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XGBOD: Improving Supervised Outlier Detection with Unsupervised Representation Learning
Yue Zhao, Maciej K. Hryniewicki
TL;DR
Outlier detection is hindered by rare positives and limited labels, motivating a hybrid approach. XGBOD learns unsupervised outlier representations, selects useful ones, and applies XGBoost, achieving the best result on six of seven datasets in Experiment I.
Problem
Rare outliers, unavailable ground truth, and severe imbalance limit the generalization of supervised outlier detection.
Method
XGBOD generates unsupervised outlier-score representations, selects useful scores, combines them with original features, and trains XGBoost on the improved space.
Results
XGBOD achieves the best result on six of seven datasets for both ROC and P@N in Experiment I, except Mammography.
Takeaways & Limitations
XGBOD provides improved predictive capabilities over competing approaches while avoiding balanced-subsample construction and averaging.
Takeaways & Limitations
The study identifies future work in selecting features before generating TOS and adding or replacing TOS-selection methods.
Abstract
from arXiv · showhide
A new semi-supervised ensemble algorithm called XGBOD (Extreme Gradient Boosting Outlier Detection) is proposed, described and demonstrated for the enhanced detection of outliers from normal observations in various practical datasets. The proposed framework combines the strengths of both supervised and unsupervised machine learning methods by creating a hybrid approach that exploits each of their individual performance capabilities in outlier detection. XGBOD uses multiple unsupervised outlier mining algorithms to extract useful representations from the underlying data that augment the predictive capabilities of an embedded supervised classifier on an improved feature space. The novel approach is shown to provide superior performance in comparison to competing individual detectors, the full ensemble and two existing representation learning based algorithms across seven outlier datasets.
I. INTRODUCTION
Outlier detection is difficult because outliers are rare and labels are often unavailable, limiting supervised generalization. XGBOD addresses this by using unsupervised outlier scores as learned representations for a supervised classifier.
- Rare outliers, unavailable ground truth, and severe class imbalance limit supervised outlier detection.
- Unsupervised detectors capture complementary structures such as local density, global correlation, and hierarchical relationships without labels.
- Stacking can combine supervised label information with complex representations learned by unsupervised outlier methods.
- XGBOD augments original features with transformed outlier scores, prunes them greedily, and applies XGBoost to the refined feature space.
- Unsupervised outlier methods serve as feature-engineering instruments that enrich representations when limited data restricts deep representation learning.
B. Data Imbalance and Extreme Gradient Boosting
Outlier detection combines imbalanced classification with heterogeneous unsupervised detectors and ensemble strategies. XGBOD selects XGBoost to replace costly balanced-subsample approaches while exploiting detector diversity.
- Outliers form a minority class, making detection difficult and degrading classifier performance under imbalance.
- EasyEnsemble treats imbalance through down-sampled balanced subsamples, but execution is expensive and performance is problem-specific.
- XGBoost is chosen as the final classifier because it is regularized, scalable, accurate, and suited to imbalanced data.
- Unsupervised detectors span linear, proximity-based, statistical, probabilistic, and high-dimensional models with dataset-dependent strengths.
- Prior outlier ensembles commonly average detector outputs or induce diversity, whereas XGBOD combines unsupervised results through supervised stacking.
III. ALGORITHM DESIGN
XGBOD transforms unsupervised outlier scores into additional features, selects useful representations, and trains XGBoost on the resulting feature space. Its design favors heterogeneous detectors to capture distinct data characteristics.
- XGBOD generates unsupervised outlier-score representations, selects useful scores, combines them with original features, and predicts with XGBoost.
- Unsupervised outlier scores are treated as learned representations or unsupervised feature engineering that augment the original data.
- Each scoring function maps the dataset to real-valued transformed outlier scores describing degree of outlyingness.
- Combining k scoring functions produces an n × k outlier-score matrix used as new features.
- Heterogeneous base functions are preferred because diversity can learn distinct data characteristics and improve ensemble generalization.
- Detector selection must balance accuracy against diversity because inaccurate or highly redundant scores can weaken the ensemble.
B. Phase II: TOS Selection
Phase II reduces the augmented feature space by selecting a limited number of transformed outlier scores. Its selection criteria balance predictive accuracy, diversity, and computational efficiency.
- Selecting only p of k transformed outlier scores reduces transformations and feature-space size while retaining useful representations.
- Random Selection chooses p scores without replacement, while Accurate Selection chooses the p highest-scoring representations.
- TOS accuracy is evaluated using an appropriate metric such as ROC against ground-truth labels.
- Balance Selection discounts accuracy for scores correlated with already selected representations, favoring accurate and diverse subsets.
- The selected scores are concatenated with original features to form the refined combined feature space.
C. Phase III: Prediction with XGBoost
XGBoost classifies the combined feature space to produce the final output, improving runtime efficiency and predictive capability while enabling feature-importance-based pruning.
- XGBoost is applied to Feature Spacecomb to generate the final outlier-detection output.
- Its robustness to data imbalance and overfitting is presented as enhancing runtime efficiency and predictive capability.
- XGBoost’s internal feature importance can support more aggressive TOS pruning after fitting.
