Surrogate Interpretable Graph for Random Decision Forests

Akshat Dubey; Aleksandar An\v{z}el; Georges Hattab

REVIEW 4 major objections 6 minor 63 references

Surrogate Interpretable Graph for Random Decision Forests

T0 review · 4 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that a random forest can be reduced to a pruned feature-co-occurrence graph that gives global, human-readable explanations and stays practical where TreeSHAP becomes infeasible.

desk verdict A plausible visualization pipeline for summarizing RF decision rules as a graph, but the central scalability claim over TreeSHAP rests on a non-proof and the evaluation is too thin to support it. read the letter →

arxiv 2506.01988 v1 pith:6S2NJRY7 submitted 2025-05-17 cs.LG cs.AI

Akshat Dubey , Aleksandar Anžel , Georges Hattab This is my paper · ORCID

classification cs.LGcs.AI

keywords randomforestsfeatureinteractionsglobalinterpretabilityexplainableAImixed-integerlinearprogrammingruleextractionhealthinformaticsShapleyvalues

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

The paper proposes the surrogate interpretability graph (SIG), a pipeline that converts a trained random forest into a small directed graph whose nodes are features and whose edges record how often features appear together in the forest's decision rules. The goal is to give clinicians and domain experts a global, readable account of which feature interactions drive predictions, summarized as a table of decision-feature interactions (DFIs). The paper claims that this graph, pruned by mixed-integer linear programming with a user-set edge budget, stays interpretable and computationally practical precisely in high-dimensional health datasets where TreeSHAP interaction values become infeasible. If the claim holds, SIG offers a path to transparent explanation of tree ensembles without per-instance Shapley computations.

What carries the argument

The central object is the surrogate interpretable graph (SIG): a weighted directed graph whose nodes are features and whose edges record how often two features appear together along ordered decision paths. The load-bearing mechanism is the co-occurrence count over ordered feature pairs in extracted rules, combined with TF-IDF weighting of tokenized rules, agglomerative clustering to merge redundant rules, and a mixed-integer linear program that selects a small edge set while preserving path structure. The final DFI table lists the resulting dominant chains, such as $f_{10}\rightarrow f_{13}\rightarrow f_{12}\rightarrow f_{1}\rightarrow f_{14}$, as the model's hierarchical feature interactions.

What would settle it

Compute the full unpruned co-occurrence graph from a forest's extracted rules and compare it with the MILP-pruned SIG: if a feature appears in a majority of decision paths but is absent from the pruned graph, or if the dominant feature chains change materially when the edge budget is changed, then the claim that SIG captures the dominant global interactions is falsified.

Watch

Extended reading notes

Core claim

The central claim is that global feature interactions of a random forest can be faithfully captured by counting ordered feature co-occurrences along extracted decision paths, then compressing that co-occurrence structure into a sparse directed graph. After rules are tokenized, weighted with TF-IDF, clustered, and pruned by a MILP edge-selection objective, the resulting SIG identifies a small number of dominant decision-feature interactions, such as ten for the chronic kidney and heart datasets, six for the air-quality health dataset, five for diabetes, and four for Alzheimer's. The paper also argues, with an asymptotic comparison, that TreeSHAP's per-instance interaction computation grows quadratically in the number of features while SIG's cost remains sublinear or constant after rule extraction, making SIG the scalable option when feature counts explode.

Load-bearing premise

The whole method rests on the assumption that co-occurrence of features along decision paths, after clustering and pruning, faithfully reflects the most important global feature interactions.

Editorial extensions

If this is right

A forest's global behavior can be compressed to a graph whose edge count is chosen by the user, so explanation size stays bounded regardless of dataset size.
The DFI table gives ordered feature chains, revealing which features act as origins, intermediates, and endpoints in the forest's decision paths.
Runtime stays low after the one-time rule extraction, whereas TreeSHAP's interaction computation grows as the square of the feature count and becomes impractical for wide clinical or molecular datasets.
The same graph can be regenerated for different forests or datasets, making global interpretability a reusable artifact rather than a per-instance calculation.
Because the graph names the actual features and rules, it can be audited by non-experts, which helps meet transparency expectations in high-stakes health applications.

Reading between the lines

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

If faithfulness holds, the MILP edge budget can be tuned as a completeness-versus-simplicity dial; one could test whether features excluded from the pruned graph ever carry prediction-critical interactions.
Replacing the TF-IDF and clustering stages with direct frequency counts of co-occurring feature pairs would reveal whether the NLP-style weighting changes the recovered graph, a testable robustness check.
Applying the pipeline to gradient-boosted trees, which the paper names as future work, would test whether the ordered chains survive boosting's sequential re-weighting of trees.
A clinician-facing user study, which the paper notes is absent, could settle whether the graph's hierarchies actually improve trust and decision-making in practice.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

Short version: this is a reasonable pipeline for turning random forest decision paths into a pruned graph and a per-interaction table, but the central claim about scalability over TreeSHAP is not supported. The appendix that is supposed to prove it doesn't derive SIG's complexity at all; it writes down TreeSHAP's O(N T L^2 + N f^2) and then notes the limit as f goes to infinity is infinite. That tells us nothing about SIG's end-to-end cost. If anything, the agglomerative clustering (O(R^2) or worse) and the MILP over O(f^2) candidate edges look like they could dominate.

