Feature Attribution Methods: SHAP

• Feature Attribution Methods (SHAP) are a systematic approach that decomposes a model’s prediction into additive contributions from individual features using Shapley values.
• SHAP leverages axiomatic guarantees such as efficiency, symmetry, and linearity to ensure fair and consistent feature attributions across diverse model types.
• Advanced implementations like KernelSHAP, TreeSHAP, and DeepSHAP enable scalable explanations, while extensions address causal inference, weighting, and distribution-aware challenges.

Feature attribution methods, especially those based on the Shapley value (“SHAP” methods), are designed to decompose the output of a machine learning model into additive contributions attributable to individual input features. This framework is widely used to provide local and global explanations for complex models, including deep neural networks, tree ensembles, and distributed pipelines. Over the past several years, substantial theoretical and algorithmic progress has been made in formalizing, accelerating, and critiquing Shapley-based explanations, as well as in extending the core methodology to address limitations in specific domains.

1. Shapley-Value Foundations and Axiomatic Guarantees

The foundation of SHAP is the classical Shapley value from cooperative game theory, adapted to the setting where features $\{1,\dots,m\}$ are "players" and the model output is the "payout" for observing a coalition $S\subseteq N$ of features as present. For a model $f\colon \mathbb{R}^m\to\mathbb{R}$ with input $x$ and explicit baseline $x^b$, the (interventional) value function is defined as $v(S) = f_S(x_S)$, i.e., evaluating $f$ with only features in $S$ present. The SHAP attribution for input feature $i$ is then

$$\phi_i(f, x) = \sum_{S \subseteq N \setminus \{i\}} \frac{|S|!\,(m - |S| - 1)!}{m!}\ [f_{S \cup \{i\}}(x_{S\cup\{i\}}) - f_S(x_S)],$$

which averages feature $i$'s marginal contributions over all coalitions. Shapley-value attributions are uniquely characterized by the following axioms:

• Efficiency (local accuracy): $\sum_{i=1}^m \phi_i(f, x) = f(x) - f(\emptyset)$
• Symmetry: Features with equal marginal impact receive equal attributions.
• Dummy (missingness): Features with zero marginal impact are assigned zero attribution.
• Linearity: Attributions are additive across sums of models.

These axioms ensure fairness, local accuracy, and interpretability and have driven the adoption of SHAP in a wide variety of application domains (Lundberg et al., 2017).

2. Computational Strategies and Acceleration

Computing exact Shapley values is combinatorially expensive, scaling as $O(2^m)$ in the number of features. In practice, this is infeasible for moderate $m$. Standard estimation approaches include:

• Model-agnostic sampling: KernelSHAP, IME, and related methods sample subsets $S$ and approximate $\phi_i$ via Monte-Carlo, with cost $O(K\cdot m)$ per explanation and $K$ required for variance reduction (Lundberg et al., 2017).
• Model-specific algorithms: Tree-based models enable efficient computation via dynamic programming, as in TreeSHAP, which reduces computation to $O(T\cdot L\cdot D^2)$ for an ensemble of $T$ trees, $L$ leaves per tree, and depth $D$ (Lundberg et al., 2017).
• Backpropagation and deep pipelines: DeepSHAP leverages per-layer explainers—e.g., DeepLIFT for neural blocks, TreeSHAP for tree layers—and propagates attributions backward through pipelines, achieving $O(L)$ cost with $L$ pipeline stages and sidestepping the exponential scaling of subset enumeration (Chen et al., 2021).

Table 1: Complexity of Major SHAP Estimation Methods

Method	Complexity	Applicability
Exact Shapley	$O(2^m \cdot L)$	Any model
KernelSHAP	$O(K \cdot L)$	Any model
TreeSHAP	$O(T \cdot L \cdot D^2)$	Tree ensembles
DeepSHAP	$O(L)$	Model pipelines

DeepSHAP additionally enables distributed scenarios where access to all models' internals is impossible by composing local attributions with efficiency preservation at each stage (Chen et al., 2021).

3. Theoretical Limits and Failure Modes

Impossibility results demonstrate fundamental limitations of Shapley-based feature attribution methods. If an attribution method is both complete (attributions sum to the output difference) and linear (decomposable over additive models)—conditions satisfied by SHAP and Integrated Gradients—then it can fail to distinguish critical differences in local model behavior. Specifically, for any nontrivial model class (including neural networks with piecewise linear components), no complete & linear attribution can reliably distinguish local effects or spuriousness of features beyond random guessing (Bilodeau et al., 2022). Concrete counterexamples show that:

• SHAP can assign zero attribution to a feature whose local derivative is arbitrarily large (or negative).
• Spurious features can be masked in the attribution even if they govern the prediction in a local region.
• Attributions may depend strongly on the behavior of the model away from the query point, due to the role of the (potentially distant) baseline distribution.

This restricts the interpretation of positive or zero SHAP values; informative end-task definitions and direct counterfactual queries are required for reliable causal or sensitivity analysis (Bilodeau et al., 2022).

