Logistic regression models for aggregated data

TL;DR

This paper introduces a histogram-based approximation method for logistic regression that reduces computational costs while maintaining classification accuracy on large datasets.

Contribution

It develops a novel composite likelihood approach using histograms to enable efficient inference for large-scale logistic regression models.

Findings

Comparable classification accuracy to full data analysis

Significantly lower computational cost

Effective on large real-world datasets

Abstract

Logistic regression models are a popular and effective method to predict the probability of categorical response data. However inference for these models can become computationally prohibitive for large datasets. Here we adapt ideas from symbolic data analysis to summarise the collection of predictor variables into histogram form, and perform inference on this summary dataset. We develop ideas based on composite likelihoods to derive an efficient one-versus-rest approximate composite likelihood model for histogram-based random variables, constructed from low-dimensional marginal histograms obtained from the full histogram. We demonstrate that this procedure can achieve comparable classification rates compared to the standard full data multinomial analysis and against state-of-the-art subsampling algorithms for logistic regression, but at a substantially lower computational cost. Performance is explored through simulated examples, and analyses of large supersymmetry and satellite crop classification datasets.