What's genuinely useful: the specific integration — rule extraction, TF-IDF, clustering, MILP pruning, and the DFI table — reads as a coherent recipe, even if every ingredient is in the literature. The DFI table is a nice concrete artifact for documentation and screening, and the limitations section is honest about not having user studies. The citation list covers SIRUS, Forest-ORE, feature graphs, and TreeSHAP-IQ, so the authors are at least working in the right neighborhood.

Soft spots beyond the non-proof: the runtime chart has no error bars and no stated hyperparameters, MILP solver, or edge-budget rationale; the text admits budgets like 15, 5, 20 were adjusted after seeing results. The dominant DFIs are summaries of the same rules that were extracted to build the graph, so calling them findings about the data is circular — they are findings about the method's own construction. That is acceptable for a descriptive summary tool, but the paper claims more. And there is no comparison to the rule-extraction baselines it cites, which is a real gap if the pitch is "better interpretability."

Who is this for? A health analyst who wants a visual, global snapshot of what an RF is doing, for documentation or screening, could get value from the pipeline once it is cleaned up. A reader looking for a rigorous complexity result or validated interpretability should look elsewhere.

Recommendation: I would not send this to peer review in its current form. The headline claim is load-bearing and unsupported, and the evaluation is too thin. A desk reject with an invitation to resubmit after the complexity analysis is actually derived, the runtime study is properly configured with error bars and hyperparameters, and a baseline comparison is added would be the right call. If those pieces land, the idea could deserve referee time.

Referee Report

4 major / 6 minor

Summary. The paper proposes the Surrogate Interpretable Graph (SIG), a pipeline for global feature-interaction analysis in random forests. The pipeline extracts decision rules from trained trees (Algorithm 1), tokenizes and TF-IDF-encodes them (Algorithms 2–3), clusters rules via agglomerative clustering (Algorithm 4), and then builds a directed weighted graph whose edges are pruned by a mixed-integer linear program (Algorithm 5). The output is a sparse graph, a per-decision-feature-interaction (DFI) table, and a set of hierarchical feature-interaction chains. The authors compare SIG with TreeSHAP, claiming that SIG scales gracefully in high-dimensional healthcare datasets where TreeSHAP becomes infeasible, and they present a runtime comparison on five health datasets. The paper includes appendices with a 'mathematical proof' of TreeSHAP's quadratic-in-features complexity, additional experiments, and dataset descriptions.

Significance. The goal of the paper is worthy: a compact, global, rule-grounded visualization of feature interactions in random forests would be a useful interpretability tool for high-stakes healthcare applications. The proposed pipeline is concrete and the authors make an explicit attempt to compare against TreeSHAP, a standard baseline. The strength of the paper is its clear algorithmic skeleton (Algorithms 1–5) and the framing of the output as a human-readable graph and DFI table, with a stated intention to avoid the per-instance complexity of TreeSHAP. However, the central claims are not established. No end-to-end complexity of the SIG pipeline is derived; the MILP is not specified in enough detail to be reproduced or to justify the pruning choices; the reported DFI 'findings' are summary statistics of the same rules the method extracts, with no external validation; and the runtime comparison lacks necessary experimental detail. If the scalability claim and the objectivity of the MILP pruning were rigorously established, the contribution would be significant; in its current form, the paper is a description of a heuristic with hand-set parameters and unsupported performance conclusions.

major comments (4)

