Ensemble models are often accurate enough to deploy but too opaque to act on. Three case studies — medical, financial, industrial — where that gap had real consequences.
A hospital's cardiology department uses an ensemble of decision trees trained on the Heart Disease UCI dataset to screen patients. The model achieves 88% AUC — impressive, but clinically unusable as a black box. Physicians cannot validate, challenge, or communicate a prediction without understanding its basis.
e2tree distils the ensemble's reasoning into a five-leaf decision tree with four interpretable split rules. The tree preserves 91% of the ensemble's proximity structure (measured by eValidation()) while reducing the model to something a cardiologist can recite from memory.
Follow the six steps below, then explore the resulting tree in the interactive panel on the right.
500 trees on 75% of the Heart Disease dataset. proximity=TRUE stores co-occurrence for later use.
createDisMatrix() builds the n×n matrix D from terminal-node co-occurrence across all 500 trees. Each entry encodes how often two patients share a leaf.
One call to e2tree() with depth ≤ 4 and min-node 5. The algorithm selects only the splits that best reconstruct D.
eValidation() confirms the tree reproduces 91% of the ensemble's proximity structure — a high concordance score.
Each path from root to leaf is a complete clinical rule. Click any leaf in the explorer to read it in plain language.
loi() shows which features drove the classification for each individual patient — essential for clinical audit trails.
Click a leaf node or a patient profile below. The full path from root to leaf will animate, and the panel will explain each split in clinical language.
Click a leaf node or patient profile to read the full decision path and its clinical interpretation.
An e2tree is read top-down. At each internal node, the split condition routes the patient left (condition true) or right (condition false). When a leaf is reached, the prediction is the majority class at that node, weighted by ensemble structure.
The purity shown in each leaf (e.g. 87%) is the proportion of training observations that match the predicted class — a direct measure of local confidence. The ensemble purity is always higher than a standard CART tree trained on the same data.
Chest pain type (coded 1–4 by AHA criteria) is the single most informative feature across all 500 trees. Patients with typical angina (type 1) or asymptomatic pain (type 4, coded ≤ 2) follow the left branch; atypical or non-anginal pain goes right. This split alone separates 46% of the cohort with high confidence.
Each branch applies a different secondary criterion. For patients with chest pain ≤ 2, thalassemia type determines structural defect risk. For those with atypical pain, age is the gating factor. This mirrors the clinical heuristic: young patients with atypical symptoms are generally low risk regardless of other features.
The three green leaves represent patients the ensemble consistently routes to low risk, but with different confidence levels: 87% (no pain + normal thalassemia) is the most certain; 73% (normal thalassemia → no blocked vessels) is a softer low-risk call. Confidence tiers guide how aggressively to follow up.
When a patient has mild or no angina but shows a reversible thalassemia defect and at least one blocked major vessel, 81% of training cases in this leaf had confirmed heart disease. This is the highest-confidence actionable rule in the tree, and directly aligns with standard cardiology risk criteria.
Older patients with atypical pain but controlled cholesterol split nearly evenly across the ensemble's trees — 61% purity is the lowest leaf. The e2tree preserves this uncertainty rather than forcing a binary decision — which is exactly right for borderline cases. Those are the patients who need a stress ECG, not a label.
European banking regulation (EBA guidelines, Art. 22 GDPR) requires that automated credit decisions be explainable to applicants on request. A standard ensemble achieves 0.84 AUC on the German Credit dataset, but a compliance officer cannot narrate its logic in an appeal tribunal.
e2tree produces a four-leaf tree that accounts for 89% of the ensemble's proximity structure. Each leaf is a self-contained underwriting rule: "Applicants aged under 30 with no checking account history are low risk if their loan duration is ≤ 18 months" is a statement a compliance officer can defend in writing.
Crucially, e2tree's variable importance ranking reveals that checking account status is the primary discriminator across the ensemble — a finding that would otherwise be buried in 500 trees of opaque split statistics, and that carries direct fairness-audit implications.
No checking account + short loan duration → Good credit (82% purity). The ensemble's strongest low-risk signal.
