How ALE Plots Overcome Partial Dependence Limitations in ML

Accumulated Local Effect Plot

Partial dependence plots assume the target feature is independent of other features, which often fails in real data (e.g., height, weight, food intake). The Accumulated Local Effect (ALE) plot, proposed by Daniel W. Apley in 2016, resolves this by handling correlated features.

Both ALE and partial dependence aim to show how a target feature influences model predictions, but ALE relaxes the strict independence assumption, making it applicable to a wider range of problems, such as financial risk‑control where features like credit score are correlated with income or work experience.

From Partial Dependence to ALE

To illustrate the transition, we revisit the example of age, height, weight, and food intake. In a partial dependence plot we fix the target feature (weight) and vary it across a grid while averaging predictions over the dataset. Because weight is correlated with age and height, the independence assumption is violated.

One way to remove this correlation is to fix non‑target features at specific values, yielding a marginal plot that represents the conditional expectation of the target feature. However, the marginal plot still mixes the effects of target and non‑target features.

By applying a difference‑in‑differences approach—computing the change in the conditional expectation when the target feature moves from one grid point to another while keeping other features fixed—we isolate the pure effect of the target feature. The resulting visualization is the Accumulated Local Effect (ALE) plot.

ALE Equation

For continuous features, the partial dependence function is the expectation of the model output over the distribution of all other features. The ALE function integrates the first‑order differences of the model output with respect to the target feature across its range, then centers the result so that the average effect is zero.

In practice the integral is approximated by dividing the feature range into intervals, computing the average model predictions at the interval boundaries, and accumulating the differences. After centering, the ALE values represent the unbiased contribution of the target feature.

Advantages and Limitations of ALE

ALE provides an unbiased estimate of feature effects and can handle correlated features, avoiding the joint‑effect bias of partial dependence.

It requires fewer model evaluations than partial dependence, making it computationally faster.

Like partial dependence, ALE visualizes how a feature influences predictions, but the centered curve directly reflects changes in the average prediction, offering clearer interpretation.

Challenges include selecting the number of intervals and the inability to produce individual‑sample explanations (unlike ICE plots).

Reference: Shao Ping, Yang Jiaying, Su Sida. Interpretable Machine Learning: Methods and Practice .