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The cold posterior effect (CPE) (Wenzel et al., 2020) in Bayesian deep learning shows that, for posteriors with a temperature $T<1$, the resulting posterior predictive could have better performances than the Bayesian posterior ($T=1$). As…

Machine Learning · Statistics 2023-10-03 Yijie Zhang , Yi-Shan Wu , Luis A. Ortega , Andrés R. Masegosa

The Cold Posterior Effect (CPE) is a phenomenon in Bayesian Deep Learning (BDL), where tempering the posterior to a cold temperature often improves the predictive performance of the posterior predictive distribution (PPD). Although the term…

Machine Learning · Statistics 2025-10-27 Kenyon Ng , Chris van der Heide , Liam Hodgkinson , Susan Wei

While Bayesian neural networks (BNNs) provide a sound and principled alternative to standard neural networks, an artificial sharpening of the posterior usually needs to be applied to reach comparable performance. This is in stark contrast…

Machine Learning · Computer Science 2023-07-19 Gregor Bachmann , Lorenzo Noci , Thomas Hofmann

To get Bayesian neural networks to perform comparably to standard neural networks it is usually necessary to artificially reduce uncertainty using a "tempered" or "cold" posterior. This is extremely concerning: if the prior is accurate,…

Machine Learning · Statistics 2021-04-28 Laurence Aitchison

Recent work has observed that one can outperform exact inference in Bayesian neural networks by tuning the "temperature" of the posterior on a validation set (the "cold posterior" effect). To help interpret this phenomenon, we argue that…

Machine Learning · Statistics 2020-08-04 Ben Adlam , Jasper Snoek , Samuel L. Smith

Uncertainty quantification in reinforcement learning can greatly improve exploration and robustness. Approximate Bayesian approaches have recently been popularized to quantify uncertainty in model-free algorithms. However, so far the focus…

Machine Learning · Computer Science 2025-09-01 Pascal R. van der Vaart , Neil Yorke-Smith , Matthijs T. J. Spaan

Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are…

Machine Learning · Computer Science 2024-10-22 Yijie Zhang

During the past five years the Bayesian deep learning community has developed increasingly accurate and efficient approximate inference procedures that allow for Bayesian inference in deep neural networks. However, despite this algorithmic…

Bayesian neural networks that incorporate data augmentation implicitly use a ``randomly perturbed log-likelihood [which] does not have a clean interpretation as a valid likelihood function'' (Izmailov et al. 2021). Here, we provide several…

We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can…

Machine Learning · Computer Science 2025-05-28 Simon Dirmeier , Antonietta Mira

The radio astronomy community is adopting deep learning techniques to deal with the huge data volumes expected from the next-generation of radio observatories. Bayesian neural networks (BNNs) provide a principled way to model uncertainty in…

Instrumentation and Methods for Astrophysics · Physics 2023-11-15 Devina Mohan , Anna Scaife

Benchmark datasets used for image classification tend to have very low levels of label noise. When Bayesian neural networks are trained on these datasets, they often underfit, misrepresenting the aleatoric uncertainty of the data. A common…

Machine Learning · Computer Science 2024-03-05 Martin Marek , Brooks Paige , Pavel Izmailov

We investigate the cold posterior effect through the lens of PAC-Bayes generalization bounds. We argue that in the non-asymptotic setting, when the number of training samples is (relatively) small, discussions of the cold posterior effect…

Machine Learning · Computer Science 2022-06-23 Konstantinos Pitas , Julyan Arbel

Aleatoric uncertainty captures the inherent randomness of the data, such as measurement noise. In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance…

Machine Learning · Computer Science 2022-03-31 Sanyam Kapoor , Wesley J. Maddox , Pavel Izmailov , Andrew Gordon Wilson

The fairness of a deep neural network is strongly affected by dataset bias and spurious correlations, both of which are usually present in modern feature-rich and complex visual datasets. Due to the difficulty and variability of the task,…

Computer Vision and Pattern Recognition · Computer Science 2024-02-28 Rebecca S Stone , Nishant Ravikumar , Andrew J Bulpitt , David C Hogg

There is a growing concern that the recent progress made in AI, especially regarding the predictive competence of deep learning models, will be undermined by a failure to properly explain their operation and outputs. In response to this…

Machine Learning · Computer Science 2020-09-15 Eoin M. Kenny , Mark T. Keane

We conduct a detailed investigation of tempered posteriors and uncover a number of crucial and previously undiscussed points. Contrary to previous results, we first show that for realistic models and datasets and the tightly controlled case…

Machine Learning · Computer Science 2023-09-12 Konstantinos Pitas , Julyan Arbel

Neural Posterior Estimation (NPE) has emerged as a powerful approach for amortized Bayesian inference when the true posterior $p(\theta \mid y)$ is intractable or difficult to sample. But evaluating the accuracy of neural posterior…

Machine Learning · Statistics 2025-07-24 Vansh Bansal , Tianyu Chen , James G. Scott

Bayesian decision theory advocates the Bayes classifier as the optimal approach for minimizing the risk in machine learning problems. Current deep learning algorithms usually solve for the optimal classifier by \emph{implicitly} estimating…

Machine Learning · Computer Science 2025-07-01 Chaoqun Du , Yulin Wang , Shiji Song , Gao Huang

Accurate uncertainty quantification in graph neural networks (GNNs) is essential, especially in high-stakes domains where GNNs are frequently employed. Conformal prediction (CP) offers a promising framework for quantifying uncertainty by…

Machine Learning · Computer Science 2023-12-06 Seohyeon Cha , Honggu Kang , Joonhyuk Kang
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