SHAP Dependence Plot

A SHAP dependence plot is fundamentally a scatter plot where the x-axis represents the feature's actual value and the y-axis represents its SHAP value for each instance. A vertical dispersion of points at a specific x-value indicates interaction effects with other features. A clear, non-linear trend line reveals the model's learned functional relationship, showing exactly how and when a feature pushes predictions higher or lower.

The plot's most powerful diagnostic capability is revealing interactions through color mapping. By coloring each point based on the value of a second, interacting feature, patterns emerge:

• Systematic color gradients: Show that the main feature's effect depends on another feature's value.
• Vertical dispersion: Indicates that for the same main feature value, the SHAP value varies significantly due to another feature.
• Example: In a housing model, the effect of square footage (x-axis) might be colored by neighborhood, showing that added space is more valuable in premium areas.

Unlike traditional partial dependence plots that average effects, SHAP dependence plots preserve heterogeneity. This makes them ideal for spotting:

• Threshold effects: A feature has zero impact until a critical value is reached, then the SHAP value spikes.
• Saturation: The marginal benefit of a feature diminishes after a certain point, forming a logarithmic curve.
• Non-monotonic patterns: A feature like 'age' might have a positive effect up to a point, then turn negative, creating an inverted U-shape.

A standard Partial Dependence Plot (PDP) shows the average marginal effect, which can obscure opposing effects in subsets of data. A SHAP dependence plot shows individual conditional expectations, making it strictly more informative:

• PDP Limitation: If a feature increases predictions for half the data and decreases them for the other half, a PDP might show a flat, misleading zero-effect line.
• SHAP Advantage: The SHAP plot would show a clear split in the y-axis values, immediately alerting the analyst to a strong interaction that requires investigation.

The plot is built directly from the SHAP value matrix. For each instance, the algorithm has already computed the exact contribution of the feature in question. The dependence plot simply plots these pre-computed values against the feature's original input values. If an interaction feature is selected for coloring, the plot uses SHAP interaction values, which further decompose the attribution into main effects and pairwise interaction effects, ensuring the visualization reflects true model dynamics.

These plots are essential for model debugging and validation:

• Sanity checks: Verify that the model respects known physical or business constraints (e.g., higher income should not decrease creditworthiness).
• Detecting artifacts: Spot erratic, high-frequency oscillations in the SHAP trend that suggest the model is overfitting to noise rather than learning a robust pattern.
• Feature engineering: Identify where a feature's effect plateaus, suggesting a need for a log transformation or a clipping operation to improve model linearity.

The mathematical foundation that makes dependence plot coloring possible. SHAP interaction values capture pairwise feature effects by distributing credit among all pairs of features, not just individuals.

• Extends the standard additive SHAP decomposition
• Captures the residual effect not explained by main effects alone
• Computed via the Shapley-Taylor interaction index
• Essential for detecting heterogeneous effects where a feature's impact depends on another

The global companion to the local dependence plot. A SHAP summary plot combines feature importance with feature effects by displaying the distribution of SHAP values for every feature across an entire dataset.

• Each point represents a single instance's SHAP value
• Color encodes the feature's actual value (red high, blue low)
• Reveals non-monotonic relationships and variance in feature impact
• Serves as a diagnostic to select which features to investigate with dependence plots

The choice of SHAP formulation directly shapes the dependence plot's interpretation. Observational SHAP preserves feature correlations by conditioning on observed values, reflecting the model's behavior on the natural data manifold.

• Interventional SHAP breaks correlations by sampling from marginal distributions
• Dependence plots under interventional SHAP show causal 'what-if' effects
• Observational plots reveal associative patterns the model has learned
• Mismatched formulations can produce misleading interaction signatures

A precursor and alternative to SHAP dependence plots. PDPs show the average marginal effect of a feature on the predicted outcome, but they can obscure heterogeneous effects when interactions are present.

• PDPs average away individual variation; SHAP plots preserve it
• A flat PDP can mask strong but opposing effects in subgroups
• SHAP dependence plots reveal dispersion that PDPs hide
• Use PDPs for global trend; use SHAP dependence for instance-level detail

A critical caveat when interpreting dependence plots. Many SHAP implementations assume feature independence to reduce computational complexity, which can produce unrealistic model evaluations when features are correlated.

• Dependence plots may show extrapolated regions with no real data support
• Correlated features can cause SHAP values to be split artificially
• Always check the background dataset's correlation structure
• Use conditional expectation methods to mitigate this distortion

The instance-level counterpart to the dependence plot. While a dependence plot shows how a feature's effect varies across a population, a SHAP waterfall plot decomposes a single prediction by showing how each feature pushes the model output from the baseline value.

• Starts at the expected model output E[f(x)]
• Each bar adds or subtracts to reach the final prediction f(x)
• Complements dependence plots by grounding global patterns in a specific decision
• Essential for auditing individual high-stakes predictions