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arxiv: 2604.11200 · v1 · submitted 2026-04-13 · 💻 cs.LG · cs.AI· stat.ML

ShapShift: Explaining Model Prediction Shifts with Subgroup Conditional Shapley Values

Tom Bewley , Salim I. Amoukou , Emanuele Albini , Saumitra Mishra , Manuela Veloso This is my paper

Pith reviewed 2026-05-10 16:09 UTC · model grok-4.3

classification 💻 cs.LG cs.AIstat.ML
keywords prediction shiftShapley valuesdecision treesmodel monitoringexplainable AIdata driftsurrogate models
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The pith

ShapShift attributes model prediction shifts to changes in conditional probabilities of subgroups defined by decision trees.

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

The paper proposes ShapShift as a Shapley value method to explain shifts in average model predictions caused by changes in input distributions. It attributes the overall shift to alterations in the conditional probabilities of subgroups, with those subgroups coming from the structure of decision trees. This approach starts with exact attributions for single trees at each split node and extends to ensembles by picking the most explanatory tree while handling residuals. A model-agnostic version uses surrogate trees grown under a novel objective to apply the same idea to black-box models such as neural networks. The resulting explanations are presented as simple, faithful, and nearly complete, supporting ongoing monitoring of models in environments where data patterns evolve.

Core claim

ShapShift decomposes a model's prediction shift into contributions from changes in the conditional probabilities of interpretable subgroups. For a single decision tree the attributions are exact and follow directly from probability changes at each split node. For tree ensembles the method selects the single tree that best explains the shift and accounts for the remaining effects separately. For arbitrary models it grows surrogate trees with a custom objective function that defines the subgroups, then applies the same conditional Shapley attribution.

What carries the argument

Subgroup conditional Shapley values that attribute the total prediction shift to changes in conditional probabilities along paths defined by decision-tree splits.

If this is right

  • Model monitors can identify the specific subgroups whose probability changes drive a shift in average predictions.
  • Explanations remain interpretable even when the underlying model is a large ensemble or a neural network.
  • Approximation methods make the attributions practical for real-time monitoring despite the cost of exact computation.
  • The same subgroup decomposition can be applied across different model classes without retraining the original model.

Where Pith is reading between the lines

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

  • If tree-defined subgroups consistently explain shifts, practitioners could use them as early-warning indicators for data drift before the shift becomes large.
  • The surrogate-tree construction suggests that any model whose behavior can be approximated by partitions might admit similar shift explanations without direct access to its internals.
  • The method implicitly treats the tree structure as a sufficient statistic for the relevant aspects of the input distribution.

Load-bearing premise

That subgroups defined by decision tree structures capture the dominant drivers of the observed prediction shift and that selecting one tree plus residual handling suffices for ensembles.

What would settle it

An observed prediction shift where adjusting the conditional probabilities of the attributed subgroups fails to reproduce most of the measured change in average model output.

Figures

Figures reproduced from arXiv: 2604.11200 by Emanuele Albini, Manuela Veloso, Salim I. Amoukou, Saumitra Mishra, Tom Bewley.

