An Ensemble of Optimal Trees for Class Membership Probability Estimation

Khan, Zardad; Gul, Asma; Mahmoud, Osama; Miftahuddin, Miftahuddin; Perperoglou, Aris; Adler, Werner; Lausen, Berthold

doi:10.1007/978-3-319-25226-1_34

Cited by 20 publications

(36 citation statements)

References 12 publications

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“…This method requires n > p . Finally, we compare with two related ensemble methods: optimal tree ensembles (OTEs) (Khan et al ., ) and ensemble of subset of k ‐nearest‐neighbour classifiers, ES k nn (Gul et al ., ).…”

Section: Empirical Analysismentioning

confidence: 99%

Random-projection Ensemble Classification

Cannings

Samworth

2017

Journal of the Royal Statistical Society Series B: Statistical Methodology

109

132

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We introduce a very general method for high dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower dimensional space. In one special case that we study in detail, the random projections are divided into disjoint groups, and within each group we select the projection yielding the smallest estimate of the test error. Our random-projection ensemble classifier then aggregates the results of applying the base classifier on the selected projections, with a data-driven voting threshold to determine the final assignment. Our theoretical results elucidate the effect on performance of increasing the number of projections. Moreover, under a boundary condition that is implied by the sufficient dimension reduction assumption, we show that the test excess risk of the random-projection ensemble classifier can be controlled by terms that do not depend on the original data dimension and a term that becomes negligible as the number of projections increases. The classifier is also compared empirically with several other popular high dimensional classifiers via an extensive simulation study, which reveals its excellent finite sample performance.

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Section: Empirical Analysismentioning

confidence: 99%

Random-projection Ensemble Classification

Cannings

Samworth

2017

Journal of the Royal Statistical Society Series B: Statistical Methodology

109

132

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“…Numbers after the abbreviations mean the training set of size of n (a subsample of the data), and then, the remaining data formed the test set. ES k NN, ensemble of subset of k NN classifiers; GP, Gaussian process; k NN, k ‐nearest neighbors; LDA, linear discriminant analysis; NSC, nearest shrunken centroids; OTE, optimal tree ensemble; PenLDA, penalized LDA; QDA, quadratic discriminant analysis; RF, random forest; RP, random projection; SRD, sum of ranking differences; SVM, support vector machine; the number after the abbreviations means “sufficient dimension reduction (SDR5) assumption”…”

Section: Resultsmentioning

confidence: 99%

“…Each random projection can be considered as a perturbation of the original data, and it is thought that the “stable” effects that are sought by statisticians are found. They focused their research on the classification performance of RPEC, and misclassification rates were selected for comparison of the following classifiers: base ones—linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), k ‐nearest neighbor ( k NN), random forest (RF), support vector machines (SVMs), Gaussian process (GP) classifiers, penalized LDA (PenLDA), nearest shrunken centroids (NSCs), optimal tree ensembles (OTEs), and ensemble of subset of k NN classifiers (ES k NN). Linear and radial basis function has also been used with GP and SVM.…”

Section: Methodsmentioning

confidence: 99%

Comparison of validation variants by sum of ranking differences and ANOVA

Héberger

Kollár-Hunek

2019

Journal of Chemometrics

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The old debate is revived: Definite differences can be observed in suggestions of estimation for prediction performances of models and for validation variants according to the various scientific disciplines. However, the best and/or recommended practice for the same data set cannot be dependent on the field of usage. Fortunately, there is a method comparison algorithm, which can rank and group the validation variants; its combination with variance analysis will reveal whether the differences are significant or merely the play of random errors. Therefore, three case studies have been selected carefully to reveal similarities and differences in validation variants. The case studies illustrate the different significance of these variants well. In special circumstances, any of the influential factors for validation variants can exert significant influence on evaluation by sums of (absolute) ranking differences (SRDs): stratified (contiguous block) or repeated Monte Carlo resampling and how many times the data set is split (5‐7‐10). The optimal validation variant should be determined individually again and again. A random resampling with sevenfold cross‐validations seems to be a good compromise to diminish the bias and variance alike. If the data structure is unknown, a randomization of rows is suggested before SRD analysis. On the other hand, the differences in classifiers, validation schemes, and models proved to be always significant, and even subtle differences can be detected reliably using SRD and analysis of variance (ANOVA).

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“…The problem, how diversity in an ensemble or distances between classifiers can best be measured, is discussed extensively [15 -19]. As the connection between several proposed diversity measures and the perfor mance of the ensemble is not as straightforward as might be hoped [16,19] and not always higher diversity leads to an improved ensemble [20], the classification performance of single classifiers also was considered for ensemble pruning [21][22][23].…”

Section: Discussionmentioning

confidence: 99%

Ensemble Pruning for Glaucoma Detection in an Unbalanced Data Set

Adler¹,

Gefeller²,

Gul³

et al. 2016

Methods Inf Med

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SummaryBackground: Random forests are successful classifier ensemble methods consisting of typically 100 to 1000 classification trees. Ensemble pruning techniques reduce the computational cost, especially the memory demand, of random forests by reducing the number of trees without relevant loss of performance or even with increased performance of the sub-ensemble. The application to the problem of an early detection of glaucoma, a severe eye disease with low prevalence, based on topographical measurements of the eye background faces specific challenges. Objectives:We examine the performance of ensemble pruning strategies for glaucoma detection in an unbalanced data situation. Methods:The data set consists of 102 topographical features of the eye background of 254 healthy controls and 55 glaucoma patients. We compare the area under the receiver operating characteristic curve (AUC), and the Brier score on the total data set, in the majority class, and in the minority class of pruned random forest ensembles obtained with strategies based on the prediction accuracy of greedily grown sub-ensembles, the uncertainty weighted accuracy, and the similarity between single trees. To validate the findings and to examine the influence of the prevalence of glaucoma in the data set, we additionally perform a simulation study with lower prevalences of glaucoma. Results:In glaucoma classification all three pruning strategies lead to improved AUC and smaller Brier scores on the total data set with sub-ensembles as small as 30 to 80 trees compared to the classification results obtained with the full ensemble consisting of 1000 trees. In the simulation study, we were able to show that the prevalence of glaucoma is a critical factor and lower prevalence decreases the performance of our pruning strategies. Conclusion:The memory demand for glaucoma classification in an unbalanced data situation based on random forests could effectively be reduced by the application of pruning strategies without loss of performance in a population with increased risk of glaucoma.

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An Ensemble of Optimal Trees for Class Membership Probability Estimation

Cited by 20 publications

References 12 publications

Random-projection Ensemble Classification

Random-projection Ensemble Classification

Comparison of validation variants by sum of ranking differences and ANOVA

Ensemble Pruning for Glaucoma Detection in an Unbalanced Data Set

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