Partial Dependence Plot — Altair

A partial dependence plot (PDP) showing the marginal effect of one feature on the predicted outcome of a machine learning model. The plot displays how predictions change as a feature varies across its range, while averaging over the effects of all other features. This visualization is essential for understanding the relationship between individual features and model predictions in interpretable machine learning.

Partial Dependence Plot rendered with Altair

Python source (Altair)

""" anyplot.ai
pdp-basic: Partial Dependence Plot
Library: altair 6.1.0 | Python 3.13.13
Quality: 100/100 | Updated: 2026-05-15
"""

import os

import altair as alt
import numpy as np
import pandas as pd
from sklearn.datasets import make_regression
from sklearn.ensemble import GradientBoostingRegressor
from sklearn.inspection import partial_dependence


# 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"

# Data - Train a model and compute partial dependence
np.random.seed(42)
X, y = make_regression(n_samples=500, n_features=5, noise=10, random_state=42)
feature_names = ["Temperature", "Pressure", "Humidity", "Flow Rate", "Duration"]

# Train gradient boosting model
model = GradientBoostingRegressor(n_estimators=100, max_depth=4, random_state=42)
model.fit(X, y)

# Compute partial dependence for feature 0 (Temperature)
feature_idx = 0
grid_resolution = 80
pd_result = partial_dependence(model, X, features=[feature_idx], grid_resolution=grid_resolution, kind="average")

# Extract data
feature_values = pd_result["grid_values"][0]
pd_values = pd_result["average"][0]

# Bootstrap for confidence intervals
n_bootstrap = 50
bootstrap_pds = []
for _ in range(n_bootstrap):
    indices = np.random.choice(len(X), size=len(X), replace=True)
    X_boot = X[indices]
    pd_boot = partial_dependence(model, X_boot, features=[feature_idx], grid_resolution=grid_resolution, kind="average")
    bootstrap_pds.append(pd_boot["average"][0])

bootstrap_pds = np.array(bootstrap_pds)
ci_lower = np.percentile(bootstrap_pds, 2.5, axis=0)
ci_upper = np.percentile(bootstrap_pds, 97.5, axis=0)

# Create DataFrame for main line
df_line = pd.DataFrame({"Feature Value": feature_values, "Partial Dependence": pd_values})

# Create DataFrame for confidence band
df_band = pd.DataFrame({"Feature Value": feature_values, "CI Lower": ci_lower, "CI Upper": ci_upper})

# Create rug plot data (sample of training data distribution)
rug_sample = np.random.choice(X[:, feature_idx], size=min(100, len(X)), replace=False)
df_rug = pd.DataFrame(
    {"Feature Value": rug_sample, "y": [pd_values.min() - (pd_values.max() - pd_values.min()) * 0.05] * len(rug_sample)}
)

# Confidence band
band = (
    alt.Chart(df_band)
    .mark_area(opacity=0.2, color=BRAND)
    .encode(
        x=alt.X("Feature Value:Q", title=f"{feature_names[feature_idx]} (standardized units)"),
        y=alt.Y("CI Lower:Q", title="Partial Dependence (predicted outcome)"),
        y2="CI Upper:Q",
    )
)

# Main PDP line
line = (
    alt.Chart(df_line)
    .mark_line(strokeWidth=4, color=BRAND)
    .encode(
        x=alt.X("Feature Value:Q"),
        y=alt.Y("Partial Dependence:Q"),
        tooltip=[alt.Tooltip("Feature Value:Q", format=".2f"), alt.Tooltip("Partial Dependence:Q", format=".2f")],
    )
)

# Rug plot for data distribution
rug = alt.Chart(df_rug).mark_tick(thickness=2, size=20, color=BRAND, opacity=0.4).encode(x=alt.X("Feature Value:Q"))

# Combine layers
chart = (
    alt.layer(band, line, rug)
    .properties(
        width=1600,
        height=900,
        title=alt.Title(text="pdp-basic · altair · anyplot.ai", fontSize=28, anchor="middle"),
        background=PAGE_BG,
    )
    .configure_view(fill=PAGE_BG, stroke=INK_SOFT)
    .configure_axis(
        domainColor=INK_SOFT,
        tickColor=INK_SOFT,
        gridColor=INK,
        gridOpacity=0.10,
        labelColor=INK_SOFT,
        titleColor=INK,
        labelFontSize=18,
        titleFontSize=22,
    )
    .configure_title(color=INK)
    .configure_legend(fillColor=ELEVATED_BG, strokeColor=INK_SOFT, labelColor=INK_SOFT, titleColor=INK)
)

# Save outputs
chart.save(f"plot-{THEME}.png", scale_factor=3.0)
chart.save(f"plot-{THEME}.html")

Part of Partial Dependence Plot on anyplot.ai.

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