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Partial Dependence Plots
A partial dependence plot estimates how a model's predictions change as selected feature values vary, averaging over observed values of other features.
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Individual conditional expectation curves reveal whether that average hides different effects across individual examples.
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Partial dependence describes an average model response when one or more features are set to chosen values. For a single feature, the method takes each evaluation example, substitutes the same selected feature value, obtains a prediction, then averages across examples. Repeating this operation over a grid produces a curve. It is a view of the fitted model, not a causal estimate of what would happen if a person or system were intervened upon. The average can be useful when asking how predictions vary across a population, but it may hide important heterogeneity. Individual conditional expectation, or ICE, draws a separate line for each example while the feature changes. If lines remain parallel, effects may be similar in shape; if they spread, cross, or bend differently, the average conceals variation. Centered ICE subtracts each line's prediction at a reference point to make differences in shape easier to see. A critical limitation arises when the selected feature is correlated with other inputs. The calculation holds the other features fixed while replacing one value, which can create combinations absent from the data. A model may then be queried far outside realistic support. For example, increasing a person's age while holding a related education or career history constant may produce implausible examples. The average can be misleading even when computed correctly. Inspect data distributions and feature dependence alongside plots. Restrict the grid to observed ranges, look for sparse regions, and consider stratified or conditional alternatives. Accumulated local effects summarize local changes over regions supported by data and can reduce some extrapolation concerns, though they answer a different question. Use domain knowledge to decide whether the feature combinations make sense. A plot should state which model output is shown, such as a probability or raw score, the evaluated sample, and the range of feature values. Always read the visual as model behavior under a specific calculation, not proof of mechanism or fairness.
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The Future of Partial Dependence Plots
Model inspection tools can make it easier to compare population averages with individual traces and to flag portions of a plot where the input data are sparse. Better display of support and subgroup variation could help reviewers notice when an average describes few realistic cases. These features improve interpretation only when the underlying sample represents intended use. In high-stakes settings, a plot should complement domain review and carefully designed evaluation, not replace those checks or turn model associations into causal claims.
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A housing model's partial dependence curve shows average predicted price as floor area varies across observed homes.
ICE lines for floor area in a housing-price model fan apart, showing that the average model prediction hides different response patterns across the evaluated homes.
An analyst inspects feature correlations before interpreting a plot, since synthetic combinations may be unrealistic when features depend on one another.
A team compares partial dependence with accumulated local effects when strong dependence among inputs makes extrapolation concerning.
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What is Partial Dependence Plots?
A partial dependence plot estimates how a model's predictions change as selected feature values vary, averaging over observed values of other features. Individual conditional expectation curves reveal whether that average hides different effects across individual examples.
How does a single-feature partial dependence value at one grid point arise?
The method substitutes the selected value across evaluation examples, predicts, then averages.
What does an ICE display add beyond a partial dependence average?
ICE preserves per-example traces that averaging would collapse.
ICE lines fan apart as a feature changes. What does this suggest?
Diverging traces show that examples respond differently in the fitted model.
Why can correlated predictors make a partial dependence plot misleading?
Holding related features fixed while changing one can query combinations outside the observed data support.
What kind of claim does a partial dependence curve support most directly?
It summarizes model predictions, not a causal intervention or observed outcome response.
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