[Appendix A] The 'mathematical proof' does not establish any scalability advantage for SIG. Equation (A.1) states Time_TreeSHAP = O(N·T·L^2 + N·f^2) and then computes lim_{f→∞} Time_TreeSHAP = ∞, but it never defines or bounds the runtime of the SIG pipeline (Algorithms 1–5). The pipeline includes agglomerative clustering on an R×V TF-IDF matrix (at least O(R^2 log R) in typical implementations, and O(R^2·V) without special methods) and a MILP whose candidate edge set can be as large as O(f^2) binary variables. Table 14's entry 'Sublinear if rules are sparse and compressible' is an assumption, not a derived result. Consequently, the central claim in the Introduction and Conclusion that 'the effective complexity remains lower in practical high-dimensional scenarios, regardless of the dataset size' is unsupported by the provided analysis.
[Algorithm 5 / Section 3.5] The MILP formulation is not sufficiently specified to be reproducible or to justify the claim that it 'preserves the connection with the most information.' The objective is only stated as 'minimize total selected edges' and the constraints are named ('path consistency,' 'DAG constraint') without equations. There is no coverage term that ties selected edges to the frequency of co-occurrence in the clustered rules, so minimizing the edge count alone could select an arbitrary sparse subgraph. The edge budgets are hand-chosen per dataset (15, 5, 20), and the paper itself reports that for the diabetes and Alzheimer's datasets the initial budget of 15 edges caused 'over-optimization.' The DFI counts and hierarchical interactions therefore depend directly on arbitrary thresholds, and the reported 'dominant' interactions are not robust findings.
[Section 4, Tables 3–6] The conclusions about which features are 'responsible for the decision' or are the 'most important interacting features' are derived from co-occurrence frequencies of features in the same rules extracted from the random forest. These are descriptive summaries of the method's own construction, not validated interaction effects. The statement that 'the number of unique DFIs is 10, which also shows that the number of estimators chosen for the RF classifier, i.e., 15, is optimal' is a non sequitur: the number of DFIs is an output of the pipeline and cannot by itself establish the optimality of n_estimators. Without external validation—for example, comparison with interaction importance measures on held-out data, permutation tests, or domain-expert evaluation—the DFI tables do not support the paper's interpretive claims.
[Figure 7] The runtime comparison between SIG and TreeSHAP is not sufficient to support the scalability claim. The figure has no error bars, no confidence intervals, and no reporting of the number of runs. Crucially, the experiment omits essential hyperparameters: the number of estimators and maximum depth of the random forest, the cluster count k used in Algorithm 4, the MILP solver and its time limit, and the exact TreeSHAP implementation and settings. Without these details, the reader cannot determine whether the plotted runtimes reflect algorithmic complexity or particular solver/configuration choices. A table with the actual runtime values and the hyperparameter settings should be provided before any performance comparison is claimed.

minor comments (6)

[Section 3.2] The algorithm numbering is inconsistent: Section 3.2 refers to 'Algorithm 3' for the tokenization and standardization step, but the caption for that step is Algorithm 2, while Algorithm 3 is TF-IDF encoding in Section 3.3.
[Section 2, SII formula] The Shapley Interaction Index formula contains a malformed set notation: 'T⊆\S' should be written as a set complement, e.g., 'T ⊆ S^c' or 'T ∩ S = ∅' as stated below; the current notation is confusing and likely a typesetting error.
[Tables 3, 5, 8, 10, 12] The DFI tables appear as empty headers in the manuscript; the filled cells that indicate feature usage are not visible. Since these tables are a core result, the actual entries must be included in the printed version.
[Throughout] There are numerous typographical and terminology issues, including 'spatial interpologram' (Section 4), 'signed graph' and 'sign' for the graph, 'Cholestrol', 'ontribute', and inconsistent use of the abbreviation GRF for both 'Generalized Random Forests' and 'Graph Random Forest'.
[Section 3.4] The heuristic for choosing the number of clusters—'the square root of f + N, rounded to the nearest perfect square'—is not justified and is ambiguously stated; a perfect-square rounding rule is not standard and should be replaced by a data-dependent criterion or a sensitivity analysis.
[Appendix A] The claimed complexity bound Time_TreeSHAP = O(N·T·L^2 + N·f^2) is stated without a citation or derivation; reference [25] ('Linear Tree SHAP') is not an obvious source for this interaction-time bound, and the bound should be attributed or proven.

Circularity Check

2 steps flagged · score 5.0 of 10

DFI 'findings' are outputs of hand-set cluster and edge-budget hyperparameters, and the SIG scalability advantage is assumed in Table 14 rather than derived; no self-citation chain is load-bearing.

fitted input called prediction [Section 3.5 (Algorithm 5), Section 4 (CKD), Section B.2 (Diabetes)]
"The weight of the edge is equal to the frequency of co-occurrence in clustered rules. ... The constraints are the number of edges k to reduce the visual load. ... From the SIG (Figure: 4), we can conclude that there are 10 major DFIs ... The number of unique DFIs is 10, which also shows that the number of estimators chosen for the RF classifier, i.e., 15, is optimal. ... The reason for over-optimization was the threshold we chose during optimization (15 edges). Only 4 features satisfied the criteria, resulting in a very simple SIG. Hence ... maximum number of edges was 5."

The graph edges are defined as co-occurrence counts, and the final graph is the solution of a MILP whose stated objective is to minimize total selected edges under a user-supplied edge budget. The paper itself shows that changing the budget from 15 to 5 changed the diabetes graph from 4 features to a different structure, so the DFI tables and counts are functions of hand-set cluster counts and MILP edge limits. The reported '10 major DFIs' and the claim that 15 estimators are optimal are therefore outputs of the pipeline's own hyperparameters, not independent empirical findings; the hyperparameter is read back as a discovered property of the model.
other [Introduction, Appendix A, Table 14]
"In contrast, the SIG pipeline extracts rules once, vectorizes and clusters them, and constructs a feature-interaction graph that is optimized via MILP. The effective complexity remains lower in practical high-dimensional scenarios, regardless of the dataset size (Figure: 7). ... TimeTreeSHAP = O(N·T·L^2 + N·f^2). ... SIG ... Time vs feature size: Sublinear if rules are sparse and compressible."

