Generalized Linear Models for Aggregated Data
Avradeep Bhowmik, Joydeep Ghosh, Oluwasanmi O. Koyejo · International Conference on Artificial Intelligence and Statistics · 2015
Databases in domains such as healthcare are routinely released to the public in aggregated form. Unