Tree Algorithms in Data Mining: Comparison of rpart and RWeka... and Beyond
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1 Tree Algorithms in Data Mining: Comparison of rpart and RWeka... and Beyond Achim Zeileis
2 Motivation For publishing new tree algorithms, benchmarks against established methods are necessary. When developing the tools in party, we benchmarked against rpart, the open-source implementation of CART. Statistical journals were usually happy with that. Usual comment from machine learners: You have to benchmark against C4.5, it s much better than CART! Quinlan provided source code for C4.5, but not with a license that would allow usage. Weka had an open-source Java implementation, but hard to access from R. When we developed RWeka, we finally were able to set up some benchmark with CART and C4.5 within R.
3 Tree algorithms CART/RPart rpart: Classification and regression trees Breiman, Friedman, Olshen, Stone Cross-validation-based cost-complexity pruning: RPart0: Best prediction error. RPart1: Highest complexity parameter within 1 standard error. C4.5/J4.8 RWeka: C4.5 Quinlan, Determine size by confidence threshold C and minimal leaf size M: J4.8: Standard heuristics C = 0.25, M = 2. J4.8cv: Cross-validation for C = 0.01,..., 0.5, M = 2,..., 20. QUEST LohTools: Quick, unbiased and efficient statistical trees Loh, Shih Popularized concept of unbiased recursive partitioning in statistics. Hand-crafted convenience interface to original binaries. CTree party: Conditional inference trees Hothorn, Hornik, Zeileis Unbiased recursive partitioning based on permutation tests.
4 UCI data sets mlbench Data set # of obs. # of cat. inputs # of num. inputs breast cancer chess circle credit heart hepatitis house votes ionosphere liver Pima Indians diabetes promotergene ringnorm sonar spirals threenorm tictactoe titanic twonorm
5 Analysis 6 tree algorithms. 18 data sets. 500 bootstrap samples for each combination. Performance measure: Out-of-bag misclassification rate. Complexity measure: Number of splits + number of leafs. Individual results: Simultaneous pairwise confidence intervals Tukey all-pair comparisons. Aggregated results: Bradley-Terry model Alternatively: median linear consensus ranking,....
6 Individual results: Pima Indian diabetes J4.8cv J4.8 RPart0 J4.8 RPart1 J4.8 QUEST J4.8 CTree J4.8 RPart0 J4.8cv RPart1 J4.8cv QUEST J4.8cv CTree J4.8cv RPart1 RPart0 QUEST RPart0 CTree RPart0 QUEST RPart1 CTree RPart1 CTree QUEST Misclassification difference in percent
7 Individual results: Pima Indian diabetes J4.8cv J4.8 RPart0 J4.8 RPart1 J4.8 QUEST J4.8 CTree J4.8 RPart0 J4.8cv RPart1 J4.8cv QUEST J4.8cv CTree J4.8cv RPart1 RPart0 QUEST RPart0 CTree RPart0 QUEST RPart1 CTree RPart1 CTree QUEST Complexity difference
8 Individual results: Breast cancer J4.8cv J4.8 RPart0 J4.8 RPart1 J4.8 QUEST J4.8 CTree J4.8 RPart0 J4.8cv RPart1 J4.8cv QUEST J4.8cv CTree J4.8cv RPart1 RPart0 QUEST RPart0 CTree RPart0 QUEST RPart1 CTree RPart1 CTree QUEST Misclassification difference in percent
9 Individual results: Breast cancer J4.8cv J4.8 RPart0 J4.8 RPart1 J4.8 QUEST J4.8 CTree J4.8 RPart0 J4.8cv RPart1 J4.8cv QUEST J4.8cv CTree J4.8cv RPart1 RPart0 QUEST RPart0 CTree RPart0 QUEST RPart1 CTree RPart1 CTree QUEST Complexity difference
10 Aggregated results: Misclassification Worth parameters J4.8 J4.8cv RPart0 RPart1 QUEST CTree Objects
11 Aggregated results: Complexity Worth parameters J4.8 J4.8cv RPart0 RPart1 QUEST CTree Objects
12 Summary No clear preference between CART/RPart and C4.5/J4.8. Other tree algorithms perform similarly well. Cross-validated trees perform better than their counterparts. 1-standard error rule does not seem to be supported. And now for something different: Before: Pairwise comparisons of tree algorithms. Now: Tree algorithm for pairwise comparison data.
13 Model-based recursive partitioning Generic algorithm: 1 Fit parametric model for Y. 2 Assess stability of the model parameters over each splitting variable Z j. 3 Split sample along the Z j with strongest association: Choose breakpoint with highest improvement of the model fit. 4 Repeat steps 1 3 recursively in the subsamples until no more significant instabilities. Application: Use Bradley-Terry models in step 1. Implementation: psychotree on R-Forge.
14 Germany s Next Topmodel Study at Department of Psychology, Universität Tübingen. 192 subjects rated the attractiveness of candidates in 2nd season of Germany s Next Topmodel. 6 finalists: Barbara Meier, Anni Wendler, Hana Nitsche, Fiona Erdmann, Mandy Graff and Anja Platzer. Pairwise comparison with forced choice. Subject covariates: Gender, age, questions about interest in the show.
15 Germany s Next Topmodel
16 Germany s Next Topmodel 1 age p < q2 p = yes no 52 > 52 4 gender p = male female 0.5 Node 3 n = Node 5 n = Node 6 n = Node 7 n = B Ann H F M Anj B Ann H F M Anj B Ann H F M Anj B Ann H F M Anj
17 References Hothorn T, Leisch F, Zeileis A, Hornik K The Design and Analysis of Benchmark Experiments. Journal of Computational and Graphical Statistics, 143, doi: / x59630 Schauerhuber M, Zeileis A, Meyer D Benchmarking Open-Source Tree Learners in R/RWeka. In C Preisach, H Burkhardt, L Schmidt-Thieme, R Decker eds., Data Analysis, Machine Learning and Applications Proceedings of the 31st Annual Conference of the Gesellschaft für Klassifikation e.v., Albert-Ludwigs-Universität Freiburg, March 7 9, pp Hornik K, Buchta C, Zeileis A Open-Source Machine Learning: R Meets Weka. Computational Statistics, 242, doi: /s Strobl C, Wickelmaier F, Zeileis A Accounting for Individual Differences in Bradley-Terry Models by Means of Recursive Partitioning. Technical Report 54, Department of Statistics, Ludwig-Maximilians-Universität München. URL
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