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: seaborn 0.13.2 | Python 3.13.15
Quality: 92/100 | Updated: 2026-08-17
"""
import os
import sys
# Prevent this file from shadowing the installed seaborn package
_this_dir = os.path.dirname(os.path.abspath(__file__))
sys.path = [p for p in sys.path if not (p and os.path.abspath(p) == _this_dir)]
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
from matplotlib.colors import LinearSegmentedColormap, Normalize
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"
BRAND = "#009E73" # Imprint palette position 1 — ICE lines (low end of gradient)
PDP_COLOR = "#C475FD" # Imprint palette position 2 — PDP overlay
imprint_seq = LinearSegmentedColormap.from_list("imprint_seq", [BRAND, "#4467A3"])
sns.set_theme(
style="ticks",
rc={
"figure.facecolor": PAGE_BG,
"axes.facecolor": PAGE_BG,
"axes.edgecolor": INK_SOFT,
"axes.labelcolor": INK,
"text.color": INK,
"xtick.color": INK_SOFT,
"ytick.color": INK_SOFT,
"grid.color": INK,
"grid.alpha": 0.12,
"legend.facecolor": ELEVATED_BG,
"legend.edgecolor": INK_SOFT,
},
)
# Data — synthetic housing dataset
np.random.seed(42)
n_obs = 100
sqft = np.random.uniform(800, 3500, n_obs)
bedrooms = np.random.randint(2, 6, n_obs).astype(float)
age = np.random.uniform(0, 50, n_obs)
distance = np.random.uniform(1, 25, n_obs)
price = 0.15 * sqft + 25.0 * bedrooms - 0.5 * age - 2.5 * distance + np.random.normal(0, 30, n_obs)
X = np.column_stack([sqft, bedrooms, age, distance])
model = GradientBoostingRegressor(n_estimators=150, max_depth=4, random_state=42)
model.fit(X, price)
# Compute ICE matrix — each row is one observation, each column a grid point
n_grid = 60
sqft_grid = np.linspace(800, 3500, n_grid)
ice_matrix = np.zeros((n_obs, n_grid))
for j, val in enumerate(sqft_grid):
X_tmp = X.copy()
X_tmp[:, 0] = val
ice_matrix[:, j] = model.predict(X_tmp)
pdp = ice_matrix.mean(axis=0)
# Long-form DataFrame for seaborn
obs_ids = np.repeat(np.arange(n_obs), n_grid)
sqft_vals = np.tile(sqft_grid, n_obs)
bedrooms_vals = np.repeat(bedrooms, n_grid)
df_ice = pd.DataFrame({"obs_id": obs_ids, "sqft": sqft_vals, "price": ice_matrix.ravel(), "bedrooms": bedrooms_vals})
# Plot — 3200x1800 canvas (figsize x dpi), bbox_inches left at default (None)
fig, ax = plt.subplots(figsize=(8, 4.5), dpi=400, facecolor=PAGE_BG)
ax.set_facecolor(PAGE_BG)
# ICE lines — one per observation via seaborn lineplot with units, color-coded by
# bedrooms (a second feature) with an Imprint sequential colormap to surface
# interaction effects hidden by the flat single-color band
sns.lineplot(
data=df_ice,
x="sqft",
y="price",
units="obs_id",
hue="bedrooms",
estimator=None,
palette=imprint_seq,
linewidth=0.6,
alpha=0.35,
legend=False,
ax=ax,
)
# PDP overlay — bold average marginal effect, drawn via seaborn (not raw matplotlib)
sns.lineplot(x=sqft_grid, y=pdp, color=PDP_COLOR, linewidth=3, ax=ax, zorder=5, label="Partial Dependence (PDP)")
# Rug plot — observed sqft distribution
sns.rugplot(x=sqft, color=INK_SOFT, alpha=0.75, height=0.045, expand_margins=False, ax=ax)
# Colorbar — decodes the bedrooms color gradient on the ICE lines
bedrooms_norm = Normalize(vmin=bedrooms.min(), vmax=bedrooms.max())
sm = plt.cm.ScalarMappable(cmap=imprint_seq, norm=bedrooms_norm)
sm.set_array([])
cbar = fig.colorbar(sm, ax=ax, pad=0.02, fraction=0.035)
cbar.set_label(f"Bedrooms (ICE curve color, n={n_obs})", color=INK, fontsize=9)
cbar.ax.tick_params(colors=INK_SOFT, labelsize=7)
cbar.outline.set_edgecolor(INK_SOFT)
# Annotation — calls out the piecewise/staircase PDP shape from the tree ensemble
jump_idx = int(np.argmax(np.abs(np.diff(pdp)))) + 1
ann_x, ann_y = sqft_grid[jump_idx], pdp[jump_idx]
dx = -450 if ann_x > sqft_grid.mean() else 450
dy = 55 if ann_y < pdp.mean() else -55
ax.annotate(
"Piecewise jump —\ntree-ensemble split",
xy=(ann_x, ann_y),
xytext=(ann_x + dx, ann_y + dy),
fontsize=8,
color=INK,
ha="right" if dx < 0 else "left",
arrowprops={"arrowstyle": "->", "color": INK_SOFT, "lw": 1.1},
)
# Style
ax.set_xlabel("Square Footage (sq ft)", fontsize=10, color=INK)
ax.set_ylabel("Predicted House Price ($K)", fontsize=10, color=INK)
ax.set_title("ice-basic · python · seaborn · anyplot.ai", fontsize=12, fontweight="medium", color=INK)
ax.tick_params(axis="both", labelsize=8, colors=INK_SOFT, length=0)
sns.despine(ax=ax)
ax.spines["left"].set_color(INK_SOFT)
ax.spines["bottom"].set_color(INK_SOFT)
ax.yaxis.grid(True, alpha=0.12, linewidth=0.8, color=INK)
legend = ax.legend(
loc="upper left",
fontsize=8,
framealpha=0.92,
facecolor=ELEVATED_BG,
edgecolor=INK_SOFT,
fancybox=True,
borderpad=0.6,
)
legend.get_frame().set_linewidth(0.6)
for text in legend.get_texts():
text.set_color(INK)
# Save
plt.tight_layout()
plt.savefig(f"plot-{THEME}.png", dpi=400, facecolor=PAGE_BG)
Part of Individual Conditional Expectation (ICE) Plot on anyplot.ai.