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This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…

Statistics Theory · Mathematics 2023-01-03 Lang Liu , Zaid Harchaoui

In a sparse stochastic block model with two communities of unequal sizes we derive two posterior concentration inequalities, that imply (1) posterior (almost-)exact recovery of the community structure under sparsity bounds comparable to…

Statistics Theory · Mathematics 2021-08-17 B. J. K. Kleijn , J. van Waaij

There is considerable uncertainty about what properties, capabilities and motivations future AGIs will have. In some plausible scenarios, AGIs may pose security risks arising from accidents and defects. In order to mitigate these risks,…

Artificial Intelligence · Computer Science 2016-07-14 James Babcock , Janos Kramar , Roman Yampolskiy

The analysis of excursion sets in imaging data is essential to a wide range of scientific disciplines such as neuroimaging, climatology and cosmology. Despite growing literature, there is little published concerning the comparison of…

Methodology · Statistics 2022-01-11 Thomas Maullin-Sapey , Armin Schwartzman , Thomas E. Nichols

Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable…

What, if anything, should a frequentist say about a single realized confidence interval (CI) and its chance of having covered the parameter? Jerzy Neyman's original answer was to refuse any nondegenerate probability for coverage ex post…

Other Statistics · Statistics 2026-03-06 Scott Lee

Current concerns regarding the dependability of psychological findings call for methodological developments to provide additional evidence in support of scientific conclusions. This paper highlights the value and importance of two distinct…

Methodology · Statistics 2017-07-11 Jolynn Pek , Hao Wu

The domain of spare parts forecasting is examined, and is found to present unique uncertainty based problems in the architectural design of a knowledge-based system. A mixture of different uncertainty paradigms is required for the solution,…

Artificial Intelligence · Computer Science 2013-04-11 John B. Bacon

We study the problem of learning a high-density region of an arbitrary distribution over $\mathbb{R}^d$. Given a target coverage parameter $\delta$, and sample access to an arbitrary distribution $D$, we want to output a confidence set $S…

Data Structures and Algorithms · Computer Science 2025-05-14 Chao Gao , Liren Shan , Vaidehi Srinivas , Aravindan Vijayaraghavan

An impossibility theorem demonstrates that a particular problem or set of problems cannot be solved as described in the claim. Such theorems put limits on what is possible to do concerning artificial intelligence, especially the…

Artificial Intelligence · Computer Science 2023-06-19 Mario Brcic , Roman V. Yampolskiy

The fixed template Promise Constraint Satisfaction Problem (PCSP) is a recently proposed significant generalization of the fixed template CSP, which includes approximation variants of satisfiability and graph coloring problems. All the…

Computational Complexity · Computer Science 2019-09-12 Libor Barto

In this work, we investigate the reliability of the probabilistic binary forecast. We mathematically prove that a necessary, but not sufficient, condition for achieving a reliable probabilistic forecast is maximizing the Peirce skill score…

Space Physics · Physics 2019-05-20 Yûki Kubo

Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either…

Applications · Statistics 2018-08-20 Faranak Golestaneh , Pierre Pinson , Hoay Beng Gooi

We revisit the problem of constructing predictive confidence sets for which we wish to obtain some type of conditional validity. We provide new arguments showing how ``split conformal'' methods achieve near desired coverage levels with high…

Statistics Theory · Mathematics 2025-03-04 John C. Duchi

Requirements driven search-based testing (also known as falsification) has proven to be a practical and effective method for discovering erroneous behaviors in Cyber-Physical Systems. Despite the constant improvements on the performance and…

This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…

Methodology · Statistics 2022-12-02 Joel L. Horowitz , Sokbae Lee

For applications of machine learning in critical decisions, explainability is a primary concern, and often a regulatory requirement. Local linear methods for generating explanations, such as LIME and SHAP, have been criticized for being…

Machine Learning · Computer Science 2026-03-25 Joseph L. Breeden

The problem of existence of adaptive confidence bands for an unknown density $f$ that belongs to a nested scale of H\"{o}lder classes over $\mathbb{R}$ or $[0,1]$ is considered. Whereas honest adaptive inference in this problem is…

Statistics Theory · Mathematics 2012-02-24 Marc Hoffmann , Richard Nickl

We argue that formal certification of AI alignment over open-ended or unbounded input domains is impossible under standard assumptions in computational complexity and learning theory, and characterise what remains achievable. Two…

Machine Learning · Statistics 2026-05-28 Ayushi Agarwal

Counterfactual Explanations (CE) face several unresolved challenges, such as ensuring stability, synthesizing multiple CEs, and providing plausibility and sparsity guarantees. From a more practical point of view, recent studies [Pawelczyk…

Machine Learning · Statistics 2024-03-19 Salim I. Amoukou , Nicolas J. B Brunel