# 5 Best Ways to Draw Precision-Recall Curves with Interpolation in Python Matplotlib

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π‘ Problem Formulation: When working with classification models in machine learning, evaluating model performance is crucial. A precision-recall curve is a common tool for showcasing the trade-off between precision and recall for different thresholds. This article addresses how one can visualize such a curve using Python’s Matplotlib library, incorporating interpolation for a smoother representation. Our goal is to create a graph where the x-axis represents recall, the y-axis depicts precision, and the curve illustrates the behavior of a classification model at various threshold levels.

## Method 1: Using Matplotlib Step Function

This method demonstrates the use of Matplotlib’s step function for plotting a basic precision-recall curve. The step function is particularly useful for showing increments at each threshold, making it clear where precision and recall values change. Interpolation is achieved through a ‘step’ drawing style that fills in the areas under the curve for improved visualization.

Here’s an example:

```from sklearn.metrics import precision_recall_curve
import matplotlib.pyplot as plt
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression

# Create a simple classification dataset
X, y = make_classification(n_samples=1000, n_features=20, random_state=0)
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)

# Train a logistic regression classifier
classifier = LogisticRegression()
classifier.fit(X_train, y_train)

# Predict probabilities
probabilities = classifier.predict_proba(X_test)[:, 1]

# Calculate precision-recall pairs
precision, recall, _ = precision_recall_curve(y_test, probabilities)

# Plot precision-recall curve with interpolation
plt.step(recall, precision, where='post', color='b', alpha=0.2, label='Precision-Recall Curve')
plt.fill_between(recall, precision, step='post', alpha=0.2, color='b')
plt.xlabel('Recall')
plt.ylabel('Precision')
plt.title('Precision-Recall Curve with Interpolation')
plt.legend()
plt.show()
```

The output will display a precision-recall curve on a Matplotlib plot with filled steps, showcasing the interpolation visually.

The code snippet above begins with generating a synthetic dataset suitable for classification. A logistic regression model is then trained on the dataset. Using the `precision_recall_curve` function from `sklearn.metrics`, precision and recall values are calculated based on the test set and predicted probabilities. Finally, the Matplotlib step function plots these values, with the ‘post’ option causing the step to occur after the value, creating a right-hand-side interpolation effect and a filled area under the curve for improved readability.

## Method 2: Direct Plotting with Interpolated Values

In this method, interpolated precision values are plotted directly against recall using Matplotlib’s plot function. A finer grid of recall values is created, and precision values are interpolated using any preferred interpolation technique, such as linear interpolation from Scipy’s `interp1d`. This yields a smoother precision-recall curve.

Here’s an example:

```import numpy as np
from scipy.interpolate import interp1d

# Assume precision and recall have been computed as above
recalls_interp = np.linspace(0, 1, 100)
interp_func = interp1d(recall, precision, kind='linear')
precision_interp = interp_func(recalls_interp)

plt.plot(recalls_interp, precision_interp, label='Interpolated P-R Curve')
plt.xlabel('Recall')
plt.ylabel('Precision')
plt.title('Smooth Precision-Recall Curve')
plt.legend()
plt.show()
```

The output displays a smooth curve on a Matplotlib plot, representing the precision-recall relationship.

This method takes the precision and recall values obtained from a model’s predictions and interpolates them for a finer representation. Using SciPy’s `interp1d` function, a linear interpolation is applied across the recall range. This array of interpolated precision values is plotted against an evenly spaced range of recall values, resulting in a much smoother curve than the original step-based approach.

## Method 3: Utilizing Sklearn’s Precision-Recall Plot

Scikit-learn includes a built-in plotting utility for precision-recall curves that automatically takes care of interpolation and plotting. It simplifies the process by handling the drawing of the curve and the calculation of interpolated values internally, freeing the user from needing to write additional interpolation code.

Here’s an example:

```from sklearn.metrics import plot_precision_recall_curve

# Assume classifier and X_test are defined as above
disp = plot_precision_recall_curve(classifier, X_test, y_test)
disp.ax_.set_title('Sklearn Precision-Recall Curve')
plt.show()
```

Executing this code will render a precision-recall plot with the interpolation already applied.

The code demonstrates how to create a precision-recall plot using Scikit-learn’s built-in plotting utility, `plot_precision_recall_curve`. This function does the heavy lifting, calculating precision and recall values, as well as performing interpolation behind the scenes. The end result is a professional-quality plot ready for presentations or publications, minimizing the coding effort required for the same.

## Method 4: Custom Interpolation and Plotting

For users needing more control over the interpolation and plotting process, a custom approach can be taken. This involves manually calculating the interpolation using your own function or a more advanced interpolation technique from Scipy. This is then plotted using Matplotlib, allowing for full customization of the plot appearance and interpolation behavior.

Here’s an example:

```from scipy.interpolate import make_interp_spline

# Assume precision and recall have been computed as before
spl = make_interp_spline(recall, precision, k=3)  # B-spline interpolation
fine_recall = np.linspace(recall.min(), recall.max(), 500)
smooth_precision = spl(fine_recall)

plt.plot(fine_recall, smooth_precision, label='Custom Interpolated P-R Curve')
plt.xlabel('Recall')
plt.ylabel('Precision')
plt.title('Custom Smooth Precision-Recall Curve')
plt.legend()
plt.show()
```

The produced plot will show a custom smooth precision-recall curve.

Using a B-spline interpolation technique via Scipy’s `make_interp_spline` function, this example demonstrates a more tailored approach to creating a smooth precision-recall curve. This allows for varying the precision of the curve by adjusting the degree of the spline. Custom-defined recall values create the basis for the interpolation, which when plotted, produces a smooth and visually appealing presentation of the data.

## Bonus One-Liner Method 5: Quick Plot with Interpolated Line Plot

Last but not least, for a quick and straightforward solution, one can use Matplotlib’s plot function with a simple call to `interpolate()` method from Pandas, which can approximate missing data points within a Series or DataFrame. This is less precise but can be good for a speedy visualization need.

Here’s an example:

```import pandas as pd

# Assume precision and recall have been computed
df = pd.DataFrame({'recall': recall, 'precision': precision})
df['precision'] = df['precision'].interpolate()

plt.plot(df['recall'], df['precision'], label='Quick Interpolated P-R Curve')
plt.xlabel('Recall')
plt.ylabel('Precision')
plt.title('Quick Precision-Recall Curve')
plt.legend()
plt.show()
```

The output will be a simple interpolated precision-recall curve plot.

The snippet leverages Pandas’ interpolate function to fill in missing precision values along the recall scale. This results in an approximation of the precision-recall curve and can be done in one line of code using Pandas, then plotted simply with Matplotlib. This method offers a fast and low-effort solution although it may lack the precision of more sophisticated interpolation methods.

## Summary/Discussion

• Method 1: Using Matplotlib Step Function. Good for visually emphasizing step changes. Less smooth than interpolation but clear for stepwise data points.
• Method 2: Direct Plotting with Interpolated Values. Provides a high degree of smoothness for the curve. Requires manual creation of an interpolation function, which can be seen as complex for some users.
• Method 3: Utilizing Sklearn’s Precision-Recall Plot. Most straightforward and requires minimal code. However, offers less flexibility and control over the plotting and interpolation processes.
• Method 4: Custom Interpolation and Plotting. Offers full control and is best for customized plots. However, it is more complex and requires knowledge of advanced interpolation techniques.
• Bonus One-Liner Method 5: Quick Plot with Interpolated Line Plot. Fast and easy for instant results. Not as precise and may not be suitable for all types of datasets.