  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.
