Selected group-theoretic aspects of confirmation measure symmetries

Susmaga, Robert; Szczęch, Izabela

doi:10.1016/j.ins.2016.01.041

Cited by 6 publications

(2 citation statements)

References 11 publications

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“…• properties of symmetry being a whole set of properties that describe desirable and undesirable behaviour of measures in cases when the premise or conclusion in not satisfied, or when the premise and conclusion switch positions in a rule [6,8,16,34].…”

Section: Related Work On Confirmation Measures and Their Propertiesmentioning

confidence: 99%

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

Susmaga

Szczęch

2018

Foundations of Computing and Decision Sciences

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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.

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Section: Related Work On Confirmation Measures and Their Propertiesmentioning

confidence: 99%

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

Susmaga

Szczęch

2018

Foundations of Computing and Decision Sciences

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“…It is uncertain whether N can be ruled out by this requirement [ 15 ]. See [ 14 , 25 , 26 ] for more discussions about the symmetry/asymmetry requirement.…”

Section: Introductionmentioning

confidence: 99%

Channels’ Confirmation and Predictions’ Confirmation: From the Medical Test to the Raven Paradox

2020

Entropy

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After long arguments between positivism and falsificationism, the verification of universal hypotheses was replaced with the confirmation of uncertain major premises. Unfortunately, Hemple discovered the Raven Paradox (RP). Then, Carnap used the logical probability increment as the confirmation measure. So far, many confirmation measures have been proposed. Measure F among them proposed by Kemeny and Oppenheim possesses symmetries and asymmetries proposed by Elles and Fitelson, monotonicity proposed by Greco et al., and normalizing property suggested by many researchers. Based on the semantic information theory, a measure b* similar to F is derived from the medical test. Like the likelihood ratio, b* and F can only indicate the quality of channels or the testing means instead of the quality of probability predictions. And, it is still not easy to use b*, F, or another measure to clarify the RP. For this reason, measure c* similar to the correct rate is derived. The c* has the simple form: (a-c)/max(a, c); it supports the Nicod Criterion and undermines the Equivalence Condition, and hence, can be used to eliminate the RP. Some examples are provided to show why it is difficult to use one of popular confirmation measures to eliminate the RP. Measure F, b*, and c* indicate that fewer counterexamples' existence is more essential than more positive examples' existence, and hence, are compatible with Popper's falsification thought.Graphical Abstract:

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