Appendix A derives only the TreeSHAP bound and then takes the limit f to infinity; it never states or bounds SIG's runtime. The only SIG complexity statements are conditional assumptions in Table 14, namely 'Sublinear if rules are sparse and compressible' and 'Constant (after rule extraction)'. The introduction then reports those assumed conditions as an established comparative result: 'effective complexity remains lower ... regardless of the dataset size'. The claimed advantage thus restates Table 14's hypothesis as a proven conclusion rather than deriving it from the paper's equations.

full rationale

The paper does not rely on a load-bearing self-citation or on an imported uniqueness theorem, so the self-citation patterns are not the main issue. However, two central claims are not independent of their own inputs. First, the 'dominant' DFI tables and the conclusion that 15 estimators are optimal are produced by a pipeline whose cluster count and MILP edge budgets are hand-set; the diabetes appendix explicitly shows that changing the edge budget from 15 to 5 changes the graph. Second, the scalability claim over TreeSHAP is not derived: Appendix A bounds only TreeSHAP, while SIG's complexity is asserted in Table 14 as 'Sublinear if rules are sparse and compressible' and then reported as a result. The empirical runtime comparison in Figure 7 is real, independent evidence and prevents the paper from being entirely circular, but the interpretability findings and the asymptotic complexity advantage are substantially forced by the chosen inputs and conditions.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central claims rest on ad hoc choices for cluster count and edge budget, plus several untested assumptions about rule similarity and graph fidelity. No physical or conceptual entities are postulated; SIG is a methodological artifact rather than an invented entity.

free parameters (2)

cluster_count_k = sqrt(f + N) rounded to nearest perfect square; e.g., about 41 for CKD
Section 3.4 defines the optimal number of clusters with this ad hoc rule; no search or stability analysis is provided.
MILP_edge_budget = 15 (CKD, heart, AQIH), 5 (diabetes, after 15 over-pruned), 20 (Alzheimer)
Section 4 and Appendix B choose these limits after inspecting graphs, directly controlling which features remain in the final SIG.

assumptions (6)

domain assumption Edge co-occurrence frequency in extracted decision rules corresponds to interaction importance.
Section 3.5 uses pair counts as edge weights without validating against known interactions or SHAP interaction values.
domain assumption TF-IDF representation of tokenized rules preserves the logical similarity needed for clustering.
Section 3.3 treats rules as text documents, splitting thresholds and operators into tokens; no experiments show this preserves rule semantics.
domain assumption Agglomerative clustering with cosine similarity can merge redundant rules without losing important decision logic.
Section 3.4 assumes this; no stability or quality analysis of the clusters is provided.
ad hoc to paper The MILP formulation with a cardinality constraint preserves the most informative edges.
Algorithm 5 states the objective and constraints only at a high level; no proof of fidelity or information preservation is given.
ad hoc to paper TreeSHAP's interaction time complexity is O(N T L^2 + N f^2).
Appendix A asserts this formula and uses it to compare scalability; no derivation or citation is provided for this specific expression.
domain assumption Hierarchical order in a rule path reflects directional feature interaction.
Section 3.5 and Table 4 interpret path order as hierarchy, but split order in a tree does not imply causal or directional dependence.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Surrogate Interpretable Graph for Random Decision Forests." pith.science (2026). https://pith.science/paper/6S2NJRY7

@misc{pith2026250601988,
  author       = {Pith},
  title        = {Pith review of: Surrogate Interpretable Graph for Random Decision Forests},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6S2NJRY7}},
  note         = {Machine review of arXiv:2506.01988}
}

read the original abstract

The field of health informatics has been profoundly influenced by the development of random forest models, which have led to significant advances in the interpretability of feature interactions. These models are characterized by their robustness to overfitting and parallelization, making them particularly useful in this domain. However, the increasing number of features and estimators in random forests can prevent domain experts from accurately interpreting global feature interactions, thereby compromising trust and regulatory compliance. A method called the surrogate interpretability graph has been developed to address this issue. It uses graphs and mixed-integer linear programming to analyze and visualize feature interactions. This improves their interpretability by visualizing the feature usage per decision-feature-interaction table and the most dominant hierarchical decision feature interactions for predictions. The implementation of a surrogate interpretable graph enhances global interpretability, which is critical for such a high-stakes domain.

Figures

Figures reproduced from arXiv: 2506.01988 by the authors.

