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Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose…

Machine Learning · Statistics 2022-03-17 Gianluigi Silvestri , Emily Fertig , Dave Moore , Luca Ambrogioni

In this work, we demonstrate how to reliably estimate epistemic uncertainty while maintaining the flexibility needed to capture complicated aleatoric distributions. To this end, we propose an ensemble of Normalizing Flows (NF), which are…

Machine Learning · Computer Science 2023-10-05 Lucas Berry , David Meger

We present a new method of training energy-based models (EBMs) for anomaly detection that leverages low-dimensional structures within data. The proposed algorithm, Manifold Projection-Diffusion Recovery (MPDR), first perturbs a data point…

Machine Learning · Computer Science 2023-10-31 Sangwoong Yoon , Young-Uk Jin , Yung-Kyun Noh , Frank C. Park

Energy-based learning is a powerful learning paradigm that encapsulates various discriminative and generative approaches. An energy-based model (EBM) is typically formed of inner-model(s) that learn a combination of the different features…

Machine Learning · Computer Science 2023-06-05 Firas Laakom , Jenni Raitoharju , Alexandros Iosifidis , Moncef Gabbouj

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

Simulation-free training frameworks have been at the forefront of the generative modelling revolution in continuous spaces, leading to large-scale diffusion and flow matching models. However, such modern generative models suffer from…

Machine Learning · Computer Science 2025-10-31 Danyal Rehman , Oscar Davis , Jiarui Lu , Jian Tang , Michael Bronstein , Yoshua Bengio , Alexander Tong , Avishek Joey Bose

Reward models (RMs) are essential for aligning Large Language Models (LLMs) with human preferences. However, they often struggle with capturing complex human preferences and generalizing to unseen data. To address these challenges, we…

Computation and Language · Computer Science 2025-08-06 Anamika Lochab , Ruqi Zhang

Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…

Machine Learning · Computer Science 2023-05-31 Matthias Kirchler , Christoph Lippert , Marius Kloft

Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…

Machine Learning · Statistics 2021-11-15 Brendan Leigh Ross , Jesse C. Cresswell

This work presents strategies to learn an Energy-Based Model (EBM) according to the desired length of its MCMC sampling trajectories. MCMC trajectories of different lengths correspond to models with different purposes. Our experiments cover…

Machine Learning · Statistics 2022-05-25 Mitch Hill , Jonathan Mitchell , Chu Chen , Yuan Du , Mubarak Shah , Song-Chun Zhu

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

Training energy-based models (EBMs) with noise-contrastive estimation (NCE) is theoretically feasible but practically challenging. Effective learning requires the noise distribution to be approximately similar to the target distribution,…

Machine Learning · Computer Science 2022-11-07 Nathaniel Xu

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

Neural density estimators are flexible families of parametric models which have seen widespread use in unsupervised machine learning in recent years. Maximum-likelihood training typically dictates that these models be constrained to specify…

Machine Learning · Statistics 2019-04-12 Charlie Nash , Conor Durkan

Predictive models are highly advanced in understanding the mechanisms of brain function. Recent advances in machine learning further underscore the power of prediction for optimal representation in learning. However, there remains a gap in…

Machine Learning · Computer Science 2025-05-22 Xingsi Dong , Xiangyuan Peng , Si Wu

In this paper, we quantify the impact of using non-convergent Markov chains to train Energy-Based models (EBMs). In particular, we show analytically that EBMs trained with non-persistent short runs to estimate the gradient can perfectly…

Machine Learning · Computer Science 2026-05-07 Elisabeth Agoritsas , Giovanni Catania , Aurélien Decelle , Beatriz Seoane

We focus on the problem of efficient sampling and learning of probability densities by incorporating symmetries in probabilistic models. We first introduce Equivariant Stein Variational Gradient Descent algorithm -- an equivariant sampling…

Machine Learning · Computer Science 2021-07-30 Priyank Jaini , Lars Holdijk , Max Welling

Learning distributions over graph-structured data is a challenging task with many applications in biology and chemistry. In this work we use an energy-based model (EBM) based on multi-channel graph neural networks (GNN) to learn permutation…

Machine Learning · Computer Science 2021-08-31 Shiv Shankar

Modern reinforcement learning (RL) algorithms have found success by using powerful probabilistic models, such as transformers, energy-based models, and diffusion/flow-based models. To this end, RL researchers often choose to pay the price…

Machine Learning · Computer Science 2025-06-05 Raj Ghugare , Benjamin Eysenbach

Normalizing flows are a class of deep generative models that are especially interesting for modeling probability distributions in physics, where the exact likelihood of flows allows reweighting to known target energy functions and computing…

Machine Learning · Statistics 2023-11-27 Leon Klein , Andreas Krämer , Frank Noé