stat.MLMar 24, 2026
SaveREALITrees: Rashomon Ensemble Active Learning for Interpretable Trees
Organizations: Department of Statistics, University of Washington · Department of Computer Science, Duke University · Department of Sociology, University of Washington
Abstract
Active learning reduces labeling costs by selecting samples that maximize information gain. A dominant framework, Query-by-Committee (QBC), typically relies on perturbation-based diversity by inducing model disagreement through random feature subsetting or data blinding. While this approximates one notion of epistemic uncertainty, it sacrifices direct characterization of the plausible hypothesis space. We propose the complementary approach: Rashomon Ensembled Active Learning (REAL) which constructs a committee by exhaustively enumerating the Rashomon Set of all near-optimal models. To address functional redundancy within this set, we adopt a PAC-Bayesian framework using a Gibbs posterior to weight committee members by their empirical risk. Leveraging recent algorithmic advances, we exactly enumerate this set for the class of sparse decision trees. Across synthetic and established active learning baselines, REAL outperforms randomized ensembles, particularly in moderately noisy environments where it strategically leverages expanded model multiplicity to achieve faster convergence.
Figures & tables
Figure 1: (Top) REAL leverages noise-induced version-space diversity to maintain superior performance, with its advantage widening until extreme noise floors ( ) equalize all strategies. (Bottom) Under total misspecification ( ), all tree-based QBC strategies underperform relative to Passive Sampling. However, BREAL and UNREAL demonstrate unique resilience, outperforming the other QBC methods and maintaining early-stage efficiency despite the structural misalignment.
Figure 2: Active Learning Efficiency Heatmap ( ) . This figure displays the Efficiency Ratio ( ) of standard baselines relative to REAL, with values below ( Green ) indicating superior sample efficiency for our method. The results demonstrate that REAL reaches peak predictive performance significantly faster than randomized ensembles.
Figure 3: Relative Label Efficiency ( ) across 20 datasets. Each boxplot summarizes the labeling budget required to achieve , , and of the total possible accuracy gain. Values to the left of the dashed line ( ) indicate superior efficiency relative to Random Sampling. Both UNREAL and BREAL maintain a significantly tighter distribution and lower median than standard baselines, demonstrating that characterizing the Rashomon set provides a more reliable and robust path to cost reduction than randomized ensembles or greedy heuristics.
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
| Label | Committee Foundation | Weighting | Diversity Mechanism |
| Random | Random Forest | Uniform | Passive (Random Baseline) |
| QBC-RF ( ) | Random Forest | Uniform | Artificial (Feature Blinding) |
| B-QBC-RF ( ) | Random Forest | Gibbs | Artificial + PAC-Bayesian |
| QBC-RF ( ) | Random Forest | Uniform | Artificial (Bootstrap Only) |
| B-QBC-RF ( ) | Random Forest | Gibbs | Artificial + PAC-Bayesian |
| Uncertainty | Optimal Sparse Tree | — | Greedy |
Table 1: Overview of evaluated active learning configurations. We categorize strategies by their committee foundation and weighting scheme to isolate the performance gains of structural version-space characterization from those of PAC-Bayesian posterior weighting.
| No. | Dataset | Src | Maj% | Lin% | GBM% | Orc% | ECS | |||
| 1 | Anneal | UCI | 812 | 44 | 96.2 | 100.0 | 100.0 | 100.0 | 2 | 2.0 |
| 2 | Bank Marketing | UCI | 4,521 | 23 | 97.1 | 97.7 | 98.1 | 97.7 | 19,024 | 19,023.9 |
| 4 | Bar-7 | SOR | 1,913 | 14 | 79.0 | 79.0 | 79.0 | 79.0 | 174,331 | 174,328.0 |
| 5 | Breast Cancer WI | UCI | 699 | 10 | 91.3 | 91.4 | 91.8 | 91.3 | 116,263 | 116,260.4 |
| 6 | Car Ealuation | UCI | 1,728 | 15 | 66.7 | 79.3 | 79.3 | 79.3 | 128,546 | 128,544.6 |
| 7 | Cheap Restaurant | SOR | 2,653 | 15 | 81.8 | 96.8 | 96.8 | 95.9 | 572 | 572.0 |
Table 2: Datasets.
Figure 4: Active Learning Benchmarks. Accuracy traces across 20 real-world and structured datasets. UNREAL (Weighted and Uniform) consistently match or exceed baseline performance, demonstrating superior sample efficiency particularly in the early stages of the labeling process.
| Baselines | QBC-RF | Weighted RF | REAL (Proposed) | |||||||
| Dataset | Random | Uncertainty | Coreset | F=3 | F=Sqrt | F=All | F=Sqrt | F=All | UNREAL | BREAL |
| Synth. Xor Baseline | 137.4 | 80.7 | 98.0 | 162.2 | 164.7 | 159.4 | 137.5 | 140.3 | 2960.0 | 3035.0 |
| Synth. Xor Phi 05 | 168.2 | 113.2 | 119.7 | 196.0 | 196.0 | 197.4 | 176.3 | 177.1 | 3014.6 | 3050.2 |
| Synth. Xor Phi 10 | 186.3 | 135.2 | 135.0 | 215.9 | 215.4 | 217.8 | 195.6 | 192.3 | 3052.7 | 3043.3 |
| Synth. Xor Phi 25 | 259.4 | 203.3 | 210.6 | 286.7 | 284.1 | 287.1 | 262.8 | 266.1 | 2940.8 | 2875.1 |
| Synth. Xor Phi 45 | 294.1 | 238.5 | 246.7 | 318.3 | 315.3 | 321.2 | 293.2 | 299.3 | 1674.9 | 1661.3 |
Table 3: Median experiment runtime (seconds) across 25 simulation seeds. UNREAL and BREAL denote the standard and Bayesian variants of the UNREAL algorithm, respectively.
Figure 5: Committee Size History. Evolution of the Rashomon Effective Committee Size over active learning iterations across 20 benchmark datasets. The ECS serves as a metric of model certainty, quantifying the diversity of plausible theories within the version space as the learner explores the data manifold. A high ECS reflects a broad set of competing hypotheses, while values approaching indicate the emergence of a single dominant structural explanation.
Figure 6: Rashomon Set Size Evolution. The total count of near-optimal models identifying the -version space during each iteration. These trajectories illustrate how acquiring specific labels prunes the hypothesis space, revealing the sensitivity of model multiplicity to new evidence across diverse dataset geometries.
Figure 7: Tree Edit Distance Benchmarks. Evaluation of the alignment between the decision logic of the learned hypotheses and the ground-truth Oracle tree. A lower distance indicates that BREAL is not merely achieving predictive success through spurious correlations, but is successfully recovering the true underlying structural logic of the task.
Figure 8: Oracle Agreement Benchmarks. Tracking consensus between the active learning committee and a ground-truth "Oracle" (optimal sparse tree fitted to the full dataset). In high-multiplicity environments, Weighted UNREAL achieves higher-fidelity alignment significantly faster than randomized baselines, demonstrating that its structural uncertainty signal successfully identifies the primary decision boundaries defining the task logic.
Figure 9: Trace Plots on Parity Datasets. In high-dimensional sparse regimes ( , up to 26 noise covariates), all tree-based active learning strategies perform below Passive Sampling as noise-induced patterns dominate. As we increase the number of noisy, useless covariates, QBC-RF becomes increasingly confused by stochastic variance, whereas REAL variants demonstrate superior recovery. By focusing its query strategy on the effective version space, REAL resolves the sparse 3-bit XOR signal more reliably than QBC-RF, eventually matching the accuracy of the other baselines and exceeding the performance of randomized ensembles.