Figure 1
Figure 1. Figure 1: Using SHAPSHIFT to attribute an increase in the mean prediction of a loan approval model under a shift P → Q to subgroup conditional probabilities. The reduc￾tion of working people earning < $50k has the largest positive impact. The small unexplained term quantifies the shift not accounted for by the four given factors. explains the ensemble’s shift, account￾ing for residual effects. This requires adding a… view at source ↗
Figure 2
Figure 2. Figure 2: Calculation of SVs for subgroup conditionals to explain prediction shift in a decision tree. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Application of SHAPSHIFT to a decision tree for house price prediction. 5 Extension #1: SHAPSHIFT for Tree Ensembles Tree ensembles, such as random forests [5] and gradient boosted trees [13], are far more commonly used than single decision trees. We now describe how our method can be extended to such models. Firstly, consider what would change if the 4-leaf tree from [PITH_FULL_IMAGE:figures/full_fig_p00… view at source ↗
Figure 4
Figure 4. Figure 4: SV analysis of one member of a tree ensemble to explain ensemble-wide prediction shift, [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: illustrates this selection process on a random forest of 100 trees, each with 8 leaves, for the Breast Cancer Wisconsin dataset (see Appendix B.1 for details). We define distribution P as all cases reported in January 1989, and Q as those from later dates. Shifting from P to Q induces a prediction shift of −0.253 i.e. a 25.3% reduction in the predicted malignancy rate [PITH_FULL_IMAGE:figures/full_fig_p00… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of naïve and optimised split criteria for surrogate growth. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Aggregated performance metrics of SHAPSHIFT on 250 shifts across five Folktables datasets. ↓ / ↑ / ↕ = lower / higher / more separated is better. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Impact of tree choice on PercentUnexplained. Impact of Tree Choice In [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Impact of RF ensemble size on metrics. Comparison to Optimal Transport Baselines Prior shift explanation methods tackle somewhat different problems to ours, but with targeted ad￾ditions, we can adapt two methods proposed by Kulinski & Inouye [21] as baselines. Both begin by finding a pairing between data points from P and Q using optimal transport (OT). The first method (OT-C) then groups the paired points… view at source ↗
Figure 10
Figure 10. Figure 10: Quantitative comparison of SHAPSHIFT to adapted OT baselines on Folktables data. OT-S OT-C Ours [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Qualitative shift representations used by our method and baselines. More qualitatively, we argue that SHAPSHIFT ex￾planations achieve a stronger balance between in￾terpretability and information content than the OT baselines. As shown in [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of Kernel SHAP and pruning methods for handling large trees. Alternatively, the structure of our problem affords another way of handling large trees. Since the largest SVs are almost always for conditionals of split nodes near the root of a tree (which impact the largest pro￾portions of data), we can obtain very similar expla￾nations by applying the exact method to a heavily￾pruned version of t… view at source ↗
Figure 13
Figure 13. Figure 13: Illustration of a counterintuitive result when performing the SV analysis using subgroup [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Interpretation of our method as interventions on a causal graph. [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Empirical demonstration that P S⊆C w(S)ZS(l) ≈ P (l)+Q(l) 2 in expectation. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: PercentUnexplained results for random forest and gradient boosted tree ensembles. [PITH_FULL_IMAGE:figures/full_fig_p022_16.png] view at source ↗
read the original abstract

Changes in input distribution can induce shifts in the average predictions of machine learning models. Such prediction shifts may impact downstream business outcomes (e.g. a bank's loan approval rate), so understanding their causes can be crucial. We propose \ours{}: a Shapley value method for attributing prediction shifts to changes in the conditional probabilities of interpretable subgroups of data, where these subgroups are defined by the structure of decision trees. We initially apply this method to single decision trees, providing exact explanations based on conditional probability changes at split nodes. Next, we extend it to tree ensembles by selecting the most explanatory tree and accounting for residual effects. Finally, we propose a model-agnostic variant using surrogate trees grown with a novel objective function, allowing application to models like neural networks. While exact computation can be intensive, approximation techniques enable practical application. We show that \ours{} provides simple, faithful, and near-complete explanations of prediction shifts across model classes, aiding model monitoring in dynamic environments.

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

2 major / 2 minor

Summary. The paper proposes ShapShift, a Shapley-value-based method for attributing shifts in average model predictions to changes in conditional probabilities over interpretable subgroups defined by decision-tree structure. For single trees it claims exact computation from split-node probability changes; for ensembles it selects the single most explanatory tree and handles residuals separately; for black-box models it grows surrogate trees under a novel objective. The central claim is that the resulting attributions are simple, faithful, and near-complete across model classes and therefore useful for monitoring prediction shifts in dynamic environments.

