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Explainable Unsupervised Anomaly Detection with Random Forest

T0 review · 2 major / 7 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A random forest trained to tell real data from uniform synthetic noise learns distances that flag anomalies more accurately than common detectors.

desk verdict Worth a look for the RFuni distance idea and the honest benchmark reporting, but the headline 'large number of datasets' claim is more fragile than it looks once you see what got excluded. read the letter →

arxiv 2504.16075 v1 pith:TB2ZPMGP submitted 2025-04-22 stat.ML cs.LG

Joshua S. Harvey , Joshua Rosaler , Mingshu Li , Dhruv Desai , Dhagash Mehta This is my paper · ORCID
classification stat.MLcs.LG
keywords unsupervisedanomalydetectionrandomforestsimilaritylearningGAPproximitycounterfactualexplanationsfeatureimportanceADBenchmissingdata
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes a fully unsupervised anomaly detector built from a Random Forest that is trained to tell real data apart from synthetic data drawn uniformly over the observed feature bounds. The claim is that the resulting RFuni distances anisometrically reshape the data, pulling inliers closer together and pushing boundary points farther out, and that this transformation makes outlier detection more accurate than common unsupervised detectors across 26 benchmark datasets. The approach needs almost no preprocessing, tolerates missing values, and can be packaged with a local explanation mechanism that attributes outlier scores to specific feature changes.

What carries the argument

The load-bearing component is the RFuni representation: a Random Forest trained to discriminate real data from synthetic data sampled uniformly over the ranges of the real features, the scheme originally called Addcl2. Distances are computed from the forest's leaf structure using geometry- and accuracy-preserving (GAP) proximities, which weight in-bag and out-of-bag co-locations differently so that the distances reconstruct the forest's prediction geometry. Outlier scores are then taken as the median GAP distance from each point to the subset of points with the lowest median distances, a hyperparameter-free centrality measure. For explanations, the gradient of the outlier score field yields counterfactual trajectories, and feature importance is read from which forest partition hyperrectangles each trajectory segment crosses.

What would settle it

Run the same unsupervised anomaly detection comparison on all 47 ADBench datasets without exclusions, using the dataset labels as ground truth, and check whether RFuni still shows a statistically significant edge over the other detectors; alternatively, test RFuni specifically on the nine excluded datasets and see whether it loses its advantage there.

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Extended reading notes

Core claim

The central discovery is that training an unsupervised Random Forest against uniformly distributed synthetic data yields a similarity measure that is not metric-preserving: it deliberately expands distances at the boundary of the data manifold while compressing them near the bulk. The paper shows that outlier scores computed from these GAP distances, taken as the median distance to the most central half of the data, rank anomalies more accurately than distances learned by ExtraTrees or Euclidean baselines, and they outperform about half of the standard detectors in a benchmark comparison at the 0.1 significance level. The same forest partitions then serve as a basis for counterfactual explanations, because each trajectory that reduces an outlier score can be decomposed into the hyperrectangular partitions it crosses.

Load-bearing premise

The comparison that establishes superiority rests on excluding nine ADBench datasets whose anomaly labels the authors judge not to represent genuine anomalies, plus all datasets with fewer than 1,000 rows; if those exclusions are not defensible, the claimed advantage may not hold on the full benchmark.

Editorial extensions

If this is right

  • RFuni can be applied to raw datasets with categorical features and missing values, reducing the need for dataset-specific preprocessing in automated pipelines.
  • The learned distances support low-dimensional visualization via multidimensional scaling, making the boundary-expanding geometry directly inspectable.
  • Up to 60% missing-at-random data, RFuni remains competitive provided missing values are mean-imputed first, and it can also run natively on data with missing entries.
  • Feature importance for a detected anomaly can be read from the forest partitions crossed by a counterfactual trajectory, yielding local, model-native explanations.
  • The advantage is attributable to the RFuni transformation itself: applying the same outlier-scoring rule to Euclidean distances behaves like ExtraTrees, not like RFuni.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The boundary-expanding property might generalize beyond RFuni's specific scoring rule, so any distance-based detector applied to RFuni distances should inherit the improved separation of outliers.
  • Because RFuni is sensitive to absolute feature values rather than ranks, monotone feature transformations should change its behavior predictably, offering a direct experimental handle on the mechanism.
  • Using percentile-based bounds instead of raw data bounds for the uniform synthetic samples could make the method robust to extreme-value contamination, a limitation the paper explicitly flags.
  • The partition-crossing explanation could be adapted to any tree ensemble, including supervised forests, as a way to explain model predictions via geometric feature attributions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 7 minor