**Figure 2.** The optimized surrogate interpretable graph (SIG) for the Chronic Kidney dataset. The SIG has been pruned to remove the nodes with minimal significance using MILP. The max number of edges for this optimized version was 15. Temperature PM2_5 AQI Humidity CardiovascularCases RespiratoryCases WindSpeed [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 4.** The optimized surrogate interpretable graph (SIG) for the heart dataset. The SIG has been [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: The optimized SIG for the diabetes dataset. The SIG has been pruned to remove the nodes [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]

**Figure 6.** Figure 6: The optimized surrogate interpretable graph (SIG) for the Alzheimer dataset. The SIG has [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]

**Figure 7.** Figure 7: The comparison of runtime between SIG and TreeSHAP feature interaction for different [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 56 canonical work pages

[1]

Random forests,

L. Breiman, “Random forests,” Machine learning, vol. 45, pp. 5–32, 2001

2001
[2]

Tree-based approaches for interpretable modeling in healthcare,

J. Murris, “Tree-based approaches for interpretable modeling in healthcare,” in Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society, vol. 7, pp. 37–39, 2024

work page 2024
[3]

A multicenter random forest model for effective prognosis prediction in collaborative clinical research network,

J. Li, Y . Tian, Y . Zhu, T. Zhou, J. Li, K. Ding, and J. Li, “A multicenter random forest model for effective prognosis prediction in collaborative clinical research network,”Artificial intelligence in medicine, vol. 103, p. 101814, 2020

work page 2020
[4]

A random forest based biomarker discovery and power analysis framework for diagnostics research,

A. Acharjee, J. Larkman, Y . Xu, V . R. Cardoso, and G. V . Gkoutos, “A random forest based biomarker discovery and power analysis framework for diagnostics research,”BMC medical genomics, vol. 13, pp. 1–14, 2020

work page 2020
[5]

Classification and interaction in random forests,

S. Basu, K. Kumbier, J. Brown, and B. Yu, “Classification and interaction in random forests,” Proceedings of the National Academy of Sciences, vol. 115, no. 8, pp. 1690–1692, 2018

work page 2018
[6]

Overview of random forest methodol- ogy and practical guidance with emphasis on computational biology and bioinformatics,

A.-L. Boulesteix, S. Janitza, J. Kruppa, and I. R. König, “Overview of random forest methodol- ogy and practical guidance with emphasis on computational biology and bioinformatics,” Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, vol. 2, no. 6, pp. 493–507, 2012

work page 2012
[7]

Feature learning for interpretable, performant decision trees,

J. Good, T. Kovach, K. Miller, and A. Dubrawski, “Feature learning for interpretable, performant decision trees,” Advances in Neural Information Processing Systems, vol. 36, pp. 66571–66582, 2023

work page 2023
[8]

Interaction forests: Identifying and exploiting interpretable interactions,

R. Hornung and A.-L. Boulesteix, “Interaction forests: Identifying and exploiting interpretable interactions,” Journal of Computational and Graphical Statistics, 2021

work page 2021

Show all 63 references

[9]

Random forest for bioinformatics,

Y . Qi, “Random forest for bioinformatics,”Ensemble machine learning: Methods and applica- tions, pp. 307–323, 2012

2012
[10]

A random forest approach to capture genetic effects in the presence of population structure,

J. Stephan, O. Stegle, and A. Beyer, “A random forest approach to capture genetic effects in the presence of population structure,” Nature communications, vol. 6, no. 1, p. 7432, 2015

2015
[11]

Perceptions and needs of artificial intelligence in health care to increase adoption: scoping review,

H. S. J. Chew and P. Achananuparp, “Perceptions and needs of artificial intelligence in health care to increase adoption: scoping review,” Journal of medical Internet research, vol. 24, no. 1, p. e32939, 2022

2022
[12]

Explaining random forests using bipolar argumentation and markov networks,

N. Potyka, X. Yin, and F. Toni, “Explaining random forests using bipolar argumentation and markov networks,” in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 37, pp. 9453–9460, 2023

2023
[13]

Hierarchical shrinkage: Improving the accuracy and interpretability of tree-based models.,

A. Agarwal, Y . S. Tan, O. Ronen, C. Singh, and B. Yu, “Hierarchical shrinkage: Improving the accuracy and interpretability of tree-based models.,” in International Conference on Machine Learning, pp. 111–135, PMLR, 2022

2022
[14]

Learning interpretable rules for scalable data repre- sentation and classification,

Z. Wang, W. Zhang, N. Liu, and J. Wang, “Learning interpretable rules for scalable data repre- sentation and classification,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 46, no. 2, pp. 1121–1133, 2023

2023
[15]

Sirus: Stable and interpretable rule set for classification,

C. Bénard, G. Biau, S. Da Veiga, and E. Scornet, “Sirus: Stable and interpretable rule set for classification,” Electronic Journal of Statistics, vol. 15, pp. 427–505, 2021

2021
[16]

