Why Do Tree Ensemble Approximators Not Outperform the Recursive-Rule eXtraction Algorithm?
Abstract
:1. Introduction
- 1.
- Introduction of a New Interpretability Metric: We propose a metric designed to evaluate and compare the interpretability of different types of rule sets. This metric addresses the gap in quantitative assessments of the interpretability of rule sets.
- 2.
- Comparative Analysis of Rule Sets: We provide an exhaustive comparison of decision list- and DT-based rule sets generated by the tree ensemble approximator. Our analysis provides new insights into the strengths and weaknesses of each type of rule set. Furthermore, we explain why categorical and numerical attributes should be treated separately.
- 3.
- Focus on the Interpretability of Categorical and Numerical Attributes: We explain the necessity of separating categorical and numerical attributes. This focus addresses a significant gap in current research as many existing methods overlook the distinction between categorical and numerical attributes.
2. Related Work
3. Materials and Methods
3.1. Datasets
3.2. Baseline
4. Proposed Methodology
4.1. Data Preprocessing
4.2. Interpretability Metrics
4.3. Model Evaluation and Hyperparameter Optimization
4.4. Summary of Evaluation Schemes for Each CV-Fold
Algorithm 1 Evaluation scheme for each CV-fold |
Require: Training dataset , Validation dataset , Test dataset , Method M Ensure: The score set S for rule set
|
5. Results
5.1. Classification Results
5.2. Interpretability Results
5.3. Summary of Comparative Experiments
5.4. Two Examples
5.4.1. bank-marketing
5.4.2. german
6. Discussion
6.1. Why Should We Avoid a Mixture of Categorical and Numerical Attributes?
6.2. Optimal Selection of the Pareto Solutions
6.3. Decision Lists vs. Decision Trees
6.4. as a Metric of Interpretability
6.5. Limitations
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Dataset Sources
Dataset | ID | URL |
---|---|---|
heart | 53 | https://archive.ics.uci.edu/dataset/145/statlog+heart (13 March 2024) |
australian | 40981 | https://archive.ics.uci.edu/dataset/143/statlog+australian+credit+approval (13 March 2024) |
mammographic | 45557 | https://archive.ics.uci.edu/dataset/161/mammographic+mass (13 March 2024) |
tic-tac-toe | 50 | https://archive.ics.uci.edu/dataset/101/tic+tac+toe+endgame (13 March 2024) |
german | 44096 | https://archive.ics.uci.edu/dataset/144/statlog+german+credit+data (13 March 2024) |
biodeg | 1494 | https://archive.ics.uci.edu/dataset/254/qsar+biodegradation (13 March 2024) |
banknote | 1462 | https://archive.ics.uci.edu/dataset/267/banknote+authentication (13 March 2024) |
bank-marketing | 1558 | https://archive.ics.uci.edu/dataset/222/bank+marketing (13 March 2024) |
spambase | 44 | https://archive.ics.uci.edu/dataset/94/spambase (13 March 2024) |
occupancy | - | https://archive.ics.uci.edu/dataset/357/occupancy+detection (13 March 2024) |
Appendix B. Implementation Details and Hyperparameters
Appendix B.1. XGBoost
Parameter | Space |
---|---|
UniformInt (1, 10) | |
LogUniform (1 × 10−4,1.0) | |
# Iterations | 50 |
Appendix B.2. FBTs
