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This paper studies the fundamental learning problem of the energy-based model (EBM). Learning the EBM can be achieved using the maximum likelihood estimation (MLE), which typically involves the Markov Chain Monte Carlo (MCMC) sampling, such…

Machine Learning · Computer Science 2023-12-06 Jiali Cui , Tian Han

Energy-based models (EBMs) are a flexible class of deep generative models and are well-suited to capture complex dependencies in multimodal data. However, learning multimodal EBM by maximum likelihood requires Markov Chain Monte Carlo…

Machine Learning · Computer Science 2026-05-04 Jiali Cui , Zhiqiang Lao , Heather Yu

This paper proposes a joint training method to learn both the variational auto-encoder (VAE) and the latent energy-based model (EBM). The joint training of VAE and latent EBM are based on an objective function that consists of three…

Computer Vision and Pattern Recognition · Computer Science 2020-06-12 Tian Han , Erik Nijkamp , Linqi Zhou , Bo Pang , Song-Chun Zhu , Ying Nian Wu

The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture; one of them parameterizes the model's likelihood. Fitting its parameters via maximum likelihood (ML) is…

Machine Learning · Computer Science 2021-06-03 Francisco J. R. Ruiz , Michalis K. Titsias , Taylan Cemgil , Arnaud Doucet

In this paper, we propose a novel generative model that utilizes a conditional Energy-Based Model (EBM) for enhancing Variational Autoencoder (VAE), termed Energy-Calibrated VAE (EC-VAE). Specifically, VAEs often suffer from blurry…

Computer Vision and Pattern Recognition · Computer Science 2024-07-19 Yihong Luo , Siya Qiu , Xingjian Tao , Yujun Cai , Jing Tang

Variational autoencoders (VAEs) are popular likelihood-based generative models which can be efficiently trained by maximizing an Evidence Lower Bound (ELBO). There has been much progress in improving the expressiveness of the variational…

Machine Learning · Statistics 2023-08-29 Marcel Hirt , Vasileios Kreouzis , Petros Dellaportas

Auto-encoding Variational Bayes (AEVB) is a powerful and general algorithm for fitting latent variable models (a promising direction for unsupervised learning), and is well-known for training the Variational Auto-Encoder (VAE). In this…

Machine Learning · Computer Science 2022-08-17 Yang Zhi-Han

Energy-based models (EBMs) offer a flexible framework for parameterizing probability distributions using neural networks. However, learning EBMs by exact maximum likelihood estimation (MLE) is generally intractable, due to the need to…

Machine Learning · Computer Science 2025-08-20 Michael E. Sander , Vincent Roulet , Tianlin Liu , Mathieu Blondel

We propose a variational autoencoder (VAE) approach for parameter estimation in nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs) using longitudinal data from multiple subjects. In moderate dimensions,…

Methodology · Statistics 2026-02-11 Zhe Li , Mélanie Prague , Rodolphe Thiébaut , Quentin Clairon

Energy-based models (EBMs) are powerful probabilistic models, but suffer from intractable sampling and density evaluation due to the partition function. As a result, inference in EBMs relies on approximate sampling algorithms, leading to a…

Machine Learning · Computer Science 2020-01-10 Dieterich Lawson , George Tucker , Bo Dai , Rajesh Ranganath

Energy-based models (EBMs) have recently been successful in representing complex distributions of small images. However, sampling from them requires expensive Markov chain Monte Carlo (MCMC) iterations that mix slowly in high dimensional…

Machine Learning · Computer Science 2021-11-08 Zhisheng Xiao , Karsten Kreis , Jan Kautz , Arash Vahdat

Markov chain Monte Carlo (MCMC), such as Langevin dynamics, is valid for approximating intractable distributions. However, its usage is limited in the context of deep latent variable models owing to costly datapoint-wise sampling iterations…

Machine Learning · Computer Science 2022-10-12 Shohei Taniguchi , Yusuke Iwasawa , Wataru Kumagai , Yutaka Matsuo

Energy-based modeling is a promising approach to unsupervised learning, which yields many downstream applications from a single model. The main difficulty in learning energy-based models with the "contrastive approaches" is the generation…

Machine Learning · Computer Science 2021-11-30 Kirill Neklyudov , Priyank Jaini , Max Welling

This paper studies the fundamental problem of learning deep generative models that consist of multiple layers of latent variables organized in top-down architectures. Such models have high expressivity and allow for learning hierarchical…

Machine Learning · Statistics 2020-07-21 Erik Nijkamp , Bo Pang , Tian Han , Linqi Zhou , Song-Chun Zhu , Ying Nian Wu

Sampling trajectories from a distribution followed by ranking them based on a specified cost function is a common approach in autonomous driving. Typically, the sampling distribution is hand-crafted (e.g a Gaussian, or a grid). Recently,…

Robotics · Computer Science 2024-04-26 Simon Idoko , Basant Sharma , Arun Kumar Singh

Energy-Based Models (EBMs) present a flexible and appealing way to represent uncertainty. Despite recent advances, training EBMs on high-dimensional data remains a challenging problem as the state-of-the-art approaches are costly, unstable,…

Machine Learning · Computer Science 2021-06-08 Will Grathwohl , Jacob Kelly , Milad Hashemi , Mohammad Norouzi , Kevin Swersky , David Duvenaud

Maximum likelihood estimation is widely used in training Energy-based models (EBMs). Training requires samples from an unnormalized distribution, which is usually intractable, and in practice, these are obtained by MCMC algorithms such as…

Machine Learning · Computer Science 2021-04-23 Zhisheng Xiao , Qing Yan , Yali Amit

Learning energy-based model (EBM) requires MCMC sampling of the learned model as an inner loop of the learning algorithm. However, MCMC sampling of EBMs in high-dimensional data space is generally not mixing, because the energy function,…

Machine Learning · Statistics 2022-03-17 Erik Nijkamp , Ruiqi Gao , Pavel Sountsov , Srinivas Vasudevan , Bo Pang , Song-Chun Zhu , Ying Nian Wu

Variational autoencoders (VAEs) are powerful generative models with the salient ability to perform inference. Here, we introduce a quantum variational autoencoder (QVAE): a VAE whose latent generative process is implemented as a quantum…

Variational Auto-Encoders (VAEs) are known to generate blurry and inconsistent samples. One reason for this is the "prior hole" problem. A prior hole refers to regions that have high probability under the VAE's prior but low probability…

Machine Learning · Computer Science 2025-10-02 Debottam Dutta , Chaitanya Amballa , Zhongweiyang Xu , Yu-Lin Wei , Romit Roy Choudhury
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