Null importance: Disentangling relevance for interpretable machine learning
Garvesh Raskutti, Kris Sankaran, Jiaxin Ye
stat.ML · cs.LG
Quick verdict
A unified 'null importance' lens for feature relevance: elegant, useful taxonomy; proofs sound but unsurprising, empirical evidence mostly qualitative.
Summary
The paper argues that 'feature importance' conflates fundamentally different notions of relevance and formalizes them through 'null importance': population-level statements of when a feature is irrelevant under a chosen criterion. Section 2 defines functional (global/local/pointwise), statistical (marginal and conditional mutual information), risk-based (gap in optimal population risk within a function class), and causal (supremum interventional divergence) nulls. Two applications carry the argument: common fairness criteria correspond to different nulls (demographic parity = marginal statistical; equalized odds = conditional; individual fairness as local functional; counterfactual fairness = causal), and debates in genomic perturbation evaluation reduce to disagreements about which null is targeted. Section 3 gives sufficient conditions for equivalences — deterministic non-redundant data-generating processes, Bayes-complete classes with strictly proper losses, randomization — plus counterexamples separating the notions. Section 4 classifies roughly fourteen methods (correlation, mutual information, lasso, knockoffs, GCM, LOCO, MDI, risk-based and causal Shapley, MinShap, Integrated Gradients, saliency, PD, ALE) by targeted null and whether zero statistics identify it; Shapley averaging and PD/ALE aggregation can mask conditional nullity. Simulations (ten mechanisms D1-D10), an MNIST attribution study, and a TCGA multiomics analysis (twelve methods, PCA of importance profiles, PC1 80.1%) illustrate practical divergences. Limitations: many formal results are standard, evidence is largely qualitative (seven replicates, no uncertainty quantification), and fairness mappings simplify individual-level notions.
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Assessment at a glance
5
risk flags identified
● high 0
● medium 3
● low 2
5 strengths · 5 weaknesses · 5 author questions
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Key claims under review
- The term 'feature importance' conflates distinct notions of relevance that are precisely captured by different population-level null importance properties (functional, marginal/conditional statistical, risk-based, causal).
- These nulls coincide only under explicit sufficient conditions — deterministic non-redundant mechanisms, Bayes-complete classes with strictly proper losses, randomization — and provably diverge otherwise (Lemmas 1–4, Examples 3.1–3.5).
- Common fairness criteria correspond to different null importance notions, so fairness impossibility results reflect conflicting relevance choices rather than mathematical pathologies.
- A method's targeted null differs from what its zero statistic identifies: Shapley averaging, PD, ALE and Integrated Gradients provide at most one-way null guarantees (Table 1).
- Simulations (D1–D10) and the MNIST/TCGA case studies show these distinctions change concrete conclusions about what a prediction model has learned.
Strengths
Unifying vocabulary with practical teeth
The targeted-null vs identified-null distinction (Section 4, Table 1) turns vague 'which importance method?' choices into checkable claims; it correctly demotes risk-based Shapley, PD and ALE to one-way or non-guarantees via concrete chain and interaction examples (f = xj·xk for PD).
Fairness criteria recast as null properties
Section 2.5 maps demographic parity, equalized odds, proxy fairness, individual fairness and counterfactual fairness onto marginal-statistical, conditional-statistical, local-functional and causal nulls, linking known impossibility results to a common statistical language.
Theory-to-experiment alignment
Timely perturbation-modeling analysis
Reproducibility provisions
Weaknesses
Modest formal novelty
Qualitative empirical evidence
Overreaching fairness equivalences
Internal inconsistencies and editing artifacts
Unanalyzed MinSHAP collapse
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Scope & Claims
This Statistical Science submission (arXiv:2609.19511, UW–Madison statistics group) tackles the ambiguity of 'feature importance' by defining population-level null importance properties: functional (global/local/pointwise, Definitions 2.2–2.4), statistical marginal and conditional via mutual information (2.5–2.6), risk-based as the gap between optimal population risks within a hypothesis class (2.7–2.8), and causal as the supremum interventional divergence (2.9–2.10). Three claims anchor the paper: (i) standard nulls answer different scientific questions; (ii) they coincide only under explicit sufficient conditions and provably separate otherwise (Lemmas 1–4 against Examples 3.1–3.5); (iii) method families target different nulls, and their zero statistics often fail to identify even those targets (Section 4, Table 1). Two application chapters carry the argument — fairness criteria (2.5) and genomic perturbation evaluation (2.6) — followed by synthetic benchmarks (5.1), an MNIST attribution study (5.2), and a TCGA multiomics analysis (5.3).
The remaining sections cover Methodology Assessment, Statistical Evidence, Results & Reproducibility, Limitations & Risks, and Verdict & Recommendations.
- All 5 strengths & 5 weaknesses, analyzed in detail
- 5 risk flags with severity, section & reviewer questions
- Methods & statistical evidence assessment
- 5 questions a peer reviewer would ask
- Full six-dimension evaluation report & recommendations
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Frequently asked questions
What is 'null importance' in this paper?
It is a population-level statement of what it means for a feature to be irrelevant under a chosen relevance criterion — for example, zero mutual information with the response, no improvement in optimal predictive risk when the feature is added, or an invariant interventional outcome distribution. The paper uses these nulls to compare what different feature-importance methods actually test.
Do different feature importance methods measure the same thing?
No. Correlation screening targets marginal association, knockoffs and the GCM target conditional independence, LOCO targets predictive risk, and gradient methods target sensitivity of the prediction function. A zero score can mean different things, and per Table 1 several methods (Shapley averages, PD, ALE) may not even identify their own intended null.
Is a zero Shapley value the same as a feature being unimportant?
Not necessarily. Shapley values average marginal contributions over all coalitions, so a feature that adds nothing once all other features are present can still receive positive attribution, and signed contributions can cancel to zero even when the feature has real effects in some coalitions.
Is code and data available for this paper?
Yes. The authors provide a GitHub repository (krisrs1128/null_importance) and deposited case-study data on Figshare (DOI 10.6084/m9.figshare.33857824); the synthetic data-generating mechanisms are fully specified in Table 2.
About this review
This is an AI-generated preliminary review by Evolve.Pub, produced from the openly available text of the paper. It is not peer review and does not represent the authors' views. The canonical record of the paper is at the publisher link above.
- Several passages were truncated in extraction (parts of Sections 2.3–2.4, 3.1.3, 4.2, 5.3 and the reference list); the review reflects the available text.
- Figures (synthetic heatmaps, TCGA PCA panels, MNIST attribution images) could not be inspected; plot-level judgments rely on captions and in-text descriptions.
- Supplementary Figures 6–9 and appendix content were not included in the extracted text.
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