Measures of rule interestingness in various perspectives of confirmation

Abstract

Confirmation is a useful concept for assessing the impact of the premise on the conclusion of a rule induced from data. Interpretation of probabilistic relationships between premise and conclusion of a rule led to four mathematical formulations of confirmation, called perspectives. The logical equivalence of these perspectives and the resulting general definition of confirmation underline the known qualitative aspect of the concept of confirmation. The quantitative aspect of confirmation is handled by definitions of particular confirmation measures. In this paper, we relate the qualitative and quantitative aspects by introducing a property of monotonicity of measures with respect to left-and right-hand side probabilities defining the perspectives. This new property permits consideration of confirmation measures in association with particular perspectives. We also identify several other properties that valuable confirmation measures should possess. A particular care is devoted to discussion of behavior of confirmation measures monotonic in different perspectives with respect to symmetry properties, taking also into account two new perspectives of Bayesian confirmation. We also prove that confirmation measures monotonic in the six perspectives are exhaustive in the sense that their set is closed under transformations related to symmetry properties. Finally, we verify which confirmation measures enjoy these properties.

GuideR: A guided separate-and-conquer rule learning in classification, regression, and survival settings

“…After that, if Σ auto flag is enabled, the algorithm adds automatically induced conditions using standard separate-and-conquer strategy (lines 6-9). When all initial rules have been processed, new ones are generated analogously; the corresponding boolean parameters are called Υ pref and Υ auto (lines [11][12][13][14][15][16][17][18][19][20].…”

“…The former leads to a very large number of rules which must then be limited by filtering according to rule interestingness measures [16,17,18]. Nevertheless, rule sets obtained by subgroup discovery are characterized by worse predictive abilities than those generated by the standard sequential covering approach.…”

“…At each step, a condition rendering the rule of highest quality is selected (lines 6-8). After that, preferred attributes are processed similarly (lines[14][15][16][17][18][19][20][21][22][23][24]. For each preferred attribute, a condition leading to the rule of highest quality is considered (line 17:InduceBestCondition function call).…”

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

“…• 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].…”

Review of Rule Quality Measurement: Metrics and Rule Evaluation Models

“…These four confirmations are each measurement method for measuring the monotony of rules in 4 different perspectives. Together with several measurements made in previous research, researchers explored the monotony and symmetry properties of the metrics [17].…”