Interpretable random forests via rule extraction,

C. Bénard, G. Biau, S. Da Veiga, and E. Scornet, “Interpretable random forests via rule extraction,” in International conference on artificial intelligence and statistics, pp. 937–945, PMLR, 2021

2021
[17]

Multi-omics integration using random forests: Chal- lenges and opportunities in precision medicine,

R. Kumar, E. Wilson, and P. Thompson, “Multi-omics integration using random forests: Chal- lenges and opportunities in precision medicine,” Briefings in Bioinformatics, vol. 25, no. 2, p. bbae012, 2024

2024
[18]

Interaction forests: Technical report,

R. Hornung and A.-L. Boulesteix, “Interaction forests: Technical report,” tech. rep., University of Munich, 2019. 11

2019
[19]

Consistent individualized feature attribution for tree ensembles,

S. M. Lundberg, G. G. Erion, and S.-I. Lee, “Consistent individualized feature attribution for tree ensembles,” arXiv preprint arXiv:1802.03888, 2018

2018 arXiv
[20]

From local explanations to global understanding with explainable ai for trees,

S. M. Lundberg, G. Erion, H. Chen, A. DeGrave, J. M. Prutkin, B. Nair, R. Katz, J. Himmelfarb, N. Bansal, and S.-I. Lee, “From local explanations to global understanding with explainable ai for trees,” Nature machine intelligence, vol. 2, no. 1, pp. 56–67, 2020

2020
[21]

Beyond treeshap: Efficient computation of any-order shapley interactions for tree ensembles,

M. Muschalik, F. Fumagalli, B. Hammer, and E. Hüllermeier, “Beyond treeshap: Efficient computation of any-order shapley interactions for tree ensembles,” in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 38(13), pp. 14388–14396, 2024

2024
[22]

Ai readiness in healthcare through storytelling xai,

A. Dubey, Z. Yang, and G. Hattab, “Ai readiness in healthcare through storytelling xai,”arXiv preprint arXiv:2410.18725, 2024

2024 arXiv
[23]

A nested model for ai design and validation,

A. Dubey, Z. Yang, and G. Hattab, “A nested model for ai design and validation,” Iscience, vol. 27, no. 9, 2024

2024
[24]

A random forest-based approach to identifying the most informative seasonality tests,

D. Ollech and K. Webel, “A random forest-based approach to identifying the most informative seasonality tests,” tech. rep., Deutsche Bundesbank, 2020

2020
[25]

Linear tree shap,

A. Bifet, J. Read, C. Xu, et al., “Linear tree shap,” Advances in Neural Information Processing Systems, vol. 35, pp. 25818–25828, 2022

2022
[26]

Trained random forests completely reveal your dataset,

J. Ferry, R. Fukasawa, T. Pascal, and T. Vidal, “Trained random forests completely reveal your dataset,” in Proceedings of the 41st International Conference on Machine Learning , pp. 13545–13569, 2024

2024
[27]

Iterative random forests to discover predictive and stable high-order interactions,

S. Basu, K. Kumbier, J. B. Brown, and B. Yu, “Iterative random forests to discover predictive and stable high-order interactions,” Proceedings of the National Academy of Sciences, vol. 115, no. 8, pp. 1943–1948, 2018

1943
[28]

Generalized random forests,

S. ATHEY , J. TIBSHIRANI, and S. WAGER, “Generalized random forests,”The Annals of Statistics, vol. 47, no. 2, pp. 1148–1178, 2019

2019
[29]

Deep exploration of random forest model boosts the interpretability of machine learning studies of complicated immune responses and lung burden of nanoparticles,

F. Yu, C. Wei, P. Deng, T. Peng, and X. Hu, “Deep exploration of random forest model boosts the interpretability of machine learning studies of complicated immune responses and lung burden of nanoparticles,” Science advances, vol. 7, no. 22, p. eabf4130, 2021

2021
[30]

A unified approach to interpreting model predictions,

S. M. Lundberg and S.-I. Lee, “A unified approach to interpreting model predictions,”Advances in neural information processing systems, vol. 30, 2017

2017
[31]

A new method for graph-based representation of text in natural language processing,

B. Probierz, A. Hrabia, and J. Kozak, “A new method for graph-based representation of text in natural language processing,” Electronics, vol. 12, no. 13, p. 2846, 2023

2023
[32]

Feature graphs for interpretable unsupervised tree ensembles: centrality, interaction, and application in disease subtyping,

C. Sirocchi, M. Urschler, and B. Pfeifer, “Feature graphs for interpretable unsupervised tree ensembles: centrality, interaction, and application in disease subtyping,” BioData Mining, vol. 18, p. 15, 2025

2025
[33]

Interaction forests: Identifying and exploiting interpretable quantitative and qualitative interaction effects,

R. Hornung and A.-L. Boulesteix, “Interaction forests: Identifying and exploiting interpretable quantitative and qualitative interaction effects,” Computational Statistics & Data Analysis , vol. 171, p. 107460, 2022

