Estimating the area under a receiver operating characteristic curve using partially ordered sets

AbstractRanked set sampling (RSS), known as a cost-effective sampling technique, requires that the ranker gives a complete ranking of the units in each set. Frey (2012) proposed a modification of RSS based on partially ordered sets, referred to as RSS-t in this paper, to allow the ranker to declare ties as much as he/she wishes. We consider the problem of estimating the area under a receiver operating characteristics (ROC) curve using RSS-t samples. The area under the ROC curve (AUC) is commonly used as a measure for the effectiveness of diagnostic markers. We develop six nonparametric estimators of the AUC with/without utilizing tie information based on different approaches. We then compare the estimators using a Monte Carlo simulation and an empirical study with real data from the National Health and Nutrition Examination Survey. The results show that utilizing tie information increases the efficiency of estimating the AUC. Suggestions about when to choose which estimator are also made available to practitioners.

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A DISCRETIZATION METHOD BASED ON MAXIMIZING THE AREA UNDER RECEIVER OPERATING CHARACTERISTIC CURVE

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s021800141350002x ◽

2013 ◽

Vol 27 (01) ◽

pp. 1350002 ◽

Cited By ~ 11

Author(s):

MURAT KURTCEPHE ◽

H. ALTAY GÜVENIR

Keyword(s):

Roc Curve ◽

Naive Bayes ◽

Characteristic Curve ◽

Naïve Bayes ◽

Machine Learning Algorithms ◽

Discretization Method ◽

Operating Characteristics ◽

Discretization Methods ◽

Real World Datasets ◽

Receiver Operating

Many machine learning algorithms require the features to be categorical. Hence, they require all numeric-valued data to be discretized into intervals. In this paper, we present a new discretization method based on the receiver operating characteristics (ROC) Curve (AUC) measure. Maximum area under ROC curve-based discretization (MAD) is a global, static and supervised discretization method. MAD uses the sorted order of the continuous values of a feature and discretizes the feature in such a way that the AUC based on that feature is to be maximized. The proposed method is compared with alternative discretization methods such as ChiMerge, Entropy-Minimum Description Length Principle (MDLP), Fixed Frequency Discretization (FFD), and Proportional Discretization (PD). FFD and PD have been recently proposed and are designed for Naïve Bayes learning. ChiMerge is a merging discretization method as the MAD method. Evaluations are performed in terms of M-Measure, an AUC-based metric for multi-class classification, and accuracy values obtained from Naïve Bayes and Aggregating One-Dependence Estimators (AODE) algorithms by using real-world datasets. Empirical results show that MAD is a strong candidate to be a good alternative to other discretization methods.

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To the spectral theory of partially ordered sets

Sibirskii matematicheskii zhurnal ◽

10.33048/smzh.2019.60.308 ◽

2018 ◽

Vol 60 (3) ◽

pp. 578-598

Author(s):

Yu. L. Ershov ◽

M. V. Schwidefsky

Keyword(s):

Spectral Theory ◽

Partially Ordered Sets ◽

Ordered Sets ◽

Partially Ordered

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Modelling Nondeterministic Concurrent Processes with Event Structures

Fundamenta Informaticae ◽

10.3233/fi-1991-14103 ◽

1991 ◽

Vol 14 (1) ◽

pp. 39-73

Author(s):

Rita Loogen ◽

Ursula Goltz

Keyword(s):

Dynamic Behaviour ◽

Partially Ordered Sets ◽

Parallel Composition ◽

Ordered Sets ◽

Communicating Sequential Processes ◽

Partially Ordered ◽

Event Structures ◽

Transition Relation ◽

Concurrent Processes ◽

Sequential Processes

We present a non-interleaving model for non deterministic concurrent processes that is based on labelled event structures. We define operators on labelled event structures like parallel composition, nondeterministic combination, choice, prefixing and hiding. These operators correspond to the operations of the “Theory of Communicating Sequential Processes” (TCSP). Infinite processes are defined using the metric approach. The dynamic behaviour of event structures is defined by a transition relation which describes the execution of partially ordered sets of actions, abstracting from internal events.

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