Relationship Visualization

This gallery page showcases the plot_relationship function, which provides a unique polar perspective on the relationship between true observed values and model predictions.

Note

You need to run the code snippets locally to generate the plot images referenced below. Ensure the image paths in the .. image:: directives match where you save the plots.

True vs. Predicted Relationship

Uses plot_relationship() to map true values to the angular axis and normalized predicted values to the radial axis. This creates a spiral-like plot that reveals the consistency and correlation of model predictions across the entire range of true values.

import kdiagram.plot.relationship as kdr
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

# --- Data Generation ---
np.random.seed(42)
n_points = 150
# Create a clear, non-linear true signal
y_true = np.linspace(0, 10, n_points)**1.5 + np.sin(
    np.linspace(0, 10, n_points)
) * 2

# Model 1: Good fit with some noise
y_pred1 = y_true + np.random.normal(0, 1.5, n_points)
# Model 2: Worse fit, under-predicts high values
y_pred2 = y_true * 0.8 + np.random.normal(0, 2.5, n_points)

# --- Plotting ---
kdr.plot_relationship(
    y_true,
    y_pred1,
    y_pred2,
    names=["Good Model", "Biased Model"],
    title="Gallery: True vs. Predicted Relationship",
    theta_scale="proportional",  # Map angle to y_true value
    acov="default",
    s=40,
    # Save the plot (adjust path relative to this file)
    savefig="gallery/images/gallery_plot_relationship.png",
)
plt.close()

🧠 Analysis and Interpretation

The Relationship Plot offers a novel way to visualize the correlation between true values and model predictions, moving beyond a standard Cartesian scatter plot.

Key Features:

• Angle (θ): The angular position is directly proportional to the true value (y_true). The plot spirals outwards from the lowest true value to the highest.

• Radius (r): The radial distance is the normalized predicted value (y_pred), scaled to the range [0, 1].

• Points: Each point represents a single sample. Different colors distinguish between different models.

🔍 In this Example:

• Good Model (Blue): The blue points form a relatively tight, consistent spiral. As the angle increases (meaning y_true increases), the radius also tends to increase, showing a strong positive correlation. The scatter around the spiral path represents the prediction noise.

• Biased Model (Orange): The orange points are more scattered and form a less defined spiral. Critically, at larger angles (higher true values), the orange points are consistently at a smaller radius than the blue points, visually demonstrating the model’s tendency to under-predict high values.

💡 When to Use:

• To get an intuitive feel for the correlation and consistency of a model’s predictions across the entire data range.

• To visually compare the performance of multiple models. A “tighter” spiral indicates a better, more consistent model.

• To identify non-linear biases, where a model might perform well for low values but poorly for high values (or vice versa).

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