2022
[34]

Interpreting random forest analysis of ecological models to move from prediction to explanation,

S. M. Simon, P. Glaum, and F. S. Valdovinos, “Interpreting random forest analysis of ecological models to move from prediction to explanation,” Scientific Reports, vol. 13, no. 1, p. 3881, 2023

2023
[35]

Graph random forest: a graph embedded algorithm for identifying highly connected important features,

L. Tian, W. Wu, and T. Yu, “Graph random forest: a graph embedded algorithm for identifying highly connected important features,” Biomolecules, vol. 13, no. 7, p. 1153, 2023

2023
[36]

Improving the explainability of random forest classifier–user centered approach,

D. Petkovic, R. Altman, M. Wong, and A. Vigil, “Improving the explainability of random forest classifier–user centered approach,” in Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing, vol. 23, p. 204, 2018. 12

2018
[37]

Random forest model and sample explainer for non-experts in machine learning–two case studies,

D. Petkovic, A. Alavi, D. Cai, and M. Wong, “Random forest model and sample explainer for non-experts in machine learning–two case studies,” in Pattern Recognition. ICPR International Workshops and Challenges: Virtual Event, January 10–15, 2021, Proceedings, Part III, pp. 62– ...

2021
[38]

Geometry-and accuracy-preserving random forest proximities,

J. S. Rhodes, A. Cutler, and K. R. Moon, “Geometry-and accuracy-preserving random forest proximities,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 9, pp. 10947–10959, 2023

2023
[39]

Interpreting tree ensembles with intrees,

H. Deng, “Interpreting tree ensembles with intrees,” International Journal of Data Science and Analytics, vol. 7, no. 4, pp. 277–287, 2019

2019
[40]

A comparison among interpretative proposals for random forests,

M. Aria, C. Cuccurullo, and A. Gnasso, “A comparison among interpretative proposals for random forests,” Machine Learning with Applications, vol. 6, p. 100094, 2021

2021
[41]

Connecting interpretability and robustness in decision trees through separation,

M. Moshkovitz, Y .-Y . Yang, and K. Chaudhuri, “Connecting interpretability and robustness in decision trees through separation,” in International Conference on Machine Learning, pp. 7839– 7849, PMLR, 2021

2021
[42]

A framework for inherently interpretable optimization models,

M. Goerigk and M. Hartisch, “A framework for inherently interpretable optimization models,” European Journal of Operational Research, vol. 310, no. 3, pp. 1312–1324, 2023

2023
[43]

Optimal decision trees for categorical data via integer programming,

O. Günlük, J. Kalagnanam, M. Li, M. Menickelly, and K. Scheinberg, “Optimal decision trees for categorical data via integer programming,” Journal of global optimization, vol. 81, pp. 233–260, 2021

2021
[44]

Optimal interpretable decision trees using integer linear programming techniques,

P. Murali, H. Zhu, D. T. Phan, and L. Nguyen, “Optimal interpretable decision trees using integer linear programming techniques,” June 13 2023. US Patent 11,676,039

2023
[45]

Forest-ore: Mining an optimal rule ensemble to interpret random forest models,

M. Haddouchi and A. Berrado, “Forest-ore: Mining an optimal rule ensemble to interpret random forest models,” Engineering Applications of Artificial Intelligence, vol. 143, p. 109997, 2025

2025
[46]

On representing linear programs by graph neural networks,

Z. Chen, J. Liu, X. Wang, J. Lu, and W. Yin, “On representing linear programs by graph neural networks,” arXiv preprint arXiv:2209.12288, 2022

2022 arXiv
[47]

Deep graph matching meets mixed-integer linear programming: Relax at your own risk?,

Z. Xu, P. Chen, R. Raveaux, X. Yang, and H. Liu, “Deep graph matching meets mixed-integer linear programming: Relax at your own risk?,” arXiv preprint arXiv:2108.00394, 2021

2021 arXiv
[48]

A mixed integer linear programming method for optimizing layout of irrigated pumping well in oasis,

T. Ma, J. Wang, Y . Liu, H. Sun, D. Gui, and J. Xue, “A mixed integer linear programming method for optimizing layout of irrigated pumping well in oasis,” Water, vol. 11, no. 6, p. 1185, 2019

2019
[49]

Towards foundation models for mixed integer linear programming,

S. Li, J. Kulkarni, I. Menache, C. Wu, and B. Li, “Towards foundation models for mixed integer linear programming,” arXiv preprint arXiv:2410.08288, 2024

2024 arXiv
[50]

Liu, A Scalable Graph-based Mixed-Integer Linear Programming Approach for the Examina- tion Timetabling Problem

T. Liu, A Scalable Graph-based Mixed-Integer Linear Programming Approach for the Examina- tion Timetabling Problem. PhD thesis, Politecnico di Torino, 2018

2018
[51]

