Baseline Value

The baseline value is the expected model prediction over the background dataset. Formally, it is the average prediction when all features are missing: E[f(x)] where the expectation is taken over the background distribution.

• Acts as the intercept term in the additive explanation model
• Represents the prediction before any feature information is known
• Every SHAP value measures deviation from this baseline

The Efficiency Property of Shapley values guarantees that the sum of all feature attributions plus the baseline value exactly equals the model's prediction for any instance.

• f(x) = baseline + Σ SHAP values
• Ensures complete decomposition of the prediction
• No unexplained residual remains
• Critical for auditability in regulated industries

The baseline value depends critically on the background dataset used to compute it. This dataset represents the distribution of 'missing' feature values.

• Training data mean: Most common choice, represents average case
• Median sample: Robust to outliers in skewed distributions
• Domain-specific reference: A clinically normal patient, a zero-signal state
• K-means centroids: Multiple baselines for clustered data
• The choice directly impacts SHAP value interpretation

In a SHAP waterfall plot, the baseline value appears as the starting point at the bottom of the chart. Each feature's SHAP value is then stacked sequentially, pushing the prediction upward or downward.

• E[f(x)] sits at the base of the waterfall
• Red arrows push above the baseline (positive contribution)
• Blue arrows push below the baseline (negative contribution)
• The final bar equals f(x), the actual prediction
• Provides intuitive visual decomposition for single-instance explanations

The method of computing the baseline distinguishes two SHAP formulations:

• Interventional SHAP: Breaks feature correlations by sampling from the marginal distribution. The baseline is the unconditional expectation. Reflects causal 'what-if' interventions.
• Observational SHAP: Preserves correlations by conditioning on observed features. The baseline respects the joint distribution. Reflects model behavior on the natural data manifold.
• The choice affects how correlated features are attributed

In the SHAP library, the baseline value is computed automatically from the background dataset passed to the Explainer object.

• shap.Explainer(model, background_data) computes E[f(x)] internally
• For TreeSHAP, the background dataset also defines the feature splitting paths
• For DeepSHAP, a single reference sample or mean is often used
• The base_value attribute of a SHAP explanation object stores this value
• Can be accessed via explanation.base_values for inspection