Uncertainty quantification of the 4th kind; optimal posterior accuracy-uncertainty tradeoff with the minimum enclosing ball

Bajgiran, Hamed Hamze; Franch, Pau Batlle; Owhadi, Houman; Scovel, Clint; Shirdel, Mahdy; Stanley, Michael; Tavallali, Peyman

doi:10.1016/j.jcp.2022.111608

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…The method is based on taking a decision-theoretic view of the problem. As such, it falls under the emerging area of Decision-Theoretic Uncertainty Quantification (DTUQ; see, e.g., [21]). In this method, we regard the confidence interval for 𝜃 as a decision rule and optimize its expected width with respect to a prior distribution on 𝝀 among those rules that guarantee specified frequentist coverage.…”

Section: Jinst 17 P10013mentioning

confidence: 99%

Uncertainty quantification for wide-bin unfolding: one-at-a-time strict bounds and prior-optimized confidence intervals

2022

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Unfolding is an ill-posed inverse problem in particle physics aiming to infer a true particle-level spectrum from smeared detector-level data. For computational and practical reasons, these spaces are typically discretized using histograms, and the smearing is modeled through a response matrix corresponding to a discretized smearing kernel of the particle detector. This response matrix depends on the unknown shape of the true spectrum, leading to a fundamental systematic uncertainty in the unfolding problem. To handle the ill-posed nature of the problem, common approaches regularize the problem either directly via methods such as Tikhonov regularization, or implicitly by using wide-bins in the true space that match the resolution of the detector. Unfortunately, both of these methods lead to a non-trivial bias in the unfolded estimator, thereby hampering frequentist coverage guarantees for confidence intervals constructed from these methods. We propose two new approaches to addressing the bias in the wide-bin setting through methods called One-at-a-time Strict Bounds (OSB) and Prior-Optimized (PO) intervals. The OSB intervals are a bin-wise modification of an existing guaranteed-coverage procedure, while the PO intervals are based on a decision-theoretic view of the problem. Importantly, both approaches provide well-calibrated frequentist confidence intervals even in constrained and rank-deficient settings. These methods are built upon a more general answer to the wide-bin bias problem, involving unfolding with fine bins first, followed by constructing confidence intervals for linear functionals of the fine-bin counts. We test and compare these methods to other available methodologies in a wide-bin deconvolution example and a realistic particle physics simulation of unfolding a steeply falling particle spectrum.

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Section: Jinst 17 P10013mentioning

confidence: 99%

Uncertainty quantification for wide-bin unfolding: one-at-a-time strict bounds and prior-optimized confidence intervals

2022

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“…Those includes other methods with probabilistic predictions [Nix and Weigend 1994], making interval predictions [Koenker 2005; Angelopoulos and Bates 2021], assigning each prediction with a confidence score [Jumper et al 2021], as well as distance-based uncertainty [Sheridan et al 2004;Liu and Wallqvist 2018;Hirschfeld et al 2020]. More recently, a variant of Bayesian uncertainty quantification methods called uncertainty quantification of the 4th kind (UQ4K) [Bajgiran et al 2022] has been proposed to alleviate "brittleness of Bayesian inference", which is a phenomenon that Bayesian inference could be sensitive to the choice of prior [Owhadi et al 2015]. In UQ4K, the authors have developed UQ in the game theory framework.…”

Section: Uncertainty Quantificationmentioning

confidence: 99%

Artificial intelligence in recommender systems

Zhang

Jin

2020

Complex Intell. Syst.

237

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Recommender systems provide personalized service support to users by learning their previous behaviors and predicting their current preferences for particular products. Artificial intelligence (AI), particularly computational intelligence and machine learning methods and algorithms, has been naturally applied in the development of recommender systems to improve prediction accuracy and solve data sparsity and cold start problems. This position paper systematically discusses the basic methodologies and prevailing techniques in recommender systems and how AI can effectively improve the technological development and application of recommender systems. The paper not only reviews cutting-edge theoretical and practical contributions, but also identifies current research issues and indicates new research directions. It carefully surveys various issues related to recommender systems that use AI, and also reviews the improvements made to these systems through the use of such AI approaches as fuzzy techniques, transfer learning, genetic algorithms, evolutionary algorithms, neural networks and deep learning, and active learning. The observations in this paper will directly support researchers and professionals to better understand current developments and new directions in the field of recommender systems using AI.

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A review of uncertainty quantification and its applications in numerical simulation of scramjet combustor

Li¹,

Zhang²,

Zhang³

et al. 2023

International Journal of Thermofluids

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Uncertainty quantification of the 4th kind; optimal posterior accuracy-uncertainty tradeoff with the minimum enclosing ball

Cited by 3 publications

References 33 publications

Uncertainty quantification for wide-bin unfolding: one-at-a-time strict bounds and prior-optimized confidence intervals

Uncertainty quantification for wide-bin unfolding: one-at-a-time strict bounds and prior-optimized confidence intervals

Artificial intelligence in recommender systems

A review of uncertainty quantification and its applications in numerical simulation of scramjet combustor

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