Parameter | Space |
---|---|
UniformInt (1, 10) | |
{auc, None} | |
# Iterations | 50 |
Appendix B.3. RuleCOSI+
Parameter | Space |
---|---|
Uniform (0.0, 0.95) | |
Uniform (0.0, 0.5) | |
c | Uniform (0.1, 0.5) |
# Iterations | 50 |
Appendix B.4. Re-RX with J48graft
- [59]
Parameter | Space |
---|---|
UniformInt (1, 5) | |
LogUniform (5 × 10−3, 0.1) | |
LogUniform (1 × 10−6, 1 × 10−2) | |
# Iterations | 50 |
Parameter | Space |
---|---|
{2, 4, 8, …, 128} | |
Uniform (0.1, 0.5) | |
LogUniform (0.001, 0.25) | |
Uniform (0.05, 0.4) | |
Uniform (0.05, 0.4) | |
# Iterations | 50 |
Appendix B.5. DT
Parameter | Space |
---|---|
UniformInt (1, 10) | |
Uniform (0.0, 0.5) | |
Uniform (0.0, 0.5) | |
# Iterations | 100 |
Appendix B.6. J48graft
Parameter | Space |
---|---|
{2, 4, 8, …, 128} | |
Uniform (0.1, 0.5) | |
# Iterations | 100 |
Appendix C. Results for Other Metrics
Dataset | FBTs | RuleCOSI+ | Re-RX with J48graft | J48graft | DT |
---|---|---|---|---|---|
heart | |||||
australian | |||||
mammographic | |||||
tic-tac-toe | |||||
german | |||||
biodeg | |||||
banknote | |||||
bank-marketing | |||||
spambase | |||||
occupancy | |||||
ranking | 4.0 | 2.1 | 2.5 | 4.1 | 2.3 |
Dataset | FBTs | RuleCOSI+ | Re-RX with J48graft | J48graft | DT |
---|---|---|---|---|---|
heart | |||||
australian | |||||
mammographic | |||||
tic-tac-toe | |||||
german | |||||
biodeg | |||||
banknote | |||||
bank-marketing | |||||
spambase | |||||
occupancy | |||||
ranking | 2.8 | 3.3 | 3.3 | 2.5 | 3.1 |
Dataset | FBTs | RuleCOSI+ | Re-RX with J48graft | J48graft | DT |
---|---|---|---|---|---|
heart | |||||
australian | |||||
mammographic | |||||
tic-tac-toe | |||||
german | |||||
biodeg | |||||
banknote | |||||
bank-marketing | |||||
spambase | |||||
occupancy | |||||
ranking | 2.9 | 1.1 | 3.9 | 3.8 | 3.0 |
Dataset | FBTs | RuleCOSI+ | Re-RX with J48graft | J48graft | DT |
---|---|---|---|---|---|
heart | |||||
australian | |||||
mammographic | |||||
tic-tac-toe | |||||
german | |||||
biodeg | |||||
banknote | |||||
bank-marketing | |||||
spambase | |||||
occupancy | |||||
ranking | 3.0 | 2.1 | 4.0 | 3.0 | 2.9 |
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Metrics | Description |
---|---|
Number of rules | This metric is the total number of rules. |
Number of conditions | This metric is the sum of the total or average number of conditions. |
Complexity [40] | This metric relates the complexity, namely the number of conditions, to the number of classes. |
Fraction uncover [41] | This metric measures the proportion of data points covered by at least one rule in the rule set. |
Fraction overlap [41] | This metric calculates the degree to which rules in the rule set redundantly cover the same data points. |
Uniq [39] | This metric quantifies the amount of non-redundant conditions contained in the rule set. |
[42] | This metric is the weighted sum of the number of different attributes, based on the coverage of each rule. |