Chronic kidney disease dataset

R. E. Kharoua, “Chronic kidney disease dataset.” Kaggle, 2024. URL: https://www.kaggle.com/dsv/8658224

2024
[52]

Air quality and health impact dataset

R. E. Kharoua, “Air quality and health impact dataset.” Kaggle, 2024. URL: https://www.kaggle.com/dsv/8675842

2024
[53]

A deep instance generative framework for milp solvers under limited data availability,

Z. Geng, X. Li, J. Wang, X. Li, Y . Zhang, and F. Wu, “A deep instance generative framework for milp solvers under limited data availability,”Advances in Neural Information Processing Systems, vol. 36, pp. 26025–26047, 2023

2023
[54]

Xgboost: A scalable tree boosting system,

T. Chen and C. Guestrin, “Xgboost: A scalable tree boosting system,” inProceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining, pp. 785–794, 2016. 13

2016
[55]

A general framework for identifying hierarchical interactions and its application to genomics data,

X. Zhang, X. Shi, Y . Liu, X. Liu, and S. Ma, “A general framework for identifying hierarchical interactions and its application to genomics data,” Journal of Computational and Graphical Statistics, vol. 32, no. 3, pp. 873–883, 2023

2023
[56]

Heart Disease

A. Janosi, W. Steinbrunn, M. Pfisterer, and R. Detrano, “Heart Disease.” UCI Machine Learning Repository, 1989. DOI: https://doi.org/10.24432/C52P4X

1989 doi
[57]

Using the adap learning algorithm to forecast the onset of diabetes mellitus,

J. W. Smith, J. E. Everhart, W. C. Dickson, W. C. Knowler, and R. S. Johannes, “Using the adap learning algorithm to forecast the onset of diabetes mellitus,” in Proceedings of the annual symposium on computer application in medical care, p. 261, 1988

1988
[58]

Alzheimer’s disease dataset

R. E. Kharoua, “Alzheimer’s disease dataset.” Kaggle, 2024. URL: https://www.kaggle.com/dsv/8668279. 14 A Mathematical Proof We have: f = number of features (1) T = number of trees (2) d = maximum depth of trees (3) L≈ 2d = number of leaves per tree (4) R = number of extracted...

2024
[59]

0: ’Very High’ (HealthImpactScore >= 80)
[60]

1: ’High’ (60 <= HealthImpactScore < 80)
[61]

2: ’Moderate’ (40 <= HealthImpactScore < 60)
[62]

3: ’Low’ (20 <= HealthImpactScore < 40)
[63]

4: ’Very Low’ (HealthImpactScore < 20) 24

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Random forests,

L. Breiman, “Random forests,” Machine learning, vol. 45, pp. 5–32, 2001

2001

[2] [2]

Tree-based approaches for interpretable modeling in healthcare,

J. Murris, “Tree-based approaches for interpretable modeling in healthcare,” in Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society, vol. 7, pp. 37–39, 2024

work page 2024

[3] [3]

A multicenter random forest model for effective prognosis prediction in collaborative clinical research network,

J. Li, Y . Tian, Y . Zhu, T. Zhou, J. Li, K. Ding, and J. Li, “A multicenter random forest model for effective prognosis prediction in collaborative clinical research network,”Artificial intelligence in medicine, vol. 103, p. 101814, 2020

work page 2020

[4] [4]

A random forest based biomarker discovery and power analysis framework for diagnostics research,

A. Acharjee, J. Larkman, Y . Xu, V . R. Cardoso, and G. V . Gkoutos, “A random forest based biomarker discovery and power analysis framework for diagnostics research,”BMC medical genomics, vol. 13, pp. 1–14, 2020

work page 2020

[5] [5]

Classification and interaction in random forests,

S. Basu, K. Kumbier, J. Brown, and B. Yu, “Classification and interaction in random forests,” Proceedings of the National Academy of Sciences, vol. 115, no. 8, pp. 1690–1692, 2018

work page 2018

[6] [6]

Overview of random forest methodol- ogy and practical guidance with emphasis on computational biology and bioinformatics,

A.-L. Boulesteix, S. Janitza, J. Kruppa, and I. R. König, “Overview of random forest methodol- ogy and practical guidance with emphasis on computational biology and bioinformatics,” Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, vol. 2, no. 6, pp. 493–507, 2012

work page 2012

[7] [7]

Feature learning for interpretable, performant decision trees,

J. Good, T. Kovach, K. Miller, and A. Dubrawski, “Feature learning for interpretable, performant decision trees,” Advances in Neural Information Processing Systems, vol. 36, pp. 66571–66582, 2023

work page 2023

[8] [8]

Interaction forests: Identifying and exploiting interpretable interactions,

R. Hornung and A.-L. Boulesteix, “Interaction forests: Identifying and exploiting interpretable interactions,” Journal of Computational and Graphical Statistics, 2021

work page 2021