arXiv subjects

Marie Ely Piceno

Publications and source records attributed to Marie Ely Piceno.

3 recordsLinked to original sources

arXiv2020

Analysis of Co-Occurrence Patterns in Data through Modular and Clan Decompositions of Gaifman Graphs

We argue that the existing knowledge about modular decomposition of graphs and clan decomposition of 2-structures can be put to use advantageously in a context of data analysis. We show how to obtain visual descriptions of co-occurrence patterns by employing these decompositions on possibly generalized Gaifman graphs associated to datasets. We provide both theoretical advances that connect the proposed process to other data mining aspects (namely, closed set mining), as well as implemented algorithmics leading to an open-source tool that demonstrates our approach.

cs.DB↗

arXiv2019

Relative Entailment Among Probabilistic Implications

We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is defined in terms of a threshold on a conditional probability of the consequent, given the antecedent: we are dealing with what the data analysis community calls confidence of partial implications or association rules. Existing studies of redundancy among these partial implications have characterized so far only entailment from one premise and entailment from two premises, both in the stand-alone case and in the case of presence of additional classical implications (this is what we call "relative entailment"). By exploiting a previously noted alternative view of the entailment in terms of linear programming duality, we characterize exactly the cases of entailment from arbitrary numbers of premises, again both in the stand-alone case and in the case of presence of additional classical implications. As a result, we obtain decision algorithms of better complexity; additionally, for each potential case of entailment, we identify a critical confidence threshold and show that it is, actually, intrinsic to each set of premises and antecedent of the conclusion.

cs.LO↗

arXiv2018

Decomposition of quantitative Gaifman graphs as a data analysis tool

We argue the usefulness of Gaifman graphs of first-order relational structures as an exploratory data analysis tool. We illustrate our approach with cases where the modular decompositions of these graphs reveal interesting facts about the data. Then, we introduce generalized notions of Gaifman graphs, enhanced with quantitative information, to which we can apply more general, existing decomposition notions via 2-structures; thus enlarging the analytical capabilities of the scheme. The very essence of Gaifman graphs makes this approach immediately appropriate for the multirelational data framework.

cs.DB↗