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Consider learning a generative model for time-series data. The sequential setting poses a unique challenge: Not only should the generator capture the conditional dynamics of (stepwise) transitions, but its open-loop rollouts should also…

Machine Learning · Statistics 2023-11-03 Daniel Jarrett , Ioana Bica , Mihaela van der Schaar

Energy-based models (EBMs) are a simple yet powerful framework for generative modeling. They are based on a trainable energy function which defines an associated Gibbs measure, and they can be trained and sampled from via well-established…

Machine Learning · Computer Science 2021-05-06 Carles Domingo-Enrich , Alberto Bietti , Eric Vanden-Eijnden , Joan Bruna

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…

Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doubly-intractable distributions in which there are…

Computation · Statistics 2012-07-02 Iain Murray , Zoubin Ghahramani , David MacKay

Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, little work has been done on examining or empowering…

Machine Learning · Computer Science 2015-12-16 Chongxuan Li , Jun Zhu , Tianlin Shi , Bo Zhang

It is a long-standing challenge to accurately and efficiently compute thermodynamic quantities of many-body systems at thermal equilibrium. The conventional methods, e.g., Markov chain Monte Carlo, require many steps to equilibrate. The…

Statistical Mechanics · Physics 2025-12-10 Shuo-Hui Li , Yao-Wen Zhang , Ding Pan

These lecture notes provide an introduction to recent advances in generative modeling methods based on the dynamical transportation of measures, by means of which samples from a simple base measure are mapped to samples from a target…

Machine Learning · Computer Science 2023-10-18 Michael S. Albergo , Eric Vanden-Eijnden

We show that Generative Adversarial Networks (GANs) may be fruitfully exploited to learn stochastic dynamics, surrogating traditional models while capturing thermal fluctuations. Specifically, we showcase the application to a…

Statistical Mechanics · Physics 2025-07-30 Daniele Lanzoni , Olivier Pierre-Louis , Roberto Bergamaschini , Francesco Montalenti

We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD…

Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable…

Machine Learning · Computer Science 2024-02-27 José Manuel de Frutos , Pablo M. Olmos , Manuel A. Vázquez , Joaquín Míguez

Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…

Machine Learning · Statistics 2026-03-11 Lei Li , Zhen Wang , Lishuo Zhang

We propose probabilistic task modelling -- a generative probabilistic model for collections of tasks used in meta-learning. The proposed model combines variational auto-encoding and latent Dirichlet allocation to model each task as a…

Machine Learning · Computer Science 2022-03-21 Cuong C. Nguyen , Thanh-Toan Do , Gustavo Carneiro

Generative models have shown strong generation ability while efficient likelihood estimation is less explored. Energy-based models~(EBMs) define a flexible energy function to parameterize unnormalized densities efficiently but are notorious…

Machine Learning · Computer Science 2024-06-11 Cong Geng , Tian Han , Peng-Tao Jiang , Hao Zhang , Jinwei Chen , Søren Hauberg , Bo Li

Developments in deep generative models have allowed for tractable learning of high-dimensional data distributions. While the employed learning procedures typically assume that training data is drawn i.i.d. from the distribution of interest,…

Machine Learning · Computer Science 2017-05-24 Ari Seff , Alex Beatson , Daniel Suo , Han Liu

Modern applications and progress in deep learning research have created renewed interest for generative models of text and of images. However, even today it is unclear what objective functions one should use to train and evaluate these…

Machine Learning · Statistics 2015-11-17 Ferenc Huszár

While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…

Machine Learning · Statistics 2026-04-14 Randy Martinez , Rong Tang , Lizhen Lin

Understanding the impact of data structure on the computational tractability of learning is a key challenge for the theory of neural networks. Many theoretical works do not explicitly model training data, or assume that inputs are drawn…

Machine Learning · Statistics 2022-05-23 Sebastian Goldt , Bruno Loureiro , Galen Reeves , Florent Krzakala , Marc Mézard , Lenka Zdeborová

Deep generative models (DGMs) have recently demonstrated remarkable success in capturing complex probability distributions over graphs. Although their excellent performance is attributed to powerful and scalable deep neural networks, it is,…

Machine Learning · Computer Science 2025-03-18 Milan Papež , Martin Rektoris , Václav Šmídl , Tomáš Pevný

The simulation of discrete karst networks presents a significant challenge due to the complexity of the physicochemical processes occurring within various geological and hydrogeological contexts over extended periods. This complex interplay…

Machine Learning · Statistics 2025-06-12 Dany Lauzon , Julien Straubhaar , Philippe Renard

In this paper, we address technical difficulties that arise when applying Markov chain Monte Carlo (MCMC) to hierarchical models designed to perform clustering in the space of latent parameters of subject-wise generative models.…

Quantitative Methods · Quantitative Biology 2020-12-15 Yu Yao , Klaas E. Stephan
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