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To tune or not to tune: rule evaluation for metaheuristic-based sequential covering algorithms

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Abstract

While many papers propose innovative methods for constructing individual rules in separate-and-conquer rule learning algorithms, comparatively few study the heuristic rule evaluation functions used in these algorithms to ensure that the selected rules combine into a good rule set. Underestimating the impact of this component has led to suboptimal design choices in many algorithms. The main goal of this paper is to demonstrate the importance of heuristic rule evaluation functions by improving existing rule induction techniques and to provide guidelines for algorithm designers. We first select optimal heuristic rule learning functions for several metaheuristic-based algorithms and empirically compare the resulting heuristics across algorithms. This results in large and significant improvements of the predictive accuracy for two techniques. We find that despite the absence of a global optimal choice for all algorithms, good default choices can be shared across algorithms with similar search biases. A near-optimal selection can thus be found for new algorithms with minor experimental tuning. Lastly, a major contribution is made towards balancing a model’s predictive accuracy with its comprehensibility. We construct a Pareto front of optimal solutions for this trade-off and show that gains in comprehensibility and/or accuracy are possible for the techniques studied. The parametrized heuristics enable users to select the desired balance as they offer a high flexibility when it comes to selecting the desired accuracy and comprehensibility in rule miners.

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Notes

  1. A more general approach is the weighted covering strategy in which the weights are simply reduced. While the separate-and-conquer strategy is a special case, it is far more widespread.

  2. Several terms are encountered in the literature that refer to heuristic rule evaluation functions. Alternative terminology includes ‘rule learning heuristic’, ‘(rule) evaluation function’, ‘fitness function’ and ‘(rule) quality measure’. For the sake of brevity, the term ‘heuristic’ is used in this text where applicable.

  3. The RIPPER algorithm is an exception as corrections can still be made in the post-processing step.

  4. Negative fitness values are also not allowed in these algorithms. For this reason, all parametrized heuristics described in the previous section were incremented with a constant to bring the lowest possible value at precisely zero.

  5. AntMiner is available at http://sourceforge.net/projects/guiantminer/

  6. AntMiner+ is available at http://www.antminerplus.com

  7. PSO/ACO2 is available at http://sourceforge.net/projects/psoaco2/

  8. An implementation of HIDER is available as part of the KEEL software project (Alcalá-Fdez et al. 2009, 2011) at http://www.keel.es/

  9. The probability of an individual to be selected is proportional to its fitness value. This method thus uses the exact values returned by the fitness function.

  10. We use the RIPPER implementation included in the Weka project (Hall et al. 2009) at http://www.cs.waikato.ac.nz/ml/weka/

  11. When using non-gain heuristics in our experiments, the best rule is returned as the last rule is suboptimal in that case.

  12. anneal, audiology, breast-cancer, cleveland-heart-disease, contact-lenses, credit, glass2, glass, hepatitis, horse-colic, hypothyroid, iris, krkp, labor, lymphography, monk1, monk2, monk3, mushroom, sick-euthyroid, soybean, tic-tac-toe, titanic, vote-1, vote, vowel, wine

  13. auto-mpg, autos, balance-scale, balloons, breast-w, breast-w-d, bridges2, credit-g, diabetes, echocardiogram, flag, hayes-roth, heart-h, heart-statlog, ionosphere, machine, primarytumor, promoters, segment, solar-flare, sonar, vehicle, zoo

  14. The UCI datasets are available at http://archive.ics.uci.edu/ml/. The Titanic dataset is available as part of the Delve project of the University of Toronto at http://www.cs.toronto.edu/~delve/.

  15. The statistical tool used to perform the Friedman test and advanced post-hoc procedures can be found at http://sci2s.ugr.es/keel/multipleTest.zip

  16. The data of these experiments is available online at http://www.antminerplus.com

  17. The ACO search starts with an environment that is not specialized and has to learn to add specific terms to the rules (top-down). In PSO and genetic algorithms, the initialization of the swarm/population with either general or specific particles/solutions determines the top-down or bottom-up nature. HIDER initializes with very specific instances (bottom-up). PSO/ACO2 adds conditions to rules in two phases (top-down). The first phase is a limited ACO/PSO hybrid search (top-down). The second phase is a limited PSO search with a non-specializing seeding (top-down).

  18. Our tuning data contains significant and large positive (Spearman) correlations of the observed best performing parameter compared across the different parametrized heuristics. This indicates that the bias requirements of the datasets are somewhat stable.

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Acknowledgments

This work was carried out using the Stevin Supercomputer Infrastructure at Ghent University. We would like to thank the Flemish Research Council for the financial support (FWO Odysseus grant B.0915.09). We are also grateful to the creators of the open source implementations used in this work.

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Authors and Affiliations

  1. Faculty of Economics and Business Administration, Ghent University, Ghent, Belgium

    Bart Minnaert & Manu De Backer

  2. Faculty of Applied Economics, University of Antwerp, Antwerp, Belgium

    Bart Minnaert, David Martens & Manu De Backer

  3. Department of Decision Sciences Information Management, K.U. Leuven, Leuven, Belgium

    Manu De Backer & Bart Baesens

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  1. Bart Minnaert
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Correspondence to Bart Minnaert.

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Minnaert, B., Martens, D., De Backer, M. et al. To tune or not to tune: rule evaluation for metaheuristic-based sequential covering algorithms. Data Min Knowl Disc 29, 237–272 (2015). https://doi.org/10.1007/s10618-013-0339-5

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