Significance. If the near-complete claim can be substantiated, the method would offer a practical, axiom-grounded tool for diagnosing distribution-shift effects on deployed models, which is relevant to high-stakes monitoring tasks. The grounding in standard Shapley axioms and the tree-structured subgroup definition are clear strengths; however, the absence of residual bounds or quantitative validation for the ensemble case limits the immediate impact.

major comments (2)
  1. [ensemble extension] The ensemble extension (described after the single-tree case) selects one tree and attributes the remainder to a residual term. The manuscript provides neither an analytic bound on the residual fraction nor empirical measurements of its magnitude across the reported experiments. Because the central claim of 'near-complete' explanations across model classes rests on this residual being negligible, the lack of such quantification is load-bearing.
  2. [surrogate-tree variant] The surrogate-tree construction for black-box models relies on a novel objective function whose derivation is only sketched. Without an explicit statement of the objective, a proof that the resulting attributions remain faithful to the original model's conditional-probability shifts, or ablation results showing sensitivity to the surrogate, the model-agnostic claim cannot be evaluated.
minor comments (2)
  1. [abstract] The abstract states that 'exact computation can be intensive' and that 'approximation techniques enable practical application,' yet no concrete approximation algorithm, complexity analysis, or reference to the relevant section is supplied.
  2. [methods] Notation for the conditional Shapley values and the precise definition of 'subgroup' should be introduced with a single, self-contained equation early in the methods section to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The comments highlight important areas for strengthening the validation of the ensemble and surrogate extensions, which we address below. We plan to incorporate the suggested clarifications and additional analyses in a revised manuscript.

read point-by-point responses

  1. Referee: The ensemble extension (described after the single-tree case) selects one tree and attributes the remainder to a residual term. The manuscript provides neither an analytic bound on the residual fraction nor empirical measurements of its magnitude across the reported experiments. Because the central claim of 'near-complete' explanations across model classes rests on this residual being negligible, the lack of such quantification is load-bearing.

    Authors: We agree that explicit quantification of the residual is necessary to support the near-complete claim. Deriving a general analytic bound is difficult because the residual depends on the specific ensemble structure, data distribution, and tree selection heuristic. However, we will add empirical measurements of the residual fraction (as a percentage of the total shift) for all ensemble experiments in the revised manuscript. These measurements will be reported alongside the existing results to demonstrate that the residual is typically small in practice. We will also expand the description of the tree-selection criterion to clarify how it minimizes the residual. revision: partial

  2. Referee: The surrogate-tree construction for black-box models relies on a novel objective function whose derivation is only sketched. Without an explicit statement of the objective, a proof that the resulting attributions remain faithful to the original model's conditional-probability shifts, or ablation results showing sensitivity to the surrogate, the model-agnostic claim cannot be evaluated.

    Authors: We acknowledge that the surrogate-tree section requires a more complete presentation. In the revision we will state the novel objective function in explicit mathematical form, including the precise optimization criterion used to grow the surrogate. We will add a short theoretical argument showing that the conditional Shapley values computed on the surrogate remain faithful to the original model's subgroup probability shifts under the chosen objective, and we will include ablation experiments that vary the surrogate hyperparameters and report the resulting attribution stability. These changes will allow readers to evaluate the model-agnostic extension directly. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation builds on standard Shapley axioms and independent extensions

full rationale

The paper defines ShapShift by applying Shapley values to attribute shifts in average predictions to changes in conditional subgroup probabilities, where subgroups are induced by decision tree splits. For single trees this yields exact attributions at nodes, following directly from the value function without redefining the target shift in terms of the attributions themselves. The ensemble extension (selecting one tree plus residuals) and surrogate-tree variant (with novel objective) are presented as practical constructions motivated by computational needs, not as outputs forced by fitting or self-referential definitions. No load-bearing self-citations, uniqueness theorems imported from prior author work, or ansatzes smuggled via citation appear in the derivation chain. The method remains self-contained against external Shapley axioms and tree structure, with no step reducing by construction to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields no concrete free parameters, invented entities, or non-standard axioms; the method rests on the standard efficiency and additivity properties of Shapley values plus the assumption that tree splits define meaningful subgroups.

axioms (1)
  • standard math Shapley value axioms (efficiency, symmetry, dummy player, additivity)
    Invoked as the foundation for attributing the total prediction shift to subgroup probability changes.

pith-pipeline@v0.9.0 · 5485 in / 1337 out tokens · 82344 ms · 2026-05-10T16:09:56.331221+00:00 · methodology

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