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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

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

Due to the intractable partition function, training energy-based models (EBMs) by maximum likelihood requires Markov chain Monte Carlo (MCMC) sampling to approximate the gradient of the Kullback-Leibler divergence between data and model…

Machine Learning · Statistics 2021-12-28 Jianwen Xie , Zilong Zheng , Ping Li

This paper studies the fundamental problem of learning multi-layer generator models. The multi-layer generator model builds multiple layers of latent variables as a prior model on top of the generator, which benefits learning complex data…

Computer Vision and Pattern Recognition · Computer Science 2023-10-13 Jiali Cui , Ying Nian Wu , Tian Han

Energy-Based Models (EBMs), also known as non-normalized probabilistic models, specify probability density or mass functions up to an unknown normalizing constant. Unlike most other probabilistic models, EBMs do not place a restriction on…

Machine Learning · Computer Science 2021-02-19 Yang Song , Diederik P. Kingma

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

Multimodal generative models are crucial for various applications. We propose an approach that combines an expressive energy-based model (EBM) prior with Markov Chain Monte Carlo (MCMC) inference in the latent space for multimodal…

Machine Learning · Computer Science 2024-08-21 Shiyu Yuan , Carlo Lipizzi , Tian Han

This study investigates the effects of Markov chain Monte Carlo (MCMC) sampling in unsupervised Maximum Likelihood (ML) learning. Our attention is restricted to the family of unnormalized probability densities for which the negative log…

Machine Learning · Statistics 2019-12-02 Erik Nijkamp , Mitch Hill , Tian Han , Song-Chun Zhu , Ying Nian Wu

We propose to learn energy-based model (EBM) in the latent space of a generator model, so that the EBM serves as a prior model that stands on the top-down network of the generator model. Both the latent space EBM and the top-down network…

Machine Learning · Statistics 2020-10-30 Bo Pang , Tian Han , Erik Nijkamp , Song-Chun Zhu , Ying Nian Wu

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

We show that the bias of the approximate maximum-likelihood estimation (MLE) objective of a persistent chain energy-based model (EBM) is precisely equal to the thermodynamic excess work of an overdamped Langevin dynamical system. We then…

Statistical Mechanics · Physics 2025-10-06 Jeff Hnybida , Simon Verret

This paper studies the fundamental problem of learning energy-based model (EBM) in the latent space of the generator model. Learning such prior model typically requires running costly Markov Chain Monte Carlo (MCMC). Instead, we propose to…

Machine Learning · Computer Science 2022-09-20 Zhisheng Xiao , Tian Han

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

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 (ML) learning for energy-based models (EBMs) is challenging, partly due to non-convergence of Markov chain Monte Carlo.Several variations of ML learning have been proposed, but existing methods all fail to achieve both…

Machine Learning · Statistics 2023-04-24 Xinwei Zhang , Zhiqiang Tan , Zhijian Ou

Energy-based models (EBM) have become increasingly popular within computer vision. EBMs bring a probabilistic approach to training deep neural networks (DNN) and have been shown to enhance performance in areas such as calibration,…

Machine Learning · Computer Science 2023-04-05 Jacob Piland , Christopher Sweet , Priscila Saboia , Charles Vardeman , Adam Czajka

An energy-based model (EBM) is a popular generative framework that offers both explicit density and architectural flexibility, but training them is difficult since it is often unstable and time-consuming. In recent years, various training…

Machine Learning · Computer Science 2023-03-07 Hankook Lee , Jongheon Jeong , Sejun Park , Jinwoo Shin

The Energy-Based Model (EBM) framework is a very general approach to generative modeling that tries to learn and exploit probability distributions only defined though unnormalized scores. It has risen in popularity recently thanks to the…

Machine Learning · Computer Science 2022-02-25 Léo Gagnon , Guillaume Lajoie

Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is best measured by the cross-entropy (CE) of the model distribution relative to…

Machine Learning · Computer Science 2023-12-14 Davide Carbone , Mengjian Hua , Simon Coste , Eric Vanden-Eijnden

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
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