Individual Conditional Expectation (ICE) Plot

Unlike a Partial Dependence Plot (PDP), which shows a single global average curve, an ICE plot visualizes one line per instance. This disaggregation reveals heterogeneous effects where the direction of a feature's impact differs across subgroups. If all ICE curves follow a similar shape, the PDP is a reliable summary. If curves diverge or intersect, it signals complex interactions that a PDP would mask.

A standard ICE plot can be difficult to read when instances have vastly different baseline predictions. Centered ICE (c-ICE) normalizes all curves to start at zero at a specific feature value, isolating the differential effect of the feature. This makes it easier to visually identify clusters of instances that respond similarly, even if their absolute predicted values differ.

Derivative ICE (d-ICE) plots the partial derivative of the prediction with respect to the feature for each instance. This reveals where and for whom the feature has a strong influence. If d-ICE curves are flat and identical, no interaction exists. Significant variation in the derivatives across instances is a direct visual indicator of feature interactions in the model.

To generate an ICE plot for a feature (x_S):

• Select a grid of values for (x_S).
• For each instance (i), create a set of synthetic copies where all features except (x_S) are held constant at their observed values, and (x_S) is set to each grid value.
• Predict on all synthetic copies.
• Plot the predicted value against the grid values for each instance. This brute-force approach is model-agnostic but computationally linear in the number of instances and grid points.

ICE plots are a primary diagnostic tool for uncovering non-linear relationships and subgroup effects. For example, an ICE plot of age against predicted health risk might reveal that risk increases with age for most patients but decreases for a specific subgroup with a particular genetic marker. This granular insight is critical for auditing fairness and validating domain logic before deployment.

ICE plots suffer from overplotting when the number of instances is large, making individual curves indistinguishable. They also visualize the effect of only one or two features at a time and assume feature independence during the perturbation process, which can generate unrealistic synthetic data points in regions of the feature space with zero density. Subsampling and transparency are common mitigation strategies.

The direct global complement to the ICE plot. While an ICE plot visualizes the prediction function for each individual instance, a PDP shows the average marginal effect of a feature. The PDP is calculated by taking the mean of all ICE curves at each feature value. Comparing ICE plots against the PDP line immediately reveals if the average effect is masking heterogeneous relationships or interactions.

A critical variant that removes level effects to isolate interaction effects. Standard ICE curves often start at different prediction values, making heterogeneity hard to see. c-ICE normalizes all curves to start at zero at a chosen anchor point. This 'centering' makes it visually obvious when instances diverge, confirming that the feature of interest interacts with other features to produce different response slopes.

A visualization that plots the partial derivative of the prediction function with respect to the feature for each instance. While standard ICE shows the functional relationship, d-ICE reveals where and for whom the feature has a strong influence. A flat d-ICE curve at zero indicates a region of no effect, while sharp spikes identify feature values where the model's decision boundary is highly sensitive for specific subgroups.

An unbiased alternative to both PDP and ICE when features are highly correlated. ICE and PDP can produce unrealistic extrapolations by averaging over impossible data combinations. ALE computes the local effect by accumulating the average differences in predictions over conditional distributions. It is the preferred tool for visualizing feature effects when multicollinearity is present in the data.

The quantitative metric that validates visual findings from ICE plots. The Friedman's H-statistic measures the variance of the prediction function attributable to interactions between features. If ICE curves show significant crossing or divergence, the H-statistic quantifies this interaction strength. A value of zero indicates no interaction, while a high value confirms that the heterogeneous effects observed in the ICE plot are statistically meaningful.

A game-theoretic attribution method that decomposes a single prediction into feature contributions. While ICE shows how a prediction changes as you vary one feature, SHAP explains the exact composition of a prediction at a fixed point. SHAP dependence plots often overlay ICE-like visualizations with color-coded interaction effects, bridging local attribution with the functional form revealed by ICE curves.