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We are motivated by the problem of providing strong generalization guarantees in the context of meta-learning. Existing generalization bounds are either challenging to evaluate or provide vacuous guarantees in even relatively simple…

Machine Learning · Computer Science 2021-10-27 Alec Farid , Anirudha Majumdar

Most classification models work by first predicting a posterior probability distribution over all classes and then selecting that class with the largest estimated probability. In many settings however, the quality of posterior probability…

Computation and Language · Computer Science 2020-05-04 Taehee Jung , Dongyeop Kang , Hua Cheng , Lucas Mentch , Thomas Schaaf

Conformal Prediction provides distribution-free prediction intervals with guaranteed coverage, but its reliance on a single global calibration threshold obscures the sources of uncertainty at the instance level. In particular, it conflates…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

Methodology · Statistics 2026-02-03 Magid Sabbagh , David A. Stephens

As we move away from the data, the predictive uncertainty should increase, since a great variety of explanations are consistent with the little available information. We introduce Distance-Aware Prior (DAP) calibration, a method to correct…

Machine Learning · Statistics 2022-07-19 Gianluca Detommaso , Alberto Gasparin , Andrew Wilson , Cedric Archambeau

Despite extensive research on neural network calibration, existing methods typically apply global transformations that treat all predictions uniformly, overlooking the heterogeneous reliability of individual predictions. Furthermore, the…

Machine Learning · Computer Science 2025-10-22 Hassan Gharoun , Mohammad Sadegh Khorshidi , Kasra Ranjbarigderi , Fang Chen , Amir H. Gandomi

Data uncertainty in practical person reID is ubiquitous, hence it requires not only learning the discriminative features, but also modeling the uncertainty based on the input. This paper proposes to learn the sample posterior and the class…

Computer Vision and Pattern Recognition · Computer Science 2020-07-20 Yan Zhang , Zhilin Zheng , Binyu He , Li Sun

Model misspecification is a long-standing enigma of the Bayesian inference framework as posteriors tend to get overly concentrated on ill-informed parameter values towards the large sample limit. Tempering of the likelihood has been…

Methodology · Statistics 2019-12-13 Owen Thomas , Jukka Corander

We establish a general, non-asymptotic error analysis framework for understanding the effects of incremental approximations made by practical approaches for Bayesian sequential learning (BSL) on their long-term inference performance. Our…

Statistics Theory · Mathematics 2025-07-29 Liliang Wang , Alex A. Gorodetsky

Gaussian variational approximations are widely used for summarizing posterior distributions in Bayesian models, especially in high-dimensional settings. However, a drawback of such approximations is the inability to capture skewness or more…

Methodology · Statistics 2026-04-02 Lucas Kock , Linda S. L. Tan , Prateek Bansal , David J. Nott

In this position paper, we argue that many post-mortem generalization measures -- those computed on trained networks -- are \textbf{fragile}: small training modifications that barely affect the performance of the underlying deep neural…

Machine Learning · Computer Science 2026-02-12 Shuofeng Zhang , Ard Louis

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…

Computer Vision and Pattern Recognition · Computer Science 2024-08-01 Dominik Narnhofer , Andreas Habring , Martin Holler , Thomas Pock

The consideration of predictive uncertainty in medical imaging with deep learning is of utmost importance. We apply estimation of both aleatoric and epistemic uncertainty by variational Bayesian inference with Monte Carlo dropout to…

Image and Video Processing · Electrical Eng. & Systems 2021-04-27 Max-Heinrich Laves , Sontje Ihler , Jacob F. Fast , Lüder A. Kahrs , Tobias Ortmaier

The Bayesian conjugate gradient method offers probabilistic solutions to linear systems but suffers from poor calibration, limiting its utility in uncertainty quantification tasks. Recent approaches leveraging postiterations to construct…

Machine Learning · Statistics 2025-08-13 Niall Vyas , Disha Hegde , Jon Cockayne

Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…

Computation · Statistics 2026-01-07 Joshua J Bon , David J Warne , David J Nott , Christopher Drovandi

Constrained learning is prevalent in many statistical tasks. Recent work proposes distance-to-set penalties to derive estimators under general constraints that can be specified as sets, but focuses on obtaining point estimates that do not…

Methodology · Statistics 2022-10-25 Rick Presman , Jason Xu

Continual learning for large language models is typically evaluated through accuracy retention under sequential fine-tuning. We argue that this perspective is incomplete, because uncertainty reliability can degrade earlier and more sharply…

Machine Learning · Computer Science 2026-04-28 Ibne Farabi Shihab , Sanjeda Akter , Anuj Sharma

Density estimation represents one of the most successful applications of Bayesian nonparametrics. In particular, Dirichlet process mixtures of normals are the gold standard for density estimation and their asymptotic properties have been…

Statistics Theory · Mathematics 2015-07-02 Antonio Canale , Pierpaolo De Blasi

In observational causal inference, domain knowledge often leaves multiple covariate adjustments plausible, yet which sets satisfy ignorability is untestable. Different adjustment sets can yield conflicting estimates of the average treatment…

Methodology · Statistics 2026-03-23 Aditya Ghosh , Dominik Rothenhäusler

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…

Methodology · Statistics 2026-03-10 Yang Liu , Jonathan P. Williams , Jan Hannig