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Based on the auxiliary subspace techniques, a hierarchical basis a posteriori error estimator is proposed for the Stokes problem in two and three dimensions. For the error estimator, we need to solve only two global diagonal linear systems…

Numerical Analysis · Mathematics 2023-03-22 Jiachuan Zhang , Ran Zhang , Xiaoshen Wang

Click-Through Rate (CTR) prediction models are integral to a myriad of industrial settings, such as personalized search advertising. Current methods typically involve feature extraction from users' historical behavior sequences combined…

Machine Learning · Computer Science 2025-07-16 Lingwei Kong , Lu Wang , Changping Peng , Zhangang Lin , Ching Law , Jingping Shao

Calibration requires predictor outputs to be consistent with their Bayesian posteriors. For machine learning predictors that do not distinguish between small perturbations, calibration errors are continuous in predictions, e.g., smooth…

Machine Learning · Computer Science 2025-04-23 Jason Hartline , Yifan Wu , Yunran Yang

We propose a second-order time to collision (TTC) considering non-static acceleration and turning with realistic assumptions. This is equivalent to considering that the steering wheel is held at a fixed angle with constant pressure on the…

Optimization and Control · Mathematics 2025-02-13 Hossein Nick Zinat Matin , Yuneil Yeo , Amelie Ju-Kang Ngo , Antonio R. Paiva , Jean Utke , Maria Laura Delle Monache

Learning-to-Rank (LTR) is a supervised machine learning approach that constructs models specifically designed to order a set of items or documents based on their relevance or importance to a given query or context. Despite significant…

Information Retrieval · Computer Science 2026-04-17 Camilo Gomez , Pengyang Wang , Yanjie Fu

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…

Machine Learning · Computer Science 2023-12-05 Yusuf Sale , Viktor Bengs , Michele Caprio , Eyke Hüllermeier

Discovery of an accurate causal Bayesian network structure from observational data can be useful in many areas of science. Often the discoveries are made under uncertainty, which can be expressed as probabilities. To guide the use of such…

Artificial Intelligence · Computer Science 2017-12-27 Fattaneh Jabbari , Mahdi Pakdaman Naeini , Gregory F. Cooper

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…

Machine Learning · Computer Science 2021-06-15 Meet P. Vadera , Soumya Ghosh , Kenney Ng , Benjamin M. Marlin

Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…

Methodology · Statistics 2025-11-21 Garritt L. Page , Andrés F. Barrientos , David B. Dahl , David B. Dunson

Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…

Quantum Physics · Physics 2021-09-22 Samuel P. Nolan , Augusto Smerzi , Luca Pezzè

Transfer learning assumes classifiers of similar tasks share certain parameter structures. Unfortunately, modern classifiers uses sophisticated feature representations with huge parameter spaces which lead to costly transfer. Under the…

Machine Learning · Statistics 2015-10-20 Song Liu , Kenji Fukumizu

The Click-Through Rate (CTR) prediction task is critical in industrial recommender systems, where models are usually deployed on dynamic streaming data in practical applications. Such streaming data in real-world recommender systems face…

Information Retrieval · Computer Science 2023-07-17 Qi-Wei Wang , Hongyu Lu , Yu Chen , Da-Wei Zhou , De-Chuan Zhan , Ming Chen , Han-Jia Ye

We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…

Statistics Theory · Mathematics 2021-02-12 Qiyang Han

Computer model calibration is a crucial step in building a reliable computer model. In the face of massive physical observations, a fast estimation for the calibration parameters is urgently needed. To alleviate the computational burden, we…

Statistics Theory · Mathematics 2022-11-24 Shurui Lv , Yan Wang , Jun Yu

It is now well known that neural networks can be wrong with high confidence in their predictions, leading to poor calibration. The most common post-hoc approach to compensate for this is to perform temperature scaling, which adjusts the…

Computer Vision and Pattern Recognition · Computer Science 2022-07-25 Tom Joy , Francesco Pinto , Ser-Nam Lim , Philip H. S. Torr , Puneet K. Dokania

A stochastic second-order trust region method is proposed, which can be viewed as a second-order extension of the trust-region-ish (TRish) algorithm proposed by Curtis et al. (INFORMS J. Optim. 1(3) 200-220, 2019). In each iteration, a…

Optimization and Control · Mathematics 2019-11-19 Frank E. Curtis , Rui Shi

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Methodology · Statistics 2018-02-14 Daniela Calvetti , Matthew M. Dunlop , Erkki Somersalo , Andrew M. Stuart

Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these…

Methodology · Statistics 2026-03-23 Tiffany Cai , Philip Greengard , Ben Goodrich , Andrew Gelman

In the e-commerce advertising scenario, estimating the true probabilities (known as a calibrated estimate) on Click-Through Rate (CTR) and Conversion Rate (CVR) is critical. Previous research has introduced numerous solutions for addressing…

Machine Learning · Computer Science 2024-05-22 Shuai Yang , Hao Yang , Zhuang Zou , Linhe Xu , Shuo Yuan , Yifan Zeng

An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics:…

Numerical Analysis · Mathematics 2019-11-06 L. M. M. van den Bos , B. Sanderse , W. A. A. M. Bierbooms , G. J. W. van Bussel