SHAP-based Analysis for Model Interpretability

• SHAP-based analysis is a post-hoc method that uses Shapley values to decompose model predictions into feature contributions based on cooperative game theory.
• The TreeSHAP algorithm efficiently computes exact attributions for tree ensembles by leveraging decision path structures, enabling scalable analysis.
• Practical use cases span local and global interpretability, guiding model selection, feature engineering, and operational decision-making.

SHAP-based analysis refers to the quantitative post-hoc dissection of complex machine learning model predictions using the SHapley Additive exPlanations (SHAP) framework. SHAP decomposes each output into a sum of featurewise contributions, with each contribution quantifying, according to cooperative game theory, the marginal effect of including that feature while averaging over all possible coalitions of other features. The adoption of SHAP-based analysis has enabled high-resolution model interpretability with strong theoretical guarantees for local accuracy, consistency, and missingness. Computational advances such as TreeSHAP have made SHAP-based analysis scalable for tree ensembles and have driven its application across a range of scientific, engineering, and biomedical domains.

1. Mathematical Foundations of SHAP Attribution

The core of SHAP-based analysis is the Shapley value. For a predictive model $f$ on $M$ input features, the Shapley value for feature $i$ is given by

$$\phi_i = \sum_{S \subseteq F \setminus \{i\}} \frac{|S|! (M-|S|-1)!}{M!} [f(S \cup \{i\}) - f(S)],$$

where $F$ is the full set of features, and $f(S)$ denotes the expected model prediction when only features in $S$ are known. SHAP reformulates the prediction $g(x)$ as an additive decomposition: $g(x) = \phi_0 + \sum_{i=1}^M \phi_i,$ with $\phi_0$ the expected model output and each $\phi_i$ the marginal, coalition-averaged value for feature $i$. This decomposition is unique among additive attribution methods in satisfying local accuracy, consistency (improving a feature's marginal effect cannot reduce its attribution), and missingness (uninfluential features receive zero weight) (Lundberg et al., 2017).

2. TreeSHAP Algorithm and Computational Advances

For models such as random forests and boosted trees, direct evaluation of the SHAP sum scales exponentially in $M$. The TreeSHAP algorithm exploits the decision path structure of trees to achieve $O(T \cdot L^2)$ complexity per evaluation, where $T$ is the number of trees and $L$ the average maximum depth per tree. Each tree is traversed to compute conditional probabilities at each split, and path-dependent weights are aggregated, ensuring exact Shapley values for tree ensembles (Bard et al., 30 Sep 2025).

Recent improvements include Fast TreeSHAP v1 (constrained dynamic programming, reducing computation by ignoring splits not taken) and Fast TreeSHAP v2 (precomputing all subset weights per path), yielding up to $3\times$ speedup in large-scale post-hoc model diagnosis tasks (Yang, 2021). For extremely large tabular datasets or deep forests, implementations leverage parallel C backends and efficient memory reuse.

3. SHAP-based Interpretation: Local and Global Insights

SHAP-based analysis can be performed at both the local (per-sample) and global (population-level) scales. Locally, force plots or waterfall plots are used to visualise how individual feature values—through their SHAP attributions—push the prediction up or down from the baseline. Globally, mean absolute SHAP values $|\phi_i|$ are aggregated across the test set to yield feature importance rankings. These can be visualised as bar, beeswarm, or dependence plots to highlight main effects and interactions.

For the prediction of thermospheric neutral density using a random forest (RANDM), SHAP-based analysis established that 43 nm EUV flux is the dominant background driver across quiet and storm-time periods; geomagnetic SYM-H index becomes dominant for $<$–60 nT, providing a quantitative storm-time threshold (Bard et al., 30 Sep 2025). SHAP-based analysis alone enabled the first model-based empirical definition of storm levels in neutral density prediction.

4. Interaction Effects, Redundancy, and Higher-order Explanations

While standard SHAP captures only main effects, post-processing of SHAP attributions can reveal latent feature interactions through collinearity in SHAP values or dependence plots. High cross-interaction between certain EUV bands (e.g., 43 nm and 85.55 nm) indicates possible redundancy, which can inform principled feature reduction without accuracy loss. Analysis of SHAP contributions across magnetic local times exposes physical day/night and dawn/dusk asymmetries, and higher-order domains (e.g., third-order interactions) have been recommended for future extension to capture subtle physical coupling (Bard et al., 30 Sep 2025).

5. Model Selection, Feature Engineering, and Pipeline Integration

In applied settings such as predictive maintenance, a typical SHAP-based analysis pipeline involves:

• Data preprocessing and normalization (standardization, encoding),
• Model selection via cross-validation (e.g., XGBoost, Random Forest),
• Computation of SHAP values for key models using TreeSHAP,
• Visualization and aggregation for both local (force plot, dependence plot) and global (mean $|\phi_i|$ ranking) interpretability (Zhao et al., 1 Dec 2025).

SHAP-based analysis revealed that in milling machine fault prediction, processing temperature, torque, and speed were the most informative variables, and dynamic tool replacement as well as spindle speed adjustment were implicated as proactive maintenance strategies.

6. Practical Recommendations and Theoretical Guarantees

Best practices emerging from SHAP-based analytic work include:

• Applying SHAP analysis via TreeSHAP for both local event diagnosis and global pattern discovery;
• Using feature aggregation to mitigate redundancy and inform principal component or band selection;
• Extending SHAP-based interaction decomposition to order $>2$ when physical theory or residual patterning suggests higher-order couplings;
• Using SHAP-derived quantitative thresholds (e.g., SYM-H $<-60$ nT) to guide operational event definitions and real-time alert systems (Bard et al., 30 Sep 2025);
• Broadening the application of SHAP (via TreeSHAP) to related geoscientific models, such as ionospheric TEC, ground-induced currents, or other spatiotemporal phenomena, to uncover latent dependency structures and to support data-driven operational protocols.

7. Limitations, Robustness, and Directions for Further Work

SHAP-based analysis inherits computational and conceptual challenges:

• TreeSHAP, while polynomial, can become a bottleneck for datasets with hundreds of trees or features unless optimized implementations and sampling are used.
• SHAP values quantify association, not causation: interventions indicated by attribution analysis must be physically and experimentally validated.
• Local and global SHAP attributions can depend on feature representation (e.g., binning, encoding), and sensitivity analyses are advised to ensure interpretational stability.
• Synthetic datasets or simulated fault data may not perfectly replicate operational conditions; validation of SHAP-based insights with real-world data remains essential.

Advances are recommended in the integration of additional physical indices, expansion of SHAP interactions, and systematic cross-validation with operational data to enhance the reliability, utility, and physical alignment of SHAP-based analyses (Bard et al., 30 Sep 2025).