DeepSHAP

DeepSHAP bridges two foundational interpretability frameworks. It uses DeepLIFT's linear composition rules—the Rescale and RevealCancel rules—to efficiently backpropagate contributions through the network. By setting a specific reference value and applying Shapley value axioms, DeepSHAP ensures the attributions satisfy local accuracy (the sum of feature attributions equals the model output difference from baseline) and consistency (if a feature's contribution increases, its attribution never decreases). This hybrid approach avoids the exponential computational cost of naive Shapley value estimation while preserving their game-theoretic guarantees.

DeepSHAP defines specific propagation rules for common neural network layers to approximate Shapley values efficiently:

• Linear/Dense layers: Attributions are distributed proportionally to weight-activation products, equivalent to exact Shapley values for linear models.
• Convolutional layers: Contributions are backpropagated through the filter weights, preserving spatial attribution maps critical for medical image analysis.
• Non-linear activations (ReLU, Sigmoid): DeepSHAP applies the RevealCancel rule, which handles positive and negative contributions separately to avoid zeroing out negative evidence.
• Max-pooling layers: Attribution is routed entirely to the neuron that achieved the maximum value, reflecting the true winner-take-all dynamic.

The choice of baseline or reference input critically shapes DeepSHAP attributions. The baseline represents a neutral or 'missing' input against which contributions are measured. In medical imaging, common baselines include:

• Zero baseline: A black image, representing the absence of signal.
• Blurred baseline: A Gaussian-blurred version of the input, removing fine detail while preserving average intensity.
• Mean image baseline: The average pixel value across the training dataset. DeepSHAP computes the difference-from-reference for each feature, meaning the attribution explains why the prediction differs from what the model would output for the baseline input. Selecting a clinically meaningful baseline is essential for regulatory-grade explanations.

DeepSHAP belongs to the class of additive feature attribution methods, meaning it decomposes the model's output into a sum of individual feature contributions plus a base value. For a given input x, the explanation takes the form: f(x) = φ₀ + Σ φᵢ, where φ₀ is the expected model output over the baseline distribution and each φᵢ is the Shapley value for feature i. This additivity property is essential for regulatory auditability—every pixel's contribution to a diagnostic decision can be independently verified and summed to reconstruct the exact prediction margin. It also enables direct comparison of feature importance across different inputs and models.

While KernelSHAP estimates Shapley values by sampling feature coalitions—requiring 2^M model evaluations for M features in the worst case—DeepSHAP exploits the network's internal structure to compute attributions in a single forward and backward pass. For a ResNet-50 processing a 224×224 medical image, DeepSHAP produces a full saliency map in milliseconds, compared to hours for KernelSHAP. This speed makes DeepSHAP practical for:

• Real-time clinical workflows where explanations must accompany predictions.
• Iterative model debugging during development.
• Large-scale retrospective studies requiring millions of explanations. The trade-off is that DeepSHAP assumes feature independence, which may introduce approximation error for highly correlated inputs.

A quantitative metric for evaluating explanation quality. Faithfulness measures how accurately attributed importance scores correlate with actual model behavior when features are perturbed or removed. Key evaluation approaches include:

• Perturbation-based: Remove top-attributed features and measure output change
• Deletion/Insertion curves: Track prediction confidence as features are progressively removed or added
• Correlation tests: Compare attribution rankings against ground-truth feature importance DeepSHAP explanations should be validated using these metrics to ensure clinical reliability.