Summary. The paper describes RFuni, an unsupervised anomaly detection pipeline that (i) trains a random forest to discriminate between the observed data and synthetic points drawn from a uniform distribution over the observed feature bounds (the 'Addcl2' protocol of Shi and Horvath), (ii) computes geometry- and accuracy-preserving (GAP) random-forest distances from leaf co-occurrence, and (iii) scores each point by its median GAP distance to the most central 50% of the sample, with centrality defined by each point's median GAP distance to all other points. The paper's central claim, stated in the abstract, is that RFuni distances improve unsupervised anomaly detection accuracy relative to distances from ExtraTrees and relative to 13 standard unsupervised detectors, as demonstrated on a curated subset of the ADBench benchmark (26 of 47 datasets). Supporting analyses include a two-dimensional toy model demonstrating that RFuni anisometrically expands the boundary of the data manifold (with ExtraTrees distances approximating Euclidean distances), a missing-data robustness study under MCAR up to 60% missingness, and an explainability method that constructs counterfactual trajectories along the local gradient of the outlier score and attributes feature importance by counting random-forest partition crossings along each trajectory, illustrated with an MNIST digit-4-versus-digit-9 experiment.

Significance. If the benchmark claim survives scrutiny, the contribution is meaningful: RFuni is an off-the-shelf detector that needs no per-dataset feature scaling or categorical encoding, runs on data with missing values, and can attach local counterfactual explanations to predictions, which few proximity-based unsupervised detectors offer. The evaluation has real strengths: the Euclidean-distance control with the identical scoring function isolates the effect of the RFuni transformation; the main comparison uses Wilcoxon signed-rank tests and a Friedman/Conover post-hoc analysis with Holm-Bonferroni correction; and the excluded-dataset results are reported in full (Table 1) rather than hidden. The toy-data analysis (Spearman rank correlations, MDS stress, distance histograms) provides concrete evidence for the claimed geometric mechanism. The main risk is selection dependence: the 26-dataset benchmark is chosen by criteria that are partly subjective and, by the paper's own Table 1, partly correlated with poor RFuni performance; on the full ADBench the headline claim may not hold. This is fixable within the scope of a revision.