Overdrawn account + long loan duration → Bad credit (79% purity). Clearest default signal across the ensemble.
Click a leaf or an applicant profile to animate the path and read the rule the model used — ready to paste into a GDPR Art. 22 explanation letter.
Click a leaf or applicant profile to read the decision rule and its compliance interpretation.
summary(tree) outputs each terminal node as an explicit IF-THEN rule that can be quoted verbatim in a GDPR Art. 22 explanation letter to a loan applicant.
vimp() reveals which features the ensemble actually relied on most. If a protected characteristic (age, gender) appears in the top splits, it triggers an immediate bias review.
Because e2tree preserves the ensemble's proximity structure (not just class predictions), the explainability is faithful to the model's actual decision logic — not a post-hoc approximation.
Low-purity leaves directly flag borderline applicants for human review — operationalising the "meaningful human oversight" requirement of automated decision systems.
A manufacturing plant operates 500 CNC machines. An ensemble of decision trees predicts remaining useful life (RUL, in hours) from sensor readings — a regression problem. The ensemble achieves RMSE = 12h on the test set, but maintenance planners need to know which sensor conditions drove a short-RUL prediction.
The regression e2tree partitions the sensor space into four regions with distinct RUL profiles. A maintenance engineer can read the tree and say: "If air temperature is above 305 K and rotational speed exceeds 1450 rpm, schedule maintenance within 24 hours." No data science degree required.
Local Observation Importance (loi()) shows which specific sensors drove the short-RUL prediction for each individual machine — enabling targeted diagnostic interventions rather than blanket shutdowns.
Mean RUL = 142h. Normal operating zone — no immediate intervention.
Mean RUL = 8h. Schedule maintenance immediately.
Click a leaf or a machine profile to animate the sensor path and read the maintenance recommendation — RUL prediction with full context.
Click a leaf or machine profile to read the sensor path and its maintenance recommendation.
The only difference from the classification workflow is the response variable type. e2tree adapts its dissimilarity weighting automatically.
In a regression e2tree, each terminal node predicts the mean response of training observations in that node, weighted by the ensemble's dissimilarity structure. This is analogous to CART regression but guided by ensemble proximity rather than squared-error impurity.
Same structure as classification: IF condition THEN go left, ELSE go right. Multiple splits chain into a path that narrows to a specific operating regime.
The predicted value for a new machine is the mean RUL of the training observations that share its leaf. Leaf width (spread of training RUL values) corresponds to local uncertainty — narrow leaves signal high-confidence predictions.
A leaf with high variance in training RUL values indicates a region where the ensemble was less certain. These are the machines that need additional sensor monitoring, not just a scheduled maintenance date.
loi() reveals which sensor reading most influenced the RUL estimate for each individual machine — a crucial diagnostic insight that no aggregate importance score can provide.
e2tree occupies a unique position: it is not a post-hoc approximation (like LIME or SHAP), nor does it sacrifice predictive power (like plain CART). It is a faithful structural surrogate that preserves the ensemble's logic.
| Method | Interpretability | Faithful to ensemble | Global rules | Regression | No approximation |
|---|---|---|---|---|---|
| e2tree | ✓ Single decision tree | ✓ Structurally | ✓ IF-THEN rules | ✓ | ✓ Exact surrogate |
| Full ensemble (RF) | ✗ Black box | ✓ Is the model | ✗ | ✓ | ✓ |
| Plain CART | ✓ Single tree | ✗ Independent model | ✓ | ✓ | ~ Lower accuracy |
| LIME | ~ Per-instance | ~ Local approximation | ✗ No global rules | ✓ | ✗ Approximates locally |
| SHAP | ~ Feature attributions | ✓ Game-theoretic | ✗ No decision rules | ✓ | ~ TreeSHAP is exact |
| Surrogate tree (naïve) | ✓ Single tree | ~ Prediction-level only | ✓ | ✓ | ✗ Misses structure |
"Faithful to ensemble" means the explainer reflects the ensemble's internal structure (proximity/co-occurrence), not just its output predictions.
Install from CRAN. Five lines of R. One interpretable tree.