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arxiv: 2607.01417 · v1 · pith:DUOPV6NTnew · submitted 2026-07-01 · 💻 cs.LG · stat.ML

Conditional Inference Trees and Forests for Feature Selection

Robert Milletich , Justin Downes , Steve Goley , Newel Hirst This is my paper

Pith reviewed 2026-07-03 21:14 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords conditional inference forestsfeature rankingfeature selectionpermutation testsclassificationregressiontree ensembles
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The pith

Conditional inference forests rank 4th and 3rd among feature selectors in classification and regression benchmarks.

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

The paper tests conditional inference trees and forests as tools for ranking the most useful input features before training a final predictor. It runs real-data experiments on dozens of datasets, measures how runtime settings affect speed and accuracy, and checks recovery of known important features in synthetic cases. The central finding is that these forests deliver competitive top-k rankings while using permutation tests to avoid favoring features with more possible split points. A reader would care because biased feature selection can waste computation and degrade model performance on new data.

Core claim

Conditional inference forests, which test each feature with a permutation p-value before choosing any split threshold, produce feature rankings that place fourth among seventeen classification methods on twenty-two datasets and third among eighteen regression methods on eight datasets, supporting their use for top-k feature selection.

What carries the argument

Bonferroni-corrected Monte Carlo permutation p-values computed at each node to decide which feature receives a split, independent of the number of thresholds tested.

If this is right

  • CIF can be applied directly as a feature-ranking step before training any downstream classifier or regressor.
  • Turning off adaptive stopping increases fitting time by a factor of four to eight with negligible change in final scores.
  • Exact threshold search multiplies runtime by up to ten with little accuracy gain.
  • In sparse high-dimensional settings, the random feature sampling inside the forest can exclude informative variables from many candidate splits.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same permutation-test logic could be grafted onto other tree algorithms to reduce split bias without switching to full conditional inference.
  • Runtime gains from adaptive stopping suggest that similar early-stopping rules might help permutation-based methods in other domains such as causal discovery.
  • The observed risk that informative features are sampled out of many trees points to a need for stratified or importance-weighted sampling inside the forest.

Load-bearing premise

The collection of real and synthetic datasets used is representative of the problems where top-k feature ranking matters.

What would settle it

A new collection of thirty datasets in which CIF rankings produce downstream prediction scores that fall below the median of the other sixteen or seventeen methods.

Figures

Figures reproduced from arXiv: 2607.01417 by Justin Downes, Newel Hirst, Robert Milletich, Steve Goley.

Figure 1
Figure 1. Figure 1: Classification mean rank by number of selected features. Rows show all 17 feature selection methods in the classification benchmark, averaged across downstream models at each value of k. Lower ranks are better. The columns for k = 5, 10, 25, 50, 100 use 22, 21, 15, 15, and 14 datasets, respectively. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Regression mean rank by number of selected features. Rows show all 18 feature selection methods in the regression benchmark, averaged across downstream models at each value of k. Lower ranks are better. The columns for k = 5, 10, 25, 50, 100 use 8, 8, 7, 7, and 6 datasets, respectively. 5.2 Runtime ablations The runtime ablations identify which benchmark settings have the largest effect on fitting time and… view at source ↗
Figure 3
Figure 3. Figure 3: Where CIF’s classification scores peak as k increases, by downstream learner. (A) shows, for each learner, the percentage of 15 datasets where the first evaluated k attaining the best observed CIF score falls below 100, at 100, between 100 and p, or at k=p. (B) shows the mean balanced accuracy change from k=100 to k=p. Synthetic feature recovery. Across synthetic classification datasets, 34% of the feature… view at source ↗
Figure 4
Figure 4. Figure 4: Synthetic top-k recovery curves. Columns compare single trees, forests, and boosted trees; rows show classification and regression. Each value is the percentage of selected features that are truly informative. Feature sampling in forests. A sparse simulation asks whether forest feature sampling makes splits less likely to use informative features in classification and regression settings [PITH_FULL_IMAGE:… view at source ↗
Figure 5
Figure 5. Figure 5: Tree-level feature use in one sparse classification forest design (n=250, p=1,000, two informative features, 1,000 trees). Counts are the number of trees using each feature in at least one split. CIF samples a subset of features; CIF-all evaluates all nonconstant features. Each subplot has its own y-axis range because counts differ across methods. 7 Discussion In these experiments, CIF is best supported as… view at source ↗
Figure 6
Figure 6. Figure 6: Classification CIF margins against ctree, cforest, and CIT by downstream learner and value of k. Each plotted value is the mean balanced-accuracy difference, CIF minus comparator, for one downstream learner and one value of k; positive values favor CIF. Dataset counts by k are 22, 21, 15, 15, and 14 for ctree and cforest, and 23, 22, 16, 16, and 15 for CIT. 35 [PITH_FULL_IMAGE:figures/full_fig_p035_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Regression CIF margins against ctree, cforest, and CIT by downstream learner and value of k. Each plotted value is the mean R2 difference, CIF minus comparator, for one downstream learner and one value of k; positive values favor CIF. Dataset counts by k are 8, 8, 7, 7, and 6 for each comparison. Large positive plotted values can reflect negative mean R2 for the comparator. Numeric labels show the unclippe… view at source ↗
Figure 8
Figure 8. Figure 8: Classification forest feature sampling by feature dimension p with 1,000 trees per fit. Points are means over ninformative ∈ {1, 2, 5, 10}; capped bars span the minimum-to-maximum values across those four sparse designs. (A) shows % of splits using informative features; (B) shows the number of distinct uninformative features used [PITH_FULL_IMAGE:figures/full_fig_p038_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Regression forest feature sampling by feature dimension p with 1,000 trees per fit. Points are means over ninformative ∈ {1, 2, 5, 10}; capped bars span the minimum-to-maximum values across those four sparse designs. (A) shows % of splits using informative features; (B) shows the number of distinct uninformative features used. 38 [PITH_FULL_IMAGE:figures/full_fig_p038_9.png] view at source ↗
read the original abstract

