Accumulated Local Effects (ALE) Plot

The defining advantage of ALE plots is their ability to handle correlated features reliably. While Partial Dependence Plots (PDPs) average predictions over the marginal distribution—often creating unrealistic data instances when features are dependent—ALE plots condition on the conditional distribution of features. This means the effect of a feature is computed only within neighborhoods where those data combinations actually exist, preventing the model from being evaluated on extrapolated, non-physical data points.

ALE plots are constructed by dividing the feature's value range into small intervals (often quantiles). Within each interval, the local effect is calculated as the difference in predictions when the feature value is replaced with the upper and lower bounds of that interval, holding other features constant. These local effects are then accumulated (summed) across all intervals and centered to zero. This accumulation process reveals the global trend of the feature's influence on the prediction.

ALE plots are always centered at zero, meaning the y-axis represents the difference from the average prediction. A flat line at zero indicates the feature has no effect. An upward trend shows a positive effect on the prediction relative to the average, while a downward trend shows a negative effect. This centering makes it straightforward to interpret the relative influence of a feature across its distribution, without needing to know the model's baseline intercept.

Compared to instance-level methods like SHAP or LIME, ALE plots are computationally efficient for global interpretation. The algorithm requires only a single pass through the binned data intervals to compute local effects, making it scalable to large datasets and complex models. The primary computational cost is the number of predictions required, which is proportional to the number of intervals chosen, not the number of individual instances.

Standard ALE plots are designed to isolate the first-order (main) effect of a single feature. They do not visualize interaction effects. If a feature's influence is entirely through an interaction with another variable, the ALE plot may show a flat line, correctly indicating no isolated main effect. For analyzing interactions, a second-order ALE plot can be computed, which estimates the joint effect of two features beyond their individual main effects.

ALE plots are a model-agnostic technique, meaning they can be applied to any supervised learning model—from gradient-boosted trees to deep neural networks—without needing access to model internals. They provide a global explanation by summarizing the average effect of a feature across the entire dataset, making them a powerful tool for model debugging, validation against domain knowledge, and communicating model behavior to non-technical stakeholders.

The central problem ALE plots are designed to solve. When features like 'age' and 'years of driving experience' are correlated, a PDP substitutes unrealistic combinations (e.g., age 16 with 20 years experience) into the model. This extrapolation into zero-density regions produces unreliable predictions. ALE plots avoid this by computing local differences within actual conditional distributions, making them unbiased under correlation.

The ALE algorithm operates in three steps:

• Binning: The feature is divided into intervals (e.g., deciles).
• Local Effect Calculation: Within each bin, the model's prediction difference is computed by varying the feature to the bin's upper and lower bounds, conditional on the data points actually falling in that bin.
• Accumulation: These local effects are summed and centered to zero mean, producing the final plot. This conditional computation is what makes ALE unbiased.

ALE plots are centered to zero mean, meaning the y-axis shows the deviation from the average prediction. A value of +5 at a feature level means the model predicts, on average, 5 units higher than the baseline when the feature takes that value. This differs from PDPs, which show absolute prediction values. The zero-centering makes it easy to identify where a feature has a positive or negative influence relative to the model's average behavior.