Rare Event Classification with Weighted Logistic Regression for Identifying Repeating Fast Radio Bursts

TL;DR

This paper introduces a weighted logistic regression model tailored for classifying fast radio burst sources as repeating or non-repeating, addressing class imbalance and sampling biases, and achieves high accuracy with a small parameter set.

Contribution

It proposes a statistically sound, interpretable weighted logistic regression approach with only five parameters for classifying FRBs, adaptable to the true repeater proportion.

Findings

Achieves nearly 75% classification accuracy for repeaters.

Suggests a high proportion (50-60%) of repeaters in the population.

Operates efficiently with only five parameters.

Abstract

An important task in the study of fast radio bursts (FRBs) remains the automatic classification of repeating and non-repeating sources based on their morphological properties. We propose a statistical model that considers a modified logistic regression to classify FRB sources. The classical logistic regression model is modified to accommodate the small proportion of repeaters in the data, a feature that is likely due to the sampling procedure and duration and is not a characteristic of the population of FRB sources. The weighted logistic regression hinges on the choice of a tuning parameter that represents the true proportion $\tau$ of repeating FRB sources in the entire population. The proposed method has a sound statistical foundation, direct interpretability, and operates with only 5 parameters, enabling quicker retraining with added data. Using the CHIME/FRB Collaboration sample of repeating and non-repeating FRBs and numerical experiments, we achieve a classification accuracy for repeaters of nearly 75\% or higher when $\tau$ is set in the range of $50$ to $60$\%. This implies a tentative high proportion of repeaters, which is surprising, but is also in agreement with recent estimates of $\tau$ that are obtained using other methods.