D. Theoretical Foundations
The framework interprets outlier-ensemble performance through a bias-variance tradeoff: diverse detectors can reduce variance, but inaccurate detectors may increase bias.
- Outlier ensembles have reducible squared-bias and variance errors that should be controlled together.
- Combining diverse base detectors is treated as variance reduction because it reduces ensemble sensitivity to training data.
- Including inaccurate TOS can increase model bias, helping explain why averaging all TOS does not perform well.
IV. EXPERIMENT DESIGN
The experiments compare outlier-detection frameworks using ROC and Precision@n, repeated trials, and statistical significance testing across the study’s dataset benchmark.
- ROC and Precision@n are used as the two evaluation measures for outlier-detection performance.
- Final scores are obtained by averaging results from 30 independent trials.
- Friedman testing followed by Nemenyi post-hoc testing is used to analyze performance differences among methods.
- The experiment design includes a table summarizing the datasets used in the study.
A. Outlier Datasets
The study evaluates XGBOD across seven public outlier datasets and constructs enhanced feature spaces from multiple unsupervised scoring functions, with experiments testing framework and TOS-selection effects.
- Seven real-world datasets are split into 60% training and 40% testing sets.
- Seven unsupervised outlier scoring functions provide candidate representations, after which pruning selects the most useful ones.
- Experiment I: Experiment I compares frameworks using all TOS or no TOS against Best_TOS, Full_TOS, and other baselines.
- Experiments I and II use 100 base estimators with maximum tree depth set to 3 by default.
- Experiment II: Experiment II evaluates how the number and selection algorithm of TOS affect XGBoost-based prediction.
A. Prediction Performance Analysis
XGB_Comb generally delivers the strongest detection performance, while the benefit of unsupervised representations depends on feature dimensionality, classifier choice, and TOS selection.
- Overall prediction performance: XGB_Comb achieves the best result on six of seven datasets for both ROC and P@N, except Mammography.For Mammography, XGB_Comb is inferior to XGB_Orig; the authors attribute this partly to its six-feature space.
- Overall prediction performance: Unsupervised representation learning is especially useful for high-dimensional datasets such as Arrhythmia, Mnist, and Speech.The reported feature counts are 274 for Arrhythmia, 100 for Mnist, and 600 for Speech.
- Classifier choice: Only XGB_Comb improves over XGB_Orig among the combined-space classifiers, whereas L1_Comb and L2_Comb are inferior on several datasets.L1_Comb and L2_Comb underperform XGB_Orig on Arrhythmia, Cardio, Satellite, and Mnist.
- Overall prediction performance: XGB_Comb outperforms L1_Comb and L2_Comb on both ROC and P@N, improving P@N by more than 10% on four datasets and 23.05% on Speech.L1_Comb and L2_Comb have statistically indistinguishable performance according to the Wilcoxon rank-sum test.
- Number of selected TOS: Using a subset of TOS usually outperforms using all TOS, with best P@N achieved at dataset-specific numbers of selected TOS.For example, Accurate_1 raises P@N from 0.6181 to 0.7307 on Letter and from 0.7673 to 0.8338 on Speech.
- Number of selected TOS: TOS-only representations can outperform original features on Letter and Speech, but their gains are inconsistent and do not fully replace the original features.On Arrhythmia, TOS-only representation has lower ROC than the original feature space despite its stronger t-SNE separation.
C. TOS Selection Method
The study compares three TOS selection strategies and finds that their relative performance depends on dataset and selected-feature conditions. Random Selection is generally riskier, while Accurate and Balance Selection are recommended for lower- and higher-dimensional data, respectively.
- The Friedman test finds no significant selection-method difference on Letter, Cardio, and Mnist, while differences on the other datasets are significant but lack a consistent winner.
- Random Selection can severely degrade performance when only one TOS is selected, reaching 0.1604 on Speech versus 0.1696 without TOS.
- Balance Selection tends to work better on higher-dimensional datasets, whereas Accurate Selection outperforms on datasets with fewer original features.
- Random Selection is generally the riskiest strategy, especially when selecting few TOS, although its heuristic behavior can occasionally produce superior results.
- When more TOS are selected, the three methods become more comparable because their selected TOS increasingly overlap.
D. Limitations and Future Directions
The paper identifies ongoing opportunities to improve TOS extraction, selection, and combination, while concluding that XGBOD improves outlier detection across seven benchmark datasets. Its framework combines unsupervised representations, greedy selection, and supervised ensemble-tree prediction.
- Future work includes selecting features before TOS extraction, adding selection methods, replacing selection with dimensionality reduction, and combining TOS instead of selecting them.
- XGBOD uses unsupervised detectors to improve representations, greedily selects useful TOS, and applies XGBoost on the resulting feature space.
- Across seven outlier datasets, XGBOD achieves markedly improved results compared with competing approaches.
- Using even very few TOS significantly improves outlier detection, while t-SNE visualizations show better separation between outliers and normal observations.
- Compared with other semi-supervised outlier ensembles, XGBOD avoids balanced-subsample construction and averaging, improves execution stability and efficiency, and handles features without scaling or missing-value imputation.