major comments (2)
  1. [Sec. 2.4, App. 6.1, Table 1] The central benchmark claim is established only on 26 of the 47 ADBench datasets, and the exclusion is not performance-neutral. From the paper's own Table 1, on the ten excluded datasets with at least 1,000 samples (ALOI, Cardiotocography, Fault, InternetAds, Landsat, Magic.gamma, Optdigits, Skin, SpamBase, Yeast), RFuni's AUCROC is below at least three of the five comparison detectors on seven of the ten datasets (notably Skin 0.35 vs KNN 0.72/IForest 0.67; SpamBase 0.49 vs KNN 0.73; Optdigits 0.45 vs COPOD 0.70; InternetAds 0.56 vs KNN 0.69; Fault 0.46 vs KNN 0.73; Magic.gamma 0.69 vs KNN 0.77; Yeast 0.39 vs LOF 0.46). The statement in Sec. 2.4 that 'no significant differences' were observed among detectors on excluded datasets is not sufficient to neutralize this: with 21-22 datasets and many detectors, the test is underpowered, and the claim does not address RFuni's median rank or the Conover/Holm-Bonferroni comparison specifically. Because the abstract's claim is a benchmark claim, the paper should report the full pairwise comparisons on all 47 ADBench datasets (or on a standard, pre-specified subset of ADBench) and show RFuni's rank distribution on included versus excluded datasets; otherwise the headline result cannot be distinguished from a selection effect.
  2. [App. 6.1, Sec. 2.4] The exclusion protocol is not auditable and contains a performance-based criterion. Appendix 6.1 lists three exclusion categories '# Samples', '% Anomalies', and 'Dataset', but no thresholds are provided for sample size or anomaly proportion, and dataset-specific reasons are given for only two datasets (Optdigits and ALOI, footnote 5). The ALOI justification is explicitly outcome-based ('almost all unsupervised detectors performed below chance on this dataset'); excluding a dataset because detectors fail on it is circular in a benchmark whose purpose is to evaluate detectors, and it removes precisely the kind of data on which the claim could fail. There is also a numerical inconsistency: the text states that nine datasets were excluded on label-quality grounds and that size filtering leaves 26 of 47 datasets, which implies 21 excluded datasets, while Table 1 lists 22 excluded datasets; these counts must be reconciled. In addition, the size-exclusion justification cites a paper on conformal out-of-distribution evaluation ([Novello et al., 2024]), which does not establish that AUCROC comparisons on datasets with fewer than 1,000 points are invalid. I ask the authors to replace the current post-hoc protocol with a pre-specified, data-independent inclusion rule (e.g., minimum anomaly count and maximum anomaly proportion chosen before looking at results), or to present the full-ADBench analysis as primary and the 26-dataset analysis as a sensitivity check.
minor comments (7)
  1. [Sec. 3.2, Fig. 2.b] The cross-detector comparison is reported at a lenient significance level (α=0.1 in both the Conover post-hoc table and the critical-difference diagram), and the Friedman test statistic that justifies the post-hoc analysis is not reported; the authors should state whether the claim that RFuni is significantly better than half of the other detectors survives α=0.05.
  2. [Sec. 2.3] The definition of Xcentral and O(xi) does not explicitly exclude the self-distance (which is zero in Eq. (2)); because xi belongs to Xcentral for many points, the median distance to Xcentral can include this zero, and the paper should state whether self-distances are excluded and confirm the result is insensitive to this choice.
  3. [Sec. 2.2, 2.3, 3.4] The random-forest configuration (number of trees, split criterion, minimum samples per leaf), the number of synthetic points used to train RFuni, the neighborhood size k in the gradient estimate, and the trajectory learning rate l are not reported; for a benchmark paper, a reproducibility table with these values, software versions, and code (or a code repository) is needed.
  4. [Sec. 3.3, Fig. 3.b] The normalization in Fig. 3.b (AUCROC relative to the best detector on complete data) conflates absolute degradation with relative ranking; reporting absolute AUCROC, or normalizing each detector to its own complete-data performance, would make the missingness comparison more interpretable.
  5. [References] The references 'Rhodes et al., 2023a' and 'Rhodes et al., 2023b' are the same publication listed twice, and only the 2023b entry is cited in the text (Sec. 2.2); the duplicate entry should be removed and the in-text citation reconciled.
  6. [Sec. 4] The discussion acknowledges that RFuni is sensitive to extreme values that determine the uniform bounds and proposes percentile-based bounds as a mitigation, but no experiment quantifies this sensitivity; given the abstract's claim of minimal preprocessing, an experiment comparing bound-based and percentile-based synthetic sampling would strengthen the robustness story.
  7. [Sec. 3.2, Fig. 2 captions] Typos and caption artifacts: 'maximnum' should be 'maximum' in Sec. 3.2, and the label 'LODASOD COF' in the Fig. 2.a(i) axis appears to be a rendering artifact; these should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the outlier score is computed from an unsupervised distance transform and validated against external ADBench ground-truth labels.

full rationale

The paper's derivation chain is self-contained and empirically grounded. The RFuni model is trained without using anomaly labels: synthetic data are drawn uniformly over the real data bounds (Sec. 2.1), and the random forest learns to discriminate real from synthetic examples. Distances are then computed using the externally published GAP proximity method (Eq. 1-2, citing Rhodes et al. 2023), and outlier scores are computed from median distances to the most central 50% of the data (Sec. 2.3). No parameter is fitted to the ground-truth anomaly labels, and the scoring hyperparameters are fixed rather than tuned to the benchmark. The central performance claim is evaluated against the held-out ADBench ground-truth labels, and the paper includes a control showing that the same scoring procedure applied to Euclidean distances behaves like ExtraTrees, isolating the RFuni transformation as the source of improvement. The authors' exclusions of datasets are transparently reported in Table 1 and are a benchmark-composition concern, not a circularity: excluding datasets does not make the method's output equivalent to its input. The toy demonstration designates outliers as points at the 90th percentile of distance from the center, so the observation that RFuni exaggerates distances for those points is partly self-referential, but it is illustrative and not load-bearing for the main benchmark claim. There are no load-bearing self-citations, no imported uniqueness theorems, and no ansatz smuggled in via citation. Overall, no significant circularity is present.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The method rests on known results (GAP proximities, ADBench labels) and on the choice of uniform synthetic sampling; no new entities are introduced. The main hand-chosen settings are the central-50% scoring threshold and unstated random forest hyperparameters.

