Abstract
The task of subgroup discovery (SD) is to find interpretable descriptions of subsets of a dataset that stand out with respect to a target attribute. To address the problem of mining large numbers of redundant subgroups, subgroup set discovery (SSD) has been proposed. State-of-the-art SSD methods have their limitations though, as they typically heavily rely on heuristics and/or user-chosen hyperparameters.
We propose a dispersion-aware problem formulation for subgroup set discovery that is based on the minimum description length (MDL) principle and subgroup lists. We argue that the best subgroup list is the one that best summarizes the data given the overall distribution of the target. We restrict our focus to a single numeric target variable and show that our formalization coincides with an existing quality measure when finding a single subgroup, but that—in addition—it allows to trade off subgroup quality with the complexity of the subgroup. We next propose SSD++, a heuristic algorithm for which we empirically demonstrate that it returns outstanding subgroup lists: non-redundant sets of compact subgroups that stand out by having strongly deviating means and small spread.
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Notes
- 1.
The extended version of this work is available on arXiv [16].
- 2.
To obtain code lengths in bits, all logarithms in this paper are to the base 2.
- 3.
\(L_\mathbb {N}(i)= \log k_0 + \log ^{*} i \), where \(\log ^{*} i = \log i + \log \log i + \ldots \) and \( k_0 \approx 2.865064\).
- 4.
See proof in Appendix 2 of the extended version [16].
- 5.
The full derivation of the Bayesian encoding and an in-depth explanation are given in Appendix 1 of the extended version [16].
- 6.
Derivations are given in Appendix 4 of the extended version [16].
- 7.
For the implementation of SSD++ and to reproduce the experiments see Proença [15].
- 8.
- 9.
References
Antonio, N., de Almeida, A., Nunes, L.: Hotel booking demand datasets. Data Brief 22, 41–49 (2019)
Atzmueller, M.: Subgroup discovery. Wiley Interdisc. Rev. Data Min. Knowl. Disc. 5(1), 35–49 (2015)
Belfodil, A., et al.: FSSD-a fast and efficient algorithm for subgroup set discovery. In: Proceedings of DSAA 2019 (2019)
Boley, M., Goldsmith, B.R., Ghiringhelli, L.M., Vreeken, J.: Identifying consistent statements about numerical data with dispersion-corrected subgroup discovery. Data Min. Knowl. Disc. 31(5), 1391–1418 (2017). https://doi.org/10.1007/s10618-017-0520-3
Bosc, G., Boulicaut, J.F., Raïssi, C., Kaytoue, M.: Anytime discovery of a diverse set of patterns with Monte Carlo tree search. Data Min. Knowl. Disc. 32(3), 604–650 (2018). https://doi.org/10.1007/s10618-017-0547-5
Gönen, M., Johnson, W.O., Lu, Y., Westfall, P.H.: The Bayesian two-sample t test. Am. Stat. 59(3), 252–257 (2005)
Grünwald, P., Roos, T.: Minimum description length revisited. Int. J. Math. Ind. 11(1), 1930001 (29 p.) (2019)
Grünwald, P.D.: The Minimum Description Length Principle. MIT Press, Cambridge (2007)
Klösgen, W.: Explora: a multipattern and multistrategy discovery assistant. In: Advances in Knowledge Discovery and Data Mining, pp. 249–271 (1996)
Lavrač, N., Kavšek, B., Flach, P., Todorovski, L.: Subgroup discovery with CN2-SD. J. Mach. Learn. Res. 5, 153–188 (2004)
van Leeuwen, M.: Maximal exceptions with minimal descriptions. Data Min. Knowl. Disc. 21(2), 259–276 (2010). https://doi.org/10.1007/s10618-010-0187-5
van Leeuwen, M., Knobbe, A.: Diverse subgroup set discovery. Data Min. Knowl. Disc. 25(2), 208–242 (2012). https://doi.org/10.1007/s10618-012-0273-y
Lijffijt, J., Kang, B., Duivesteijn, W., Puolamaki, K., Oikarinen, E., De Bie, T.: Subjectively interesting subgroup discovery on real-valued targets. In: 2018 IEEE ICDE, pp. 1352–1355. IEEE (2018)
Meeng, M., Knobbe, A.: For real: a thorough look at numeric attributes in subgroup discovery. Data Min. Knowl. Disc. 35(1), 158–212 (2021)
Proença, H.M. : HMProenca/SSDpp-numeric: v2020.06.0 (2020). https://github.com/HMProenca/SSDpp-numeric. Archived at https://doi.org/10.5281/zenodo.3901236
Proença, H.M., Grünwald, P., Bäck, T., van Leeuwen, M.: Discovering outstanding subgroup lists for numeric targets using MDL. Preprint arXiv:2006.09186 (2020)
Proença, H.M., Klijn, R., Bäck, T., van Leeuwen, M.: Identifying flight delay patterns using diverse subgroup discovery. In: 2018 SSCI, pp. 60–67. IEEE (2018)
Proença, H.M., van Leeuwen, M.: Interpretable multiclass classification by MDL-based rule lists. Inf. Sci. 512, 1372–1393 (2020)
Rissanen, J.: Modeling by shortest data description. Automatica 14(5), 465–471 (1978)
Rouder, J.N., Speckman, P.L., Sun, D., Morey, R.D., Iverson, G.: Bayesian t tests for accepting and rejecting the null hypothesis. Psychon. Bull. Rev. 16(2), 225–237 (2009)
Van Leeuwen, M., Galbrun, E.: Association discovery in two-view data. IEEE Trans. Knowl. Data Eng. 27(12), 3190–3202 (2015)
Vreeken, J., Van Leeuwen, M., Siebes, A.: KRIMP: mining itemsets that compress. Data Min. Knowl. Disc. 23(1), 169–214 (2011). https://doi.org/10.1007/s10618-010-0202-x
Acknowledgment
This work is part of the research programme Indo-Dutch Joint Research Programme for ICT 2014 with project number 629.002.201, SAPPAO, which is financed by the Netherlands Organisation for Scientific Research.
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Proença, H.M., Grünwald, P., Bäck, T., Leeuwen, M.v. (2021). Discovering Outstanding Subgroup Lists for Numeric Targets Using MDL. In: Hutter, F., Kersting, K., Lijffijt, J., Valera, I. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2020. Lecture Notes in Computer Science(), vol 12457. Springer, Cham. https://doi.org/10.1007/978-3-030-67658-2_2
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