pr2roc

Resample classifier precision-recall curves correctly by interconverting between PR and ROC space!
The only requirement is to know the proportion of actual positives to actual negatives in the dataset, which depends only on the true labels.

Installation

You will need to install numpy first:

pip install numpy

Then, install pr2roc from this GitHub repository directly:

pip install git+https://github.com/ameya98/pr2roc

Tested with Python 2.7 and 3.5.

Terminology

• TP: True Positives: Actual positives labelled correctly.
• TN: True Negatives: Actual negatives labelled correctly.
• FP: False Positives: Actual negatives labelled incorrectly as positive.
• FN: False Negatives: Actual positives labelled incorrectly as negative.
• TPR: True Positive Rate = TP/(TP + FN).
• FPR: False Positive Rate = FP/(FP + TN).
• Precision: TP/(TP + FP).
• Recall: True Positive Rate = TP/(TP + FN).
• ROC: Reciever Operating Characteristic: A curve comparing the TPR (y-axis) as a function of the FPR (x-axis) for a given classifier at various thresholds.
• PR: Precision-Recall: A curve comparing the precision (y-axis) as a function of the recall (x-axis) for a given classifier at various thresholds.

Usage

Modified from demo.ipynb:

from pr2roc import PRCurve
from numpy import allclose

# Define points on precision-recall curve.
recall_vals = [0.25, 0.4, 0.5]
precision_vals = [0.5, 0.3, 0.25]
pr_points = zip(recall_vals, precision_vals)

# Create the curve.
pr = PRCurve(pr_points, pos_neg_ratio=0.25)

# Resample, to get another precision-recall curve, with 100 points!.
pr_sampled = pr.resample(num_points=100)

# Convert to a ROC curve.
roc = pr.to_roc()

# We can resample this ROC curve, as well!
roc_sampled = roc.resample(num_points=100)

# Get the points (as a list of 2-tuples) on any curve with the *.points()* method.
pr_points = pr.points()

# You can re-convert the ROC curve back to a PR curve!
pr_reconverted = roc.to_pr()

# This should pass.
assert allclose(pr_reconverted.points(), pr.points())

How does the resampling work?

There is a fundamental duality between ROC space and PR space. For a fixed dataset (specifically, a fixed ratio of actual positives to actual negatives), we can convert a ROC curve to a PR curve, and vice versa.

In ROC space, linear interpolation between points on a 'discrete' ROC curve is valid, because all points on the convex hull of a ROC curve are attainable. However, linear interpolation is not justified in PR space, because it over-estimates the performance of the classifier.

The solution is to:

• Convert a PR curve to its corresponding ROC curve, using the duality between the PR and ROC spaces.
• Interpolate the ROC curve. Here, we interpolate at equally spaced values of FPR, linearly interpolating the TPR values between adjacent points.
• Convert the interpolated ROC curve back to PR space, giving us an interpolated PR curve.

See the reference below for a more detailed description of the relationship between ROC curves and PR curves.
This package is essentially an implementation of the methods in the reference.

References

Jesse Davis and Mark Goadrich. 2006. The Relationship Between Precision-Recall and ROC Curves.
In Proceedings of the 23rd International Conference on Machine Learning (ICML ’06). Association for Computing Machinery, New York, NY, USA, 233–240.
DOI: https://doi.org/10.1145/1143844.1143874