free parameters (3)
  • Proportion of central data used for scoring = 0.5
    The outlier score is the median GAP distance to the most central 50% of observations; this threshold is chosen by hand without sensitivity analysis (Sec. 2.3).
  • Random Forest hyperparameters = not reported
    Number of trees, maximum depth, minimum samples per leaf, and other RF settings are not stated; performance could vary with these choices.
  • Trajectory learning rate l = not reported
    Used for counterfactual trajectories in explainability (Sec. 3.4), not central to detection performance.
assumptions (3)
  • domain assumption GAP proximities recover geometry and predictive accuracy of the random forest
    Equations (1) and (2) are taken from Rhodes et al. (2023) and assumed valid for computing distances from random forest leaf indices.
  • domain assumption ADBench ground-truth labels correctly identify anomalies
    The evaluation treats provided labels as ground truth; the paper itself notes that some labels (e.g., the 'optdigits' zero class) may not represent true anomalies, leading to exclusions.
  • domain assumption Uniform synthetic data bounds are determined by observed data and sufficiently cover the data manifold
    Synthetic data is sampled uniformly over empirical bounds; if extreme outliers set bounds, most synthetic mass lies far from real data (acknowledged in Sec. 4).

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Cite this review

Pith. "Pith review of Explainable Unsupervised Anomaly Detection with Random Forest." pith.science (2026). https://pith.science/paper/TB2ZPMGP

@misc{pith2026250416075,
  author       = {Pith},
  title        = {Pith review of: Explainable Unsupervised Anomaly Detection with Random Forest},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TB2ZPMGP}},
  note         = {Machine review of arXiv:2504.16075}
}
read the original abstract

We describe the use of an unsupervised Random Forest for similarity learning and improved unsupervised anomaly detection. By training a Random Forest to discriminate between real data and synthetic data sampled from a uniform distribution over the real data bounds, a distance measure is obtained that anisometrically transforms the data, expanding distances at the boundary of the data manifold. We show that using distances recovered from this transformation improves the accuracy of unsupervised anomaly detection, compared to other commonly used detectors, demonstrated over a large number of benchmark datasets. As well as improved performance, this method has advantages over other unsupervised anomaly detection methods, including minimal requirements for data preprocessing, native handling of missing data, and potential for visualizations. By relating outlier scores to partitions of the Random Forest, we develop a method for locally explainable anomaly predictions in terms of feature importance.

Figures

Figures reproduced from arXiv: 2504.16075 by the authors.

Figure 1
Figure 1. Embedding two-dimensional Gaussian data with unsupervised RF distances. A) i) Data simulated from a two-dimensional Gaussian distribution. Points with distances from the origin above the 90th percentile are colored red (outliers). ii) A matrix of Euclidean distances, sorted by each point’s distance from the origin. B) Distance matrices for Random Forest GAP distances obtained from the (i) RFuni and (ii) ExtraT rees … view at source ↗
Figure 2
Figure 2. Anomaly detection performance on benchmark datasets. A) Direct comparison between anomaly detectors distances from either the ExtraTrees or RFuni Random Forest model, aggregated across benchmark datasets. Comparisons of i) ranking amongst other unsupervised detectors, ii) AUCROC score, and iii) percent of AUCROC score achieved by best performing detector for each dataset. p-values indicate result of a Wilcoxon signe… view at source ↗
Figure 3
Figure 3. Anomaly detection performance with missing data. A) The performance of RFuni and other top-performing unsupervised anomaly detectors with missing data on the Campaign dataset, evaluated with AUCROC. All detectors were tested on data imputed with the mean (dashed lines), while RFuni was also applied directly on missing data (solid line). Shaded area indicates standard deviation over 5 repeats. B) Aggregate performanc… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Explainability of RFuni anomaly detector outlier scores. A) A trajectory through the outlier gradient field on two-dimensional Gaussian data. Gradients are shown in red arrows. B) The same trajectory visualized in an MDS embedding of GAP distances computed from the RFu…
Figure 5
Figure 5. Figure 5: d visualizes the importance of each pixel to the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 5
Figure 5. Figure 5: Explainable anomaly detection with the MNIST dataset. A) The trajectory from an anomaly (digit 4, red) to inliers (digit 9, blue) in the MNIST dataset, visualized in a t-SNE embedding of the input data. B) The same trajectory visualized in an MDS embedding of GAP dista…
Figure 5
Figure 5. Figure 5: e-f. References L. Auret and C. Aldrich. Unsupervised process fault detection with random forests. Industrial & Engineering Chemistry Research, 49(19):9184–9194, 10 2010. doi:10.1021/ie901975c. D. Baron and D. Poznanski. The weirdest sdss galaxies: results from an outl…

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.