Sparse Ordinal Logistic Regression and Its Application to Brain Decoding

Emi Satake, Kei Majima, Shuntaro C. Aoki, Yukiyasu Kamitani

Brain decoding with multivariate classification and regression has provided a powerful framework for characterizing information encoded in population neural activity. Classification and regression models are respectively used to predict discrete and continuous variables of interest. However, cognitive and behavioral parameters that we wish to decode are often ordinal variables whose values are discrete but ordered, such as subjective ratings. To date, there is no established method of predicting ordinal variables in brain decoding. In this study, we present a new algorithm, sparse ordinal logistic regression (SOLR), that combines ordinal logistic regression with Bayesian sparse weight estimation. We found that, in both simulation and analyses using real functional magnetic resonance imaging (fMRI) data, SOLR outperformed ordinal logistic regression with non-sparse regularization, indicating that sparseness leads to better decoding performance. SOLR also outperformed classification and linear regression models with the same type of sparseness, indicating the advantage of the modeling tailored to ordinal outputs. Our results suggest that SOLR provides a principled and effective method of decoding ordinal variables.