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https://en.wikipedia.org/wiki/Association_rule_learning
Although the size of the power-set grows exponentially in the number of items in , efficient search is possible using the downward-closure property of support (also called anti-monotonicity) which guarantees that for a frequent itemset, all its subsets are also frequent and thus no infrequent itemset can be a subset of a frequent itemset.
http://www.cs.put.poznan.pl/iszczech/publications/HCP08_SGS_cameraready.pdf
Anti-support of a rule φ→ψ (also simply referred to as anti-support), denoted as anti-sup (φ→ψ), is equal to the number of objects in U having property φ but not having property ψ. Thus, anti–support is the number of counter-examples, i.e. objects for which the premise φ evaluates to true, but which miss the property ψ.
https://www.chegg.com/homework-help/questions-and-answers/explain-anti-monotone-property-support-measure-incorporate-property-directly-mining-algori-q22658503
a) Explain what is the anti-monotone property of the support measure and how you can incorporate this property directly into the mining algorithm to effectively prune the exponential search space of candidate itemsets.. b) Unlike the support measure, confidence does not have any monotone property. Please explain how does confidence-based pruning work and provide a proof why it works.
http://www.cs.put.poznan.pl/iszczech/publications/kkntpd_GSS_2007_prezent.pdf
Support and Confirmation or Support and Anti-Support (EAAI Journal, 2007) 18 must reside on the support - anti-support Pareto optimal border n The support – anti-support Pareto border is a set of non-dominated rules with respect to those measures, i.e. the set of rules for which there is no other rule with greater support and smaller anti-support
http://web.cs.ucla.edu/~yzsun/classes/2013Spring_CS6220/slides/07FPAdvanced.pdf
Pattern Space Pruning with Anti-Monotonicity Constraints •A constraint C is anti-monotone if the super pattern satisfies C, all of its sub-patterns do so too •In other words, anti-monotonicity: If an itemset S violates the constraint, so does any of its superset •Ex. 1. sum(S.price) v is anti-monotone
http://www.cs.uu.nl/groups/ADA/pubs/2004/monotone_constraints_in_frequent_tree_mining-deknijf,feelders.pdf
Examples of anti-monotone constraints are: minimum frequency, sum(t) constant(for positive values of thenodeattributesoft), size(t) constant. Themin-imum frequency constraint is already incorporated in structured data mining algorithms, hence other con-straints which have the anti-monotonicity property can be incorporated in the same way.
http://staffwww.itn.liu.se/~aidvi/courses/06/dm/lectures/lec7.pdf
Apriori Algorithm TNM033: Introduction to Data Mining 1 ... zApriori principle holds due to the following property of the support measure: – Support of an itemset never exceeds the support of its subsets – This is known as the anti-monotone property of support ∀X,Y :(X ⊆Y) ⇒s(X) ≥s(Y) TNM033: Introduction to Data Mining 11
https://liris.cnrs.fr/Documents/Liris-2331.pdf
monotonicity properties: a pattern is called similar to a ref-erence pattern x when its Longest Common Subsequence with x (LCS) is large enough (i.e., a monotonic constraint which enforces similarity with x) and when the number of deletions such that it becomes the LCS is small enough (i.e., an anti-monotonic constraint which prunes too dissimilar
https://support.taxslayerpro.com/hc/en-us/articles/360022836234-QBID-Rental-Property-and-Electing-the-Safe-Harbor
QBID - Rental Property and Electing the Safe Harbor The Qualified Business Income Deduction (“QBID” which is also called “Section 199A deduction”) was created in the Tax Cuts and Jobs Act (TCJA) and it allows many owners of pass-through to deduct up to 20 percent of the qualified business income from their taxable income.
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