning · Statistics 2023-12-13 Robert I. Cukier

Variational Autoencoders (VAEs) are essential for large-scale audio tasks like diffusion-based generation. However, existing open-source models often neglect auditory perceptual aspects during training, leading to weaknesses in phase…

Sound · Computer Science 2025-11-07 Kangdi Wang , Zhiyue Wu , Dinghao Zhou , Rui Lin , Junyu Dai , Tao Jiang

Variational Autoencoder (VAE)-based generative models offer flexible representation learning by incorporating meta-priors, general premises considered beneficial for downstream tasks. However, the incorporated meta-priors often involve…

Machine Learning · Computer Science 2023-02-27 Nao Nakagawa , Ren Togo , Takahiro Ogawa , Miki Haseyama

Variational autoencoders (VAEs) have witnessed great success in performing the compression of image datasets. This success, made possible by the bits-back coding framework, has produced competitive compression performance across many…

Image and Video Processing · Electrical Eng. & Systems 2022-04-06 Tom Ryder , Chen Zhang , Ning Kang , Shifeng Zhang

People can easily imagine the potential sound while seeing an event. This natural synchronization between audio and visual signals reveals their intrinsic correlations. To this end, we propose to learn the audio-visual correlations from the…

Computer Vision and Pattern Recognition · Computer Science 2021-02-16 Ye Zhu , Yu Wu , Hugo Latapie , Yi Yang , Yan Yan

Variational Auto-Encoders (VAEs) have shown great potential in the unsupervised learning of data distributions. An VAE trained on normal images is expected to only be able to reconstruct normal images, allowing the localization of anomalous…

Computer Vision and Pattern Recognition · Computer Science 2020-05-22 Leixin Zhou , Wenxiang Deng , Xiaodong Wu

Electron, optical, and scanning probe microscopy methods are generating ever increasing volume of image data containing information on atomic and mesoscale structures and functionalities. This necessitates the development of the machine…

Machine Learning · Computer Science 2023-04-03 Mani Valleti , Yongtao Liu , Sergei Kalinin

Stochastic processes provide a mathematically elegant way model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. In practice, however, efficient inference…

Machine Learning · Computer Science 2022-09-15 Swapnil Mishra , Seth Flaxman , Tresnia Berah , Harrison Zhu , Mikko Pakkanen , Samir Bhatt

Learning rich data representations from unlabeled data is a key challenge towards applying deep learning algorithms in downstream tasks. Several variants of variational autoencoders (VAEs) have been proposed to learn compact data…

Computer Vision and Pattern Recognition · Computer Science 2024-01-11 Pan Xiao , Peijie Qiu , Sungmin Ha , Abdalla Bani , Shuang Zhou , Aristeidis Sotiras

Variational autoencoders (VAEs) are a popular generative model used to approximate distributions. The encoder part of the VAE is used in amortized learning of latent variables, producing a latent representation for data samples. Recently,…

Machine Learning · Statistics 2023-05-12 Daniel G. Edelberg , Roy R. Lederman

VAEs are probabilistic graphical models based on neural networks that allow the coding of input data in a latent space formed by simpler probability distributions and the reconstruction, based on such latent variables, of the source data.…

Artificial Intelligence · Computer Science 2023-02-21 Jordi de la Torre

Existing vector quantization (VQ) based autoregressive models follow a two-stage generation paradigm that first learns a codebook to encode images as discrete codes, and then completes generation based on the learned codebook. However, they…

Computer Vision and Pattern Recognition · Computer Science 2023-05-22 Mengqi Huang , Zhendong Mao , Zhuowei Chen , Yongdong Zhang

When trained effectively, the Variational Autoencoder (VAE) is both a powerful language model and an effective representation learning framework. In practice, however, VAEs are trained with the evidence lower bound (ELBO) as a surrogate…

Machine Learning · Computer Science 2019-09-04 Bohan Li , Junxian He , Graham Neubig , Taylor Berg-Kirkpatrick , Yiming Yang

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).…

Machine Learning · Statistics 2025-05-13 Tian Qin , Wei-Min Huang