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In this paper we study the category LCA(2) of certain non-locally compact abelian topological groups, and extend the notion of Weil index. As applications we deduce some product formulas for curves over local fields and arithmetic surfaces.

Representation Theory · Mathematics 2017-08-31 Dongwen Liu , Yongchang Zhu

While the area under the ROC curve is perhaps the most common measure that is used to rank the relative performance of different binary classifiers, longstanding field folklore has noted that it can be a measure that ill-captures the…

Machine Learning · Computer Science 2024-12-19 Christopher Ratigan , Lenore Cowen

In this paper, we show the arc length of the optimal ROC curve is an $f$-divergence. By leveraging this result, we express the arc length using a variational objective and estimate it accurately using positive and negative samples. We show…

Statistics Theory · Mathematics 2022-10-19 Song Liu

Diagnostic tests are of critical importance in health care and medical research. Motivated by the impact that atypical and outlying test outcomes might have on the assessment of the discriminatory ability of a diagnostic test, we develop a…

Assessment of risk prediction models has primarily utilized measures of discrimination, the ROC curve AUC and C-statistic. These derive from the risk distributions of patients and nonpatients, which in turn are derived from a population…

Quantitative Methods · Quantitative Biology 2023-12-05 Ralph H. Stern

We propose a novel classifier accuracy metric: the Bayesian Area Under the Receiver Operating Characteristic Curve (CBAUC). The method estimates the area under the ROC curve and is related to the recently proposed Bayesian Error Estimator.…

Machine Learning · Computer Science 2019-08-26 Syeda Sakira Hassan , Heikki Huttunen , Jari Niemi , Jussi Tohka

Receiver Operating Characteristic (ROC) curves are plots of true positive rate versus false positive rate which are used to evaluate binary classification algorithms. Because the Area Under the Curve (AUC) is a constant function of the…

Machine Learning · Computer Science 2023-02-23 Kyle R. Rust , Toby D. Hocking

Receiver Operating Characteristic (ROC) curves are plots of true positive rate versus false positive rate which are useful for evaluating binary classification models, but difficult to use for learning since the Area Under the Curve (AUC)…

Machine Learning · Statistics 2021-07-06 Jonathan Hillman , Toby Dylan Hocking

In analysis of binary outcomes, the receiver operator characteristic (ROC) curve is heavily used to show the performance of a model or algorithm. The ROC curve is informative about the performance over a series of thresholds and can be…

Computation · Statistics 2020-08-10 John Muschelli

For independent $X$ and $Y$ in the inequality $P(X\leq Y+\mu)$, we give sharp lower bounds for unimodal distributions having finite variance, and sharp upper bounds assuming symmetric densities bounded by a finite constant. The lower bounds…

Probability · Mathematics 2009-03-04 Eric Clarkson , J. L. Denny , Larry Shepp

Purpose: To determine whether deep learning models can distinguish between breast cancer molecular subtypes based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). Materials and methods: In this institutional review…

Computer Vision and Pattern Recognition · Computer Science 2017-12-01 Zhe Zhu , Ehab Albadawy , Ashirbani Saha , Jun Zhang , Michael R. Harowicz , Maciej A. Mazurowski

In medical research, continuous markers are widely employed in diagnostic tests to distinguish diseased and non-diseased subjects. The accuracy of such diagnostic tests is commonly assessed using the receiver operating characteristic (ROC)…

Applications · Statistics 2014-02-11 Tu Xu , Junhui Wang , Yixin Fang

The accuracy of a diagnostic test is typically characterised using the receiver operating characteristic (ROC) curve. Summarising indexes such as the area under the ROC curve (AUC) are used to compare different tests as well as to measure…

Methodology · Statistics 2010-12-30 Fang Yao , Radu V. Craiu , Benjamin Reiser

A precise assessment of the risk of breast lesions can greatly lower it and assist physicians in choosing the best course of action. To categorise breast lesions, the majority of current computer-aided systems only use characteristics from…

Image and Video Processing · Electrical Eng. & Systems 2025-08-25 Muhaisin Tiyumba Nantogmah , Abdul-Barik Alhassan , Salamudeen Alhassan

Breast cancer cell lines are indispensable tools for unraveling disease mechanisms, enabling drug discovery, and developing personalized treatments, yet their heterogeneity and inconsistent classification pose significant challenges in…

The area under the ROC curve (AUC) is the standard measure of a biomarker's discriminatory accuracy; however, naive AUC estimates can be misleading when validation cohorts differ from the intended target population. Such covariate shifts…

Methodology · Statistics 2025-11-20 Jiajun Liu , Guangcai Mao , Xiaofei Wang

The proper use of model evaluation metrics is important for model evaluation and model selection in binary classification tasks. This study investigates how consistent different metrics are at evaluating models across data of different…

Machine Learning · Statistics 2024-12-17 Jing Li

The ROC curve is the gold standard for measuring the performance of a test/scoring statistic regarding its capacity to discriminate between two statistical populations in a wide variety of applications, ranging from anomaly detection in…

Statistics Theory · Mathematics 2023-01-25 Stéphan Clémençon , Myrto Limnios , Nicolas Vayatis

Classification performance is often not uniform over the data. Some areas in the input space are easier to classify than others. Features that hold information about the "difficulty" of the data may be non-discriminative and are therefore…

Machine Learning · Computer Science 2016-05-24 Oran Richman , Shie Mannor

Microscopic examination of slides prepared from tissue samples is the primary tool for detecting and classifying cancerous lesions, a process that is time-consuming and requires the expertise of experienced pathologists. Recent advances in…

Computer Vision and Pattern Recognition · Computer Science 2024-10-15 Saba Fatema , Brighton Nuwagira , Sayoni Chakraborty , Reyhan Gedik , Baris Coskunuzer