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This somewhat unusual proof for the fact that the reals are uncountable, which is adapted from one of Bourbaki's proofs in "Fonctions d'une variable reelle", may be of some interest.

历史与综述 · 数学 2009-01-06 Eliahu Levy

In this paper, we gain the new almost unbiased Liu-type estimators to literature for the Bell regression model. We provide the superiority of the proposed estimator to its competitors such as the maximum likelihood estimator and Liu-type…

统计理论 · 数学 2025-09-23 Caner Tanış , Yasin Asar

In the persuasion model, apart from a few special cases, comparative statics has been an open question. We answer it, delineating which shifts of the sender's interim payoff lead her optimally to choose a more informative signal. Our first…

理论经济学 · 经济学 2025-11-26 Gregorio Curello , Ludvig Sinander

All priors are not created equal. There are right and there are wrong priors. That is the main conclusion of this contribution. I use, a cooked-up example designed to create drama, and a typical textbook example to show the pervasiveness of…

数据分析、统计与概率 · 物理学 2009-11-13 Carlos C. Rodriguez

Agents, some with a bias, decide between undertaking a risky project and a safe alternative based on information about the project's efficiency. Only a part of that information is verifiable. Unbiased agents want to undertake only efficient…

综合经济学 · 经济学 2023-05-12 Aditya Kuvalekar , João Ramos , Johannes Schneider

Work in Counterfactual Explanations tends to focus on the principle of "the closest possible world" that identifies small changes leading to the desired outcome. In this paper we argue that while this approach might initially seem…

机器学习 · 计算机科学 2020-02-25 Rafael Poyiadzi , Kacper Sokol , Raul Santos-Rodriguez , Tijl De Bie , Peter Flach

The recent success of machine learning models, especially large-scale classifiers and language models, relies heavily on training with massive data. These data are often collected from online sources. This raises serious concerns about the…

人工智能 · 计算机科学 2025-11-12 Ruihan Zhang , Jun Sun , Ee-Peng Lim , Peixin Zhang

Training large-scale mixture of experts models efficiently on modern hardware requires assigning datapoints in a batch to different experts, each with a limited capacity. Recently proposed assignment procedures lack a probabilistic…

机器学习 · 计算机科学 2021-12-09 Wouter Kool , Chris J. Maddison , Andriy Mnih

Counterfactual instances are a powerful tool to obtain valuable insights into automated decision processes, describing the necessary minimal changes in the input space to alter the prediction towards a desired target. Most previous…

机器学习 · 计算机科学 2021-06-07 Robert-Florian Samoilescu , Arnaud Van Looveren , Janis Klaise

We study how a decision-maker can acquire more information from an agent by reducing her own ability to observe what the agent transmits. In a large class of binary-action games, opacity design is just as good as full commitment to actions…

理论经济学 · 经济学 2024-02-07 Mark Whitmeyer

Counterfactual inference considers a hypothetical intervention in a parallel world that shares some evidence with the factual world. If the evidence specifies a conditional distribution on a manifold, counterfactuals may be analytically…

机器学习 · 统计学 2024-07-03 Juha Karvanen , Santtu Tikka , Matti Vihola

Counterfactual explanations provide a potentially significant solution to the Explainable AI (XAI) problem, but good, native counterfactuals have been shown to rarely occur in most datasets. Hence, the most popular methods generate…

人工智能 · 计算机科学 2021-01-25 Barry Smyth , Mark T Keane

Familiar statistical tests and estimates are obtained by the direct observation of cases of interest: a clinical trial of a new drug, for instance, will compare the drug's effects on a relevant set of patients and controls. Sometimes,…

统计方法学 · 统计学 2010-12-09 Bradley Efron

We derive a family of $L^p$ estimates of the X-Ray transform of positive measures in $\mathbb R^d$, which we use to construct a $\log R$-loss counterexample to the Mizohata-Takeuchi conjecture for every $C^2$ hypersurface in $\mathbb R^d$…

经典分析与常微分方程 · 数学 2025-03-13 Hannah Cairo

In empirical research, when we have multiple estimators for the same parameter of interest, a central question arises: how do we combine unbiased but less precise estimators with biased but more precise ones to improve the inference? Under…

统计方法学 · 统计学 2026-02-19 Zhexiao Lin , Peter J. Bickel , Peng Ding

Vision-language models can encode societal biases and stereotypes, but there are challenges to measuring and mitigating these multimodal harms due to lacking measurement robustness and feature degradation. To address these challenges, we…

The increasing application of Artificial Intelligence and Machine Learning models poses potential risks of unfair behavior and, in light of recent regulations, has attracted the attention of the research community. Several researchers…

We argue that the words "objectivity" and "subjectivity" in statistics discourse are used in a mostly unhelpful way, and we propose to replace each of them with broader collections of attributes, with objectivity replaced by transparency,…

其他统计学 · 统计学 2015-08-25 Andrew Gelman , Christian Hennig

Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that…

其他统计学 · 统计学 2022-02-08 Rose D Baker

The ability of autonomous systems to provide explanations is important for supporting transparency and aiding the development of (appropriate) trust. Prior work has defined a mechanism for Belief-Desire-Intention (BDI) agents to be able to…

人工智能 · 计算机科学 2026-02-17 Michael Winikoff
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