4. Methodological Extensions and Practical Enhancements

Numerous extensions address recognized shortcomings and adapt SHAP to new tasks:

• WeightedSHAP: By learning a task-specific weighting $\alpha$ over coalition sizes, WeightedSHAP can optimize the informativeness of marginal contributions, recovering model predictions more efficiently than uniform Shapley weighting. This approach, which reduces to classical SHAP when $\alpha$ is uniform, is guaranteed not to perform worse than SHAP on utility objectives such as prediction-recovery or inclusion-exclusion accuracy (Kwon et al., 2022).
• Causal SHAP: To distinguish causation from correlation, Causal SHAP integrates causality discovered via the Peter-Clark algorithm and estimates path-specific causal effects using IDA. Feature attributions are then reweighted according to their total causal strength from each feature to the response, zeroing out purely correlational features while preserving efficiency and symmetry (Ng et al., 31 Aug 2025).
• Distribution-aware SHAP (SHAP-KL): To prevent label leakage and inflated fidelities due to class-dependent explanation methods, SHAP-KL replaces the value function by the negative KL divergence between class distributions with and without each feature. FastSHAP-KL provides amortized explanations with guarantees that subsets of top-ranked features preserve the overall label distribution (Jethani et al., 2023).
• Statistical Significance of Feature Rankings: Adaptive hypothesis-testing and sampling algorithms can identify the top-$K$ features by SHAP value with rigorous guarantees on the family-wise error rate. These procedures directly control the instability inherent in Monte Carlo estimation (Goldwasser et al., 28 Jan 2024).
• SHAP-guided regularization: Model training objectives can be augmented with entropy-based penalties on the SHAP attribution distribution to encourage sparsity and stability, thus promoting both interpretability and generalization (Saadallah, 31 Jul 2025).

5. Advanced Use Cases: Pipelines, Tree Ensembles, and LLMs

Advanced methodological progress has enabled practical application of SHAP-based attributions in settings previously considered intractable:

• Distributed and multi-stage pipelines: DeepSHAP enables attribution propagation through model pipelines comprising deep networks, tree ensembles, and linear components—even when held by different entities—while maintaining efficiency and explanatory salience (Chen et al., 2021).
• Large tree ensembles and industrial-scale deployment: WOODELF provides a unifying algorithmic framework combining decision trees, pseudo-Boolean logic, and game theory, accelerating background SHAP, path-dependent SHAP, Shapley interactions, and Banzhaf values to linear or near-linear time for massive datasets, leveraging CPU/GPU acceleration and enabling explanations at scales of millions of data points and features (Nadel et al., 12 Nov 2025).
• Stochastic LLMs: In the context of LLMs, the stochasticity of inference invalidates classical Shapley axioms unless attributions are cached per coalition or deterministic inference is enforced. llmSHAP defines variants that recover or relax these axioms, with explicit trade-offs between computational expense and axiomatic compliance (Naudot et al., 3 Nov 2025).

6. Recommendations, Best Practices, and Limitations

Given the foundational limitations and empirical variability found in feature attribution—especially with SHAP—the following practices are recommended:

• Robustness assessment: Always compute attributions across multiple runs with varied initializations and baselines, especially in deep and multi-view models, to identify consistent "core" features and deprioritize high-variance ones (Claborne et al., 30 Jul 2025).
• Distribution-aware aggregation: To justify feature removal or claim non-importance, aggregate SHAP values over the product of the marginals (“extended support”) rather than only over the original data support. In practice, column-wise permutation suffices (Bhattacharjee et al., 29 Mar 2025).
• Downstream validation: Validate attribution-driven feature selection through predictive accuracy on secondary models (e.g., random forests on selected features) and clustering quality, but always report both mean attributions and their stability (Claborne et al., 30 Jul 2025).
• Semivalue and kernel design: Consider kernel-weight generalizations (e.g., as in WeightedSHAP) to tailor attribution locality and align with domain- or task-specific desiderata (Kwon et al., 2022, Hiraki et al., 1 Jun 2024).
• Statistical guarantees: Use adaptive statistical testing to ensure the reproducibility of top-ranked features in any SHAP-based workflow (Goldwasser et al., 28 Jan 2024).

Persistent limitations of SHAP include potential misalignment with local causal structure, instability to model reinitialization, and challenges in highly correlated or dependent data regimes. In such settings, causal- or counterfactual-augmented variants should be considered, and explanations should be validated for stability and task relevance.

7. Future Directions and Open Challenges

The design, axiomatic analysis, and empirical evaluation of feature attribution methods remains a dynamic research area. Open directions include:

• Extension of causal SHAP and dependency-aware methods to high-dimensional and structured prediction tasks (Ng et al., 31 Aug 2025).
• Development of better human-interpretable SHAP explanations for concept-based, non-invertible transformations (see latent SHAP) (Bitton et al., 2022).
• Automated selection or learning of optimal attribution kernels and sampling strategies, matched to downstream utility or fidelity metrics (Kwon et al., 2022, Hiraki et al., 1 Jun 2024).
• Scalable computation via GPU and parallelization for real-time, large-scale applications, as exemplified by WOODELF (Nadel et al., 12 Nov 2025).
• Formalization of attribution-based regularization in general differentiable learning settings (Saadallah, 31 Jul 2025).
• Characterization of SHAP behavior in highly stochastic model inference pipelines, such as prompt-based or chain-of-thought LLMs (Naudot et al., 3 Nov 2025).

The interplay between theoretical guarantees, computational feasibility, and empirical reliability will continue to shape the trajectory of feature attribution research and its adoption in high-stakes decision-making pipelines.