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Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…

最优化与控制 · 数学 2025-03-18 Zahra Mehraban , Alois Pichler

Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…

机器学习 · 计算机科学 2022-09-30 Satya Borgohain , Klaus Ackermann , Ruben Loaiza-Maya

The assessment of binary classifier performance traditionally centers on discriminative ability using metrics, such as accuracy. However, these metrics often disregard the model's inherent uncertainty, especially when dealing with sensitive…

机器学习 · 计算机科学 2024-02-13 Agathe Fernandes Machado , Arthur Charpentier , Emmanuel Flachaire , Ewen Gallic , François Hu

Data classification without access to labeled samples remains a challenging problem. It usually depends on an appropriately chosen distance between features, a topic addressed in metric learning. Recently, Huizing, Cantini and Peyr\'e…

最优化与控制 · 数学 2025-07-18 Janis Auffenberg , Jonas Bresch , Oleh Melnyk , Gabriele Steidl

We present new algorithms for estimating and testing \emph{collision probability}, a fundamental measure of the spread of a discrete distribution that is widely used in many scientific fields. We describe an algorithm that satisfies…

机器学习 · 统计学 2025-04-21 Robert Busa-Fekete , Umar Syed

The design of high-precision sensing devises becomes ever more difficult and expensive. At the same time, the need for precise calibration of these devices (ranging from tiny sensors to space telescopes) manifests itself as a major…

信息论 · 计算机科学 2015-10-28 Shuyang Ling , Thomas Strohmer

Deep neural networks often produce overconfident predictions, undermining their reliability in safety-critical applications. This miscalibration is further exacerbated under distribution shift, where test data deviates from the training…

计算机视觉与模式识别 · 计算机科学 2025-08-28 Yilin Zhang , Cai Xu , You Wu , Ziyu Guan , Wei Zhao

We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have…

机器学习 · 计算机科学 2024-12-30 Gustaf Ahdritz , Aravind Gollakota , Parikshit Gopalan , Charlotte Peale , Udi Wieder

We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…

数据结构与算法 · 计算机科学 2025-12-10 Gunjan Kumar , Yash Pote , Jonathan Scarlett

We provide approximation algorithms for two problems, known as NECKLACE SPLITTING and $\epsilon$-CONSENSUS SPLITTING. In the problem $\epsilon$-CONSENSUS SPLITTING, there are $n$ non-atomic probability measures on the interval $[0, 1]$ and…

数据结构与算法 · 计算机科学 2020-07-01 Noga Alon , Andrei Graur

We initiate the study of the truthfulness of calibration measures in sequential prediction. A calibration measure is said to be truthful if the forecaster (approximately) minimizes the expected penalty by predicting the conditional…

机器学习 · 计算机科学 2024-11-22 Nika Haghtalab , Mingda Qiao , Kunhe Yang , Eric Zhao

Estimating frequencies of certain items among a population is a basic step in data analytics, which enables more advanced data analytics (e.g., heavy hitter identification, frequent pattern mining), client software optimization, and…

密码学与安全 · 计算机科学 2018-12-12 Jinyuan Jia , Neil Zhenqiang Gong

A striking result of [Acharya et al. 2017] showed that to estimate symmetric properties of discrete distributions, plugging in the distribution that maximizes the likelihood of observed multiset of frequencies, also known as the profile…

统计理论 · 数学 2020-11-03 Yanjun Han , Kirankumar Shiragur

A reliable deep learning system should be able to accurately express its confidence with respect to its predictions, a quality known as calibration. One of the most effective ways to produce reliable confidence estimates with a pre-trained…

机器学习 · 计算机科学 2024-10-10 Thomas P. Zollo , Zhun Deng , Jake C. Snell , Toniann Pitassi , Richard Zemel

This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…

统计方法学 · 统计学 2015-09-14 Raymond K. W. Wong , Curtis B. Storlie , Thomas C. M. Lee

We consider the problem of linear regression with self-selection bias in the unknown-index setting, as introduced in recent work by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [STOC 2023]. In this model, one observes $m$ i.i.d.…

统计理论 · 数学 2024-02-23 Jason Gaitonde , Elchanan Mossel

In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…

机器学习 · 计算机科学 2024-08-08 Agathe Fernandes Machado , Arthur Charpentier , Emmanuel Flachaire , Ewen Gallic , François Hu

How to estimate the uncertainty of a given model is a crucial problem. Current calibration techniques treat different classes equally and thus implicitly assume that the distribution of training data is balanced, but ignore the fact that…

计算机视觉与模式识别 · 计算机科学 2023-04-14 Jiahao Chen , Bing Su

We study the problem of approximating the total variation distance between two mixtures of product distributions over an $n$-dimensional discrete domain. Given two mixtures $\mathbb{P}$ and $\mathbb{Q}$ with $k_1$ and $k_2$ product…

数据结构与算法 · 计算机科学 2026-05-06 Weiming Feng , Yucheng Fu , Minji Yang , Anqi Zhang

A set of probabilistic predictions is well calibrated if the events that are predicted to occur with probability p do in fact occur about p fraction of the time. Well calibrated predictions are particularly important when machine learning…

机器学习 · 统计学 2014-01-14 Mahdi Pakdaman Naeini , Gregory F. Cooper , Milos Hauskrecht
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