Weighted sum of predictivity, stability, and simplicity [43] | This metric combines three critical aspects: predictivity, which assesses accuracy; stability, gauged through the Dice–Sorensen index comparing rule sets; and simplicity, measured by rule length sum, into a comprehensive weighted sum. |
Dataset | #Instances | #Features | #Cate | #Cont | Major Class Ratio |
---|---|---|---|---|---|
heart | 270 | 13 | 7 | 6 | 0.55 |
australian | 690 | 14 | 6 | 8 | 0.555 |
mammographic | 831 | 4 | 2 | 2 | 0.52 |
tic-tac-toe | 958 | 9 | 9 | 0 | 0.65 |
german | 1000 | 20 | 7 | 13 | 0.70 |
biodeg | 1055 | 41 | 0 | 41 | 0.66 |
banknote | 1372 | 4 | 0 | 4 | 0.55 |
bank-marketing | 4521 | 16 | 9 | 7 | 0.89 |
spambase | 4601 | 57 | 0 | 57 | 0.60 |
occupancy | 8143 | 5 | 0 | 5 | 0.79 |
Dataset | FBTs | RuleCOSI+ | Re-RX with J48graft | J48graft | DT |
---|---|---|---|---|---|
heart | |||||
australian | |||||
mammographic | |||||
tic-tac-toe | |||||
german | |||||
biodeg | |||||
banknote | |||||
bank-marketing | |||||
spambase | |||||
occupancy | |||||
ranking | 2.9 | 2.1 | 4.0 | 3.2 | 2.8 |
Dataset | FBTs | RuleCOSI+ | Re-RX with J48graft | J48graft | DT |
---|---|---|---|---|---|
heart | |||||
australian | |||||
mammographic | |||||
tic-tac-toe | |||||
german | |||||
biodeg | |||||
banknote | |||||
bank-marketing | |||||
spambase | |||||
occupancy | |||||
ranking | 4.5 | 1.6 | 3.3 | 3.8 | 1.8 |
Dataset | FBTs | RuleCOSI+ | Re-RX with J48graft | J48graft | DT |
---|---|---|---|---|---|
heart | |||||
australian | |||||
mammographic | |||||
tic-tac-toe | |||||
german | |||||
biodeg | |||||
banknote | |||||
bank-marketing | |||||
spambase | |||||
occupancy | |||||
ranking | 3.5 | 4.7 | 1.5 | 3.1 | 2.2 |
Method | |||
---|---|---|---|
FBTs | |||
RuleCOSI+ | |||
Re-RX with J48graft | |||
J48graft | |||
DT |
RuleCOSI+ | Coverage | |
0.744 | ||
0.148 | ||
0.109 | ||
Re-RX with J48graft | Coverage | |
0.820 | ||
0.108 | ||
0.044 | ||
0.0 | ||
0.029 | ||
DT | Coverage | |
0.891 | ||
0.025 | ||
0.084 |
Re-RX with J48graft | Coverage | |
0.971 | ||
0.0 | ||
0.029 |
RuleCOSI+ | Coverage | |
0.329 | ||
0.283 | ||
0.388 | ||
Re-RX with J48graft | Coverage | |
0.394 | ||
0.063 | ||
0.16 | ||
0.067 | ||
0.013 | ||
0.022 | ||
0.012 | ||
0.19 | ||
0.079 | ||
DT | Coverage | |
0.394 | ||
0.325 | ||
0.281 |
Re-RX with J48graft | Coverage | |
0.394 | ||
0.063 | ||
0.067 | ||
0.207 | ||
0.19 | ||
0.079 |
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Share and Cite
Onishi, S.; Nishimura, M.; Fujimura, R.; Hayashi, Y. Why Do Tree Ensemble Approximators Not Outperform the Recursive-Rule eXtraction Algorithm? Mach. Learn. Knowl. Extr. 2024, 6, 658-678. https://doi.org/10.3390/make6010031
Onishi S, Nishimura M, Fujimura R, Hayashi Y. Why Do Tree Ensemble Approximators Not Outperform the Recursive-Rule eXtraction Algorithm? Machine Learning and Knowledge Extraction. 2024; 6(1):658-678. https://doi.org/10.3390/make6010031
Chicago/Turabian StyleOnishi, Soma, Masahiro Nishimura, Ryota Fujimura, and Yoichi Hayashi. 2024. "Why Do Tree Ensemble Approximators Not Outperform the Recursive-Rule eXtraction Algorithm?" Machine Learning and Knowledge Extraction 6, no. 1: 658-678. https://doi.org/10.3390/make6010031