English
Related papers

Related papers: Bounding Evidence and Estimating Log-Likelihood in…

200 papers

The evidence lower bound (ELBO) is one of the most central objectives for probabilistic unsupervised learning. For the ELBOs of several generative models and model classes, we here prove convergence to entropy sums. As one result, we…

Machine Learning · Statistics 2025-01-17 Jan Warnken , Dmytro Velychko , Simon Damm , Asja Fischer , Jörg Lücke

The central objective function of a variational autoencoder (VAE) is its variational lower bound (the ELBO). Here we show that for standard (i.e., Gaussian) VAEs the ELBO converges to a value given by the sum of three entropies: the…

Machine Learning · Statistics 2024-04-30 Simon Damm , Dennis Forster , Dmytro Velychko , Zhenwen Dai , Asja Fischer , Jörg Lücke

The practical impact of deep learning on complex supervised learning problems has been significant, so much so that almost every Artificial Intelligence problem, or at least a portion thereof, has been somehow recast as a deep learning…

Machine Learning · Statistics 2018-03-19 Housam Khalifa Bashier Babiker , Randy Goebel

The variational lower bound (a.k.a. ELBO or free energy) is the central objective for many established as well as for many novel algorithms for unsupervised learning. Such algorithms usually increase the bound until parameters have…

Machine Learning · Statistics 2024-12-25 Jörg Lücke , Jan Warnken

The formalism of Bayesian model selection provides a very elegant way of ranking different physical models in terms of how compatible they are with a given set of observed data. However, its practical application is often hampered by the…

Cosmology and Nongalactic Astrophysics · Physics 2026-01-19 Nathan Cohen , Jan Hamann , Ameek Malhotra

This paper studies the problem of approximately unlearning a Bayesian model from a small subset of the training data to be erased. We frame this problem as one of minimizing the Kullback-Leibler divergence between the approximate posterior…

Machine Learning · Computer Science 2020-10-27 Quoc Phong Nguyen , Bryan Kian Hsiang Low , Patrick Jaillet

The marginal likelihood, also known as the evidence, is regarded as a mathematical embodiment of Occam's razor, enabling model selection that avoids overfitting. The evidence lower bound (ELBO) objective from variational inference has also…

Machine Learning · Statistics 2026-04-30 Ethan Harvey , Michael C. Hughes

Variational Graph Auto-Encoders (VGAEs) have been widely used to solve the node clustering task. However, the state-of-the-art methods have numerous challenges. First, existing VGAEs do not account for the discrepancy between the inference…

Machine Learning · Computer Science 2023-12-29 Nairouz Mrabah , Mohamed Bouguessa , Riadh Ksantini

Real world datasets often contain entries with missing elements e.g. in a medical dataset, a patient is unlikely to have taken all possible diagnostic tests. Variational Autoencoders (VAEs) are popular generative models often used for…

Machine Learning · Computer Science 2021-03-23 Mark Collier , Alfredo Nazabal , Christopher K. I. Williams

We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The…

Machine Learning · Statistics 2021-07-21 Ali Unlu , Laurence Aitchison

We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The…

Machine Learning · Statistics 2021-08-11 Ali Unlu , Laurence Aitchison

The study of model bias and variance with respect to decision boundaries is critically important in supervised classification. There is generally a tradeoff between the two, as fine-tuning of the decision boundary of a classification model…

Machine Learning · Computer Science 2020-02-25 Matthew Almeida , Wei Ding , Scott Crouter , Ping Chen

Posterior collapse plagues VAEs for text, especially for conditional text generation with strong autoregressive decoders. In this work, we address this problem in variational neural machine translation by explicitly promoting mutual…

Computation and Language · Computer Science 2019-09-23 Arya D. McCarthy , Xian Li , Jiatao Gu , Ning Dong

We analyse the properties of an unbiased gradient estimator of the ELBO for variational inference, based on the score function method with leave-one-out control variates. We show that this gradient estimator can be obtained using a new…

Machine Learning · Statistics 2020-10-30 Lorenz Richter , Ayman Boustati , Nikolas Nüsken , Francisco J. R. Ruiz , Ömer Deniz Akyildiz

Bayesian coresets speed up posterior inference in the large-scale data regime by approximating the full-data log-likelihood function with a surrogate log-likelihood based on a small, weighted subset of the data. But while Bayesian coresets…

Machine Learning · Statistics 2024-10-18 Trevor Campbell

We provide a rigorous analysis of training by variational inference (VI) of Bayesian neural networks in the two-layer and infinite-width case. We consider a regression problem with a regularized evidence lower bound (ELBO) which is…

Machine Learning · Statistics 2023-07-12 Arnaud Descours , Tom Huix , Arnaud Guillin , Manon Michel , Éric Moulines , Boris Nectoux

We propose a new Bayesian Neural Net formulation that affords variational inference for which the evidence lower bound is analytically tractable subject to a tight approximation. We achieve this tractability by (i) decomposing ReLU…

Machine Learning · Statistics 2019-06-13 Manuel Haussmann , Fred A. Hamprecht , Melih Kandemir

A key challenge in applying reinforcement learning (RL) to diffusion large language models (dLLMs) lies in the intractability of their likelihood functions, which are essential for the RL objective, necessitating corresponding approximation…

Machine Learning · Computer Science 2025-10-15 Nianyi Lin , Jiajie Zhang , Lei Hou , Juanzi Li

An information-theoretic upper bound on the generalization error of supervised learning algorithms is derived. The bound is constructed in terms of the mutual information between each individual training sample and the output of the…

Machine Learning · Computer Science 2020-08-06 Yuheng Bu , Shaofeng Zou , Venugopal V. Veeravalli

Collecting paired training data is difficult in practice, but the unpaired samples broadly exist. Current approaches aim at generating synthesized training data from unpaired samples by exploring the relationship between the corrupted and…

Image and Video Processing · Electrical Eng. & Systems 2022-09-13 Dihan Zheng , Xiaowen Zhang , Kaisheng Ma , Chenglong Bao