Individual Conditional Expectations (ICE)

ICE curves show how each individual example’s prediction changes with a feature. When ICE curves diverge, it indicates feature interactions.

import skexplain
import plotting_config

# Load the training data and pre-fit models
estimators = skexplain.load_models()
X, y = skexplain.load_data()
X = X.astype({'urban': 'category', 'rural': 'category'})

# Use the Random Forest model only
explainer = skexplain.ExplainToolkit(estimators[0], X=X, y=y)

explainer.set_plotting_config(
    display_feature_names=plotting_config.display_feature_names,
    display_units=plotting_config.display_units,
    feature_colors=plotting_config.color_dict,
)

Computing ICE Curves

ICE curves are computed with explainer.ice(). The subsample argument controls how many individual curves are drawn. Plotting more than 200 curves makes the plot hard to read.

features = ['sfc_temp', 'temp2m', 'dwpt2m', 'sfcT_hrs_bl_frez']

ice_ds = explainer.ice(
    features=features,
    subsample=200,
    n_jobs=4,
    n_bins=20,
)

# Compute ALE for the same features (used as the overlay mean line)
ale_1d_ds = explainer.ale(
    features=features,
    n_bootstrap=1,
    subsample=10000,
    n_jobs=1,
    n_bins=20,
)

Plotting ALE with ICE Overlay

Pass the ICE dataset to plot_ale via the ice_curves argument. The bold line is the ALE (mean effect) and the thin lines are individual ICE curves. Spread in the ICE curves indicates feature interactions.

fig, axes = explainer.plot_ale(
    ale=ale_1d_ds,
    ice_curves=ice_ds,
)

Color-Coded ICE Curves

Color-coding ICE curves by another feature’s value reveals interactions between features. Use the color_by argument to specify which feature to color by.

fig, axes = explainer.plot_ale(
    ale=ale_1d_ds,
    features=features,
    ice_curves=ice_ds,
    color_by='temp2m',
    figsize=(10, 6),
    wspace=0.25,
)

When the colored ICE curves separate into distinct bands (e.g., warm colors trending differently than cool colors), it indicates that the feature being plotted interacts with the color_by feature. If all colored lines follow the same trend regardless of color, there is little interaction between the two features.

ICE curves are a permutation-based method and assume feature independence, so correlated features can muddle the interpretation. Use them as an exploratory tool alongside ALE and 2D ALE for a more complete picture.