An Individual Conditional Expectation (ICE) plot visualizes how the predicted outcome of a machine learning model changes for each individual observation as a single feature varies across its range. Unlike partial dependence plots (PDP) that show the average marginal effect, ICE plots display one line per observation, revealing heterogeneous effects, feature interactions, and subgroup-specific behaviors that would be hidden by averaging. This makes ICE plots essential for detecting when a feature's effect varies across the population.
""" anyplot.ai
ice-basic: Individual Conditional Expectation (ICE) Plot
Library: matplotlib 3.11.1 | Python 3.13.15
Quality: 93/100 | Updated: 2026-08-17
"""
import os
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.lines import Line2D
from sklearn.ensemble import GradientBoostingRegressor
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
BRAND = "#009E73" # Imprint palette position 1 — ICE individual lines
ACCENT = "#C475FD" # Imprint palette position 2 — PDP average line
# Data: synthetic housing dataset
np.random.seed(42)
n_obs = 120
sqft = np.random.uniform(800, 3500, n_obs)
bedrooms = np.random.choice([2, 3, 4, 5], n_obs, p=[0.15, 0.45, 0.30, 0.10])
age_years = np.random.uniform(1, 40, n_obs)
lot_size = np.random.uniform(3000, 15000, n_obs)
price = sqft * 180 + bedrooms * 12000 - age_years * 1500 + lot_size * 2.5 + np.random.normal(0, 25000, n_obs)
X = np.column_stack([sqft, bedrooms, age_years, lot_size])
y = price
# Train gradient boosting model
model = GradientBoostingRegressor(n_estimators=150, max_depth=4, learning_rate=0.05, random_state=42)
model.fit(X, y)
# ICE curves: vary sqft (index 0) across a grid, holding other features at observed values
sqft_grid = np.linspace(sqft.min(), sqft.max(), 70)
ice_matrix = np.zeros((n_obs, len(sqft_grid)))
for j, val in enumerate(sqft_grid):
X_temp = X.copy()
X_temp[:, 0] = val
ice_matrix[:, j] = model.predict(X_temp)
pdp_line = ice_matrix.mean(axis=0)
ice_min = ice_matrix.min(axis=0)
ice_max = ice_matrix.max(axis=0)
# Locate where individual curves diverge most from the average (heterogeneity peak)
spread = ice_matrix.std(axis=0)
divergence_idx = np.argmax(spread)
divergence_sqft = sqft_grid[divergence_idx]
divergence_y = ice_max[divergence_idx]
# Plot
fig, ax = plt.subplots(figsize=(8, 4.5), dpi=400, facecolor=PAGE_BG)
ax.set_facecolor(PAGE_BG)
# Min-max envelope of individual curves — shows the full spread at a glance
ax.fill_between(sqft_grid, ice_min, ice_max, color=BRAND, alpha=0.06, linewidth=0, zorder=1)
# ICE individual lines
for i in range(n_obs):
ax.plot(sqft_grid, ice_matrix[i], color=BRAND, alpha=0.14, linewidth=0.9, zorder=2)
# PDP average line
ax.plot(sqft_grid, pdp_line, color=ACCENT, linewidth=3, zorder=5)
# Explicit y-limits with headroom for the rug plot so its position is fixed
# regardless of layout adjustments (rug sits inside the bottom margin, never
# overlapping the lowest ICE curve).
y_span = ice_max.max() - ice_min.min()
y_bottom = ice_min.min() - 0.10 * y_span
y_top = ice_max.max() + 0.04 * y_span
ax.set_ylim(y_bottom, y_top)
rug_y = ice_min.min() - 0.055 * y_span
ax.plot(sqft, np.full(n_obs, rug_y), "|", color=INK_MUTED, alpha=0.5, markersize=6, markeredgewidth=1.0, zorder=3)
# Annotation: call out where individual effects diverge most from the average
ax.annotate(
f"Effects diverge most\naround {divergence_sqft:,.0f} sqft",
xy=(divergence_sqft, divergence_y),
xytext=(0.62, 0.90),
textcoords="axes fraction",
fontsize=8,
color=INK_SOFT,
ha="left",
va="top",
arrowprops={"arrowstyle": "->", "color": INK_SOFT, "linewidth": 1.0},
bbox={"facecolor": ELEVATED_BG, "edgecolor": INK_SOFT, "alpha": 0.9, "boxstyle": "round,pad=0.4", "linewidth": 0.8},
)
# Style
ax.set_xlabel("Square Footage (sqft)", fontsize=10, color=INK)
ax.set_ylabel("Predicted House Price ($)", fontsize=10, color=INK)
ax.set_title(
"House Price by Square Footage · ice-basic · matplotlib · anyplot.ai", fontsize=12, fontweight="medium", color=INK
)
ax.tick_params(axis="both", labelsize=8, colors=INK_SOFT, length=0)
ax.yaxis.set_major_formatter(plt.FuncFormatter(lambda x, _: f"${x:,.0f}"))
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
ax.spines["left"].set_color(INK_SOFT)
ax.spines["bottom"].set_color(INK_SOFT)
ax.yaxis.grid(True, alpha=0.10, linewidth=0.8, color=INK)
ax.set_axisbelow(True)
# Legend
legend_handles = [
Line2D([0], [0], color=BRAND, alpha=0.6, linewidth=2, label=f"Individual ICE lines (n={n_obs})"),
Line2D([0], [0], color=BRAND, alpha=0.2, linewidth=8, label="Prediction range (min–max)"),
Line2D([0], [0], color=ACCENT, linewidth=3, label="Partial dependence (average)"),
]
leg = ax.legend(handles=legend_handles, fontsize=8, loc="upper left")
leg.get_frame().set_facecolor(ELEVATED_BG)
leg.get_frame().set_edgecolor(INK_SOFT)
plt.setp(leg.get_texts(), color=INK_SOFT)
plt.tight_layout()
plt.savefig(f"plot-{THEME}.png", dpi=400, facecolor=PAGE_BG)
Part of Individual Conditional Expectation (ICE) Plot on anyplot.ai.