Conditional inference trees (CIT) and conditional inference forests (CIF) reduce split-selection bias by testing features before choosing split thresholds, but repeated permutation tests and threshold searches can make these methods computationally expensive. We study CIT and CIF as top-$k$ feature-ranking methods for downstream prediction using real-data benchmarks, runtime ablations, and synthetic feature-recovery experiments. At a fixed node, if the features and permutation budget do not depend on the node responses, Bonferroni-corrected $+1$ Monte Carlo permutation $p$-values control nodewise rejection under the complete permutation null. CIF ranks 4th among 17 classification methods on 22 datasets and 3rd among 18 regression methods on 8 datasets. With Bonferroni correction held fixed, the CIF runtime ablations indicate that adaptive stopping and the number of thresholds searched have the largest measured effect on runtime: turning off adaptive stopping and using exact threshold search increase fitting time by 4.0--8.4$\times$ and 1.9--10.8$\times$, respectively, while downstream score changes are at most 0.011. Sparse high-$p$ simulations indicate that forest feature sampling can leave informative features out of many split decisions. Overall, the results support CIF as a top-$k$ feature-ranking method in the evaluated downstream prediction benchmarks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper studies conditional inference trees (CIT) and forests (CIF) as top-k feature-ranking methods for downstream prediction tasks. It provides a condition under which Bonferroni-corrected +1 Monte Carlo permutation p-values control nodewise rejection under the complete permutation null, reports that CIF ranks 4th among 17 classification methods on 22 datasets and 3rd among 18 regression methods on 8 datasets, presents runtime ablations showing that adaptive stopping and threshold search have the largest effects on runtime (with downstream score changes ≤0.011), and includes synthetic feature-recovery experiments indicating that forest feature sampling can omit informative features.

Significance. If the p-value control holds and the empirical rankings are robust, the work would provide a theoretically grounded, bias-reduced alternative to standard tree-based feature selection with competitive downstream performance and quantified runtime trade-offs. The ablations and synthetic results add practical insight into implementation choices.

major comments (1)
  1. [Abstract and runtime ablations] Abstract (p-value control statement) and runtime ablations: The paper states that at a fixed node, Bonferroni-corrected +1 Monte Carlo permutation p-values control nodewise rejection under the complete permutation null only "if the features and permutation budget do not depend on the node responses." The runtime ablations report that turning off adaptive stopping increases fitting time by 4.0–8.4× and identify it as having the largest measured effect, implying the main reported CIF results use adaptive stopping. This makes the effective permutation budget depend on observed responses, directly violating the stated precondition and removing the claimed frequentist guarantee for the nodewise p-values that justify reduced split-selection bias and reliable top-k ranking.
minor comments (2)
  1. [Abstract] The abstract reports CIF ranking 4th/17 on classification and 3rd/18 on regression but does not specify whether these are mean ranks, median ranks, or win counts, nor the exact metric (e.g., AUC, accuracy) used for downstream evaluation.
  2. [Abstract] The synthetic experiments mention "sparse high-p simulations" but the abstract does not report the exact dimensions (p, n, sparsity level) or recovery metric, making it hard to assess how representative they are of the real-data regime.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and for pointing out the potential inconsistency between the stated condition for p-value control and the use of adaptive stopping in the reported experiments. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract and runtime ablations] Abstract (p-value control statement) and runtime ablations: The paper states that at a fixed node, Bonferroni-corrected +1 Monte Carlo permutation p-values control nodewise rejection under the complete permutation null only "if the features and permutation budget do not depend on the node responses." The runtime ablations report that turning off adaptive stopping increases fitting time by 4.0–8.4× and identify it as having the largest measured effect, implying the main reported CIF results use adaptive stopping. This makes the effective permutation budget depend on observed responses, directly violating the stated precondition and removing the claimed frequentist guarantee for the nodewise p-values that justify reduced split-selection bias and reliable top-k ranking.

    Authors: We agree with the referee that the main CIF results utilize adaptive stopping, which causes the permutation budget to depend on the observed responses at each node, thereby violating the precondition for the nodewise p-value control result. The theoretical guarantee applies specifically to the case of fixed permutation budget independent of responses. We will revise the abstract to clarify the scope of the p-value control statement and add a note in the methods or discussion section explaining that adaptive stopping is employed for computational efficiency in the empirical evaluations, while the frequentist control is guaranteed only without it. The benchmark rankings and runtime ablation results are empirical observations and remain unchanged. This revision addresses the concern without altering the core findings. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical claims rest on external benchmarks

full rationale

The paper presents no derivation chain that reduces to its inputs by construction. Its strongest claims are direct empirical rankings of CIF against 17/18 other methods on 22/8 datasets plus runtime ablations and synthetic recovery experiments. The single conditional statement on p-value control is an if-then claim about a fixed-node permutation test and is not invoked to derive the reported rankings or to rename any fitted quantity as a prediction. No self-citations, ansatzes, or uniqueness theorems appear as load-bearing steps. The work is therefore self-contained against the external benchmarks it reports.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; full text would be required to audit these elements.

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discussion (0)

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