Abstract
We strive to find contexts (i.e., subgroups of entities) under which exceptional (dis-)agreement occurs among a group of individuals, in any type of data featuring individuals (e.g., parliamentarians, customers) performing observable actions (e.g., votes, ratings) on entities (e.g., legislative procedures, movies). To this end, we introduce the problem of discovering statistically significant exceptional contextual intra-group agreement patterns. To handle the sparsity inherent to voting and rating data, we use Krippendorff’s Alpha measure for assessing the agreement among individuals. We devise a branch-and-bound algorithm, named DEvIANT, to discover such patterns. DEvIANT exploits both closure operators and tight optimistic estimates. We derive analytic approximations for the confidence intervals (CIs) associated with patterns for a computationally efficient significance assessment. We prove that these approximate CIs are nested along specialization of patterns. This allows to incorporate pruning properties in DEvIANT to quickly discard non-significant patterns. Empirical study on several datasets demonstrates the efficiency and the usefulness of DEvIANT.
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Notes
- 1.
This paradigm naturally raises the question of how to address the multiple comparisons problem [19]. This is a non-trivial task in our setting, and solving it requires an extension of the significant pattern mining paradigm as a whole: its scope is bigger than this paper. We provide a brief discussion in Appendix C.
- 2.
In the same line of reasoning of [5], one can assume that the underlying distribution can be derived from what prior beliefs the end-user may have on such distribution. If only the observed expectation \(\mu \) and variance \(\sigma ^2\) are given as constraints which must hold for the underlying distribution, the maximum entropy distribution (taking into account no other prior information than the given constraints) is known to be the Normal distribution \(\mathcal {N}(\mu ,\sigma ^2)\) [3, p.413].
- 3.
Random-SMWA: Randomized algorithm - Subset with Maximum Weighted Average.
- 4.
Finding the subset having the minimum weighted average is a dual problem to finding the subset having the maximum weighted average. To solve the former problem using Random-SMWA, we modify the values of \(v_i\) to \(-v_i\) and keep the same weights \(w_i\).
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Acknowledgments
This work has been partially supported by the project ContentCheck ANR-15-CE23-0025 funded by the French National Research Agency. The authors would like to thank the reviewers for their valuable remarks. They also warmly thank Arno Knobbe, Simon van der Zon, Aimene Belfodil and Gabriela Ciuperca for interesting discussions.
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Belfodil, A., Duivesteijn, W., Plantevit, M., Cazalens, S., Lamarre, P. (2020). DEvIANT: Discovering Significant Exceptional (Dis-)Agreement Within Groups. In: Brefeld, U., Fromont, E., Hotho, A., Knobbe, A., Maathuis, M., Robardet, C. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2019. Lecture Notes in Computer Science(), vol 11906. Springer, Cham. https://doi.org/10.1007/978-3-030-46150-8_1
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