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: bokeh 3.9.2 | Python 3.13.15
Quality: 92/100 | Created: 2026-08-17
"""
import os
import time
from pathlib import Path
import numpy as np
from bokeh.io import output_file, save
from bokeh.models import ColumnDataSource, HoverTool, Range1d
from bokeh.plotting import figure
from selenium import webdriver
from selenium.webdriver.chrome.options import Options
from sklearn.ensemble import GradientBoostingRegressor
# Theme tokens (see prompts/default-style-guide.md "Background" + "Theme-adaptive Chrome")
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"
# Imprint palette (see prompts/default-style-guide.md "Categorical Palette")
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
BRAND = IMPRINT_PALETTE[0] # ALWAYS first series
# Data — gradient boosting house-price model with a square-footage x age interaction,
# so predicted price grows faster with square footage for newer houses than older ones.
np.random.seed(42)
n_obs = 80
grid_size = 60
square_footage = np.random.uniform(600, 4000, n_obs)
bedrooms = np.random.randint(1, 6, n_obs).astype(float)
house_age = np.random.uniform(0, 60, n_obs)
lot_size = np.random.uniform(2000, 20000, n_obs)
noise = np.random.normal(0, 15000, n_obs)
price = (
80 * square_footage
+ 9000 * bedrooms
- 900 * house_age
+ 1.2 * lot_size
+ 0.04 * square_footage * np.clip(60 - house_age, 0, None)
+ noise
)
features = np.column_stack([square_footage, bedrooms, house_age, lot_size])
model = GradientBoostingRegressor(n_estimators=300, max_depth=3, learning_rate=0.05, random_state=42)
model.fit(features, price)
feature_grid = np.linspace(600, 4000, grid_size)
ice_predictions = np.zeros((n_obs, grid_size))
for i in range(n_obs):
grid_features = np.tile(features[i], (grid_size, 1))
grid_features[:, 0] = feature_grid
ice_predictions[i] = model.predict(grid_features)
ice_price_k = ice_predictions / 1000
pdp_price_k = ice_price_k.mean(axis=0)
y_min, y_max = float(ice_price_k.min()), float(ice_price_k.max())
y_span = y_max - y_min
rug_y0 = y_min - 0.09 * y_span
rug_y1 = y_min - 0.03 * y_span
source = ColumnDataSource(
data={
"xs": [feature_grid.tolist()] * n_obs,
"ys": [row.tolist() for row in ice_price_k],
"obs_id": list(range(n_obs)),
}
)
# Plot
title = "ice-basic · python · bokeh · anyplot.ai"
p = figure(
width=3200,
height=1800,
title=title,
x_axis_label="Square Footage",
y_axis_label="Predicted Price ($k)",
toolbar_location=None,
min_border_bottom=160,
min_border_left=180,
min_border_top=110,
min_border_right=50,
)
p.y_range = Range1d(rug_y0 - 0.02 * y_span, y_max + 0.08 * y_span)
ice_renderer = p.multi_line(
xs="xs",
ys="ys",
source=source,
line_color=BRAND,
line_alpha=0.25,
line_width=1.5,
legend_label="Individual houses (ICE)",
)
p.line(feature_grid, pdp_price_k, line_color=INK, line_width=6, legend_label="Average effect (PDP)")
p.segment(
x0=square_footage, y0=rug_y0, x1=square_footage, y1=rug_y1, line_color=INK_SOFT, line_alpha=0.4, line_width=1.5
)
# HoverTool showcases bokeh's distinctive HTML interactivity (toolbar_location=None
# only hides the button row — hover still fires on mouse move over a line).
p.add_tools(
HoverTool(
renderers=[ice_renderer],
tooltips=[("Observation", "@obs_id"), ("Sq Ft", "$x{0,0}"), ("Price", "$y{0.0}k")],
mode="mouse",
)
)
# Style
p.title.text_font_size = "50pt"
p.xaxis.axis_label_text_font_size = "42pt"
p.yaxis.axis_label_text_font_size = "42pt"
p.xaxis.major_label_text_font_size = "34pt"
p.yaxis.major_label_text_font_size = "34pt"
p.background_fill_color = PAGE_BG
p.border_fill_color = PAGE_BG
p.outline_line_color = INK_SOFT
p.title.text_color = INK
p.xaxis.axis_label_text_color = INK
p.yaxis.axis_label_text_color = INK
p.xaxis.major_label_text_color = INK_SOFT
p.yaxis.major_label_text_color = INK_SOFT
p.xaxis.axis_line_color = INK_SOFT
p.yaxis.axis_line_color = INK_SOFT
p.xaxis.major_tick_line_color = INK_SOFT
p.yaxis.major_tick_line_color = INK_SOFT
p.xgrid.grid_line_color = None
p.ygrid.grid_line_color = INK
p.ygrid.grid_line_alpha = 0.15
p.legend.location = "top_left"
p.legend.label_text_font_size = "34pt"
p.legend.glyph_width = 60
p.legend.glyph_height = 40
p.legend.background_fill_color = ELEVATED_BG
p.legend.border_line_color = INK_SOFT
p.legend.label_text_color = INK_SOFT
# Save — write HTML, then screenshot it with headless Chrome (export_png is unreliable in CI)
output_file(f"plot-{THEME}.html")
save(p)
W, H = 3200, 1800
opts = Options()
for arg in (
"--headless=new",
"--no-sandbox",
"--disable-dev-shm-usage",
"--disable-gpu",
f"--window-size={W},{H}",
"--hide-scrollbars",
):
opts.add_argument(arg)
driver = webdriver.Chrome(options=opts)
driver.set_window_size(W, H)
driver.get(f"file://{Path(f'plot-{THEME}.html').resolve()}")
driver.execute_cdp_cmd(
"Emulation.setDeviceMetricsOverride", {"width": W, "height": H, "deviceScaleFactor": 1, "mobile": False}
)
time.sleep(3)
driver.save_screenshot(f"plot-{THEME}.png")
driver.quit()
Part of Individual Conditional Expectation (ICE) Plot on anyplot.ai.