Asymmetry Degree as a Tool for Comparing Interestingness Measures in Decision Making: The Case of Bayesian Confirmation Measures

2018 ◽  
pp. 289-298 ◽  
Author(s):  
Emilio Celotto ◽  
Andrea Ellero ◽  
Paola Ferretti
Keyword(s):  
Decision Making ◽  
Interestingness Measures ◽  
Bayesian Confirmation ◽  
Confirmation Measures

scholarly journals Can Confirmation Measures Reflect Statistically Sound Dependencies in Data? The Concordance-based Assessment

2018 ◽  
Vol 43 (1) ◽  
pp. 41-66 ◽  
Author(s):  
Robert Susmaga ◽  
Izabela Szczęch
Keyword(s):  
Interestingness Measures ◽  
Bayesian Confirmation ◽  
Confirmation Measures ◽  
Scatter Plots ◽  
Level Of Agreement

Abstract The paper considers particular interestingness measures, called confirmation measures (also known as Bayesian confirmation measures), used for the evaluation of “if evidence, then hypothesis” rules. The agreement of such measures with a statistically sound (significant) dependency between the evidence and the hypothesis in data is thoroughly investigated. The popular confirmation measures were not defined to possess such form of agreement. However, in error-prone environments, potential lack of agreement may lead to undesired effects, e.g. when a measure indicates either strong confirmation or strong disconfirmation, while in fact there is only weak dependency between the evidence and the hypothesis. In order to detect and prevent such situations, the paper employs a coefficient allowing to assess the level of dependency between the evidence and the hypothesis in data, and introduces a method of quantifying the level of agreement (referred to as a concordance) between this coefficient and the measure being analysed. The concordance is characterized and visualised using specialized histograms, scatter-plots, etc. Moreover, risk-related interpretations of the concordance are introduced. Using a set of 12 confirmation measures, the paper presents experiments designed to establish the actual concordance as well as other useful characteristics of the measures.

Finding Meaningful Bayesian Confirmation Measures

2013 ◽  
Vol 127 (1-4) ◽  
pp. 161-176 ◽  
Author(s):  
Salvatore Greco ◽  
Roman Słowiński ◽  
Izabela Szczęch
Keyword(s):  
Bayesian Confirmation ◽  
Confirmation Measures

scholarly journals Can interestingness measures be usefully visualized?

2015 ◽  
Vol 25 (2) ◽  
pp. 323-336 ◽  
Author(s):  
Robert Susmaga ◽  
Izabela Szczęch
Keyword(s):  
Wide Spectrum ◽  
Scalar Function ◽  
Three Dimensions ◽  
Interestingness Measures ◽  
Single Measure ◽  
Confirmation Measures ◽  
Common Domain ◽  
Selection For ◽  
Visualization Techniques

Abstract The paper presents visualization techniques for interestingness measures. The process of measure visualization provides useful insights into different domain areas of the visualized measures and thus effectively assists their comprehension and selection for different knowledge discovery tasks. Assuming a common domain form of the visualized measures, a set of contingency tables, which consists of all possible tables having the same total number of observations, is constructed. These originally four-dimensional data may be effectively represented in three dimensions using a tetrahedron-based barycentric coordinate system. At the same time, an additional, scalar function of the data (referred to as the operational function, e.g., any interestingness measure) may be rendered using colour. Throughout the paper a particular group of interestingness measures, known as confirmation measures, is used to demonstrate the capabilities of the visualization techniques. They cover a wide spectrum of possibilities, ranging from the determination of specific values (extremes, zeros, etc.) of a single measure, to the localization of pre-defined regions of interest, e.g., such domain areas for which two or more measures do not differ at all or differ the most.

scholarly journals Coherence and Reduction

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andrea Giuseppe Ragno
Keyword(s):  
Statistical Mechanics ◽  
Confirmation Theory ◽  
Bayesian Confirmation Theory ◽  
Numerical Examples ◽  
Bayesian Confirmation ◽  
Degree Of Coherence ◽  
Confirmation Measures ◽  
Before And After ◽  
Important Field ◽  
Scientific Reduction

Abstract Synchronic intertheoretic reductions are an important field of research in science. Arguably, the best model able to represent the main relations occurring in this kind of scientific reduction is the Nagelian account of reduction, a model further developed by Schaffner and nowadays known as the generalized version of the Nagel–Schaffner model (GNS). In their article (2010), Dizadji-Bahmani, Frigg, and Hartmann (DFH) specified the two main desiderata of a reduction á la GNS: confirmation and coherence. DFH first and, more rigorously, Tešic (2017) later analyse the confirmatory relation between the reducing and the reduced theory in terms of Bayesian confirmation theory. The purpose of this article is to analyse and compare the degree of coherence between the two theories involved in the GNS before and after the reduction. For this reason, in the first section, I will be looking at the reduction of thermodynamics to statistical mechanics and use it as an example to describe the GNS. In the second section, I will introduce three coherence measures which will then be employed in the comparison. Finally, in the last two sections, I will compare the degrees of coherence between the reducing and the reduced theory before and after the reduction and use a few numerical examples to understand the relation between coherence and confirmation measures.

scholarly journals Parameterized rough set model using rough membership and Bayesian confirmation measures

2008 ◽  
Vol 49 (2) ◽  
pp. 285-300 ◽  
Author(s):  
Salvatore Greco ◽  
Benedetto Matarazzo ◽  
Roman Słowiński
Keyword(s):  
Rough Set ◽  
Bayesian Confirmation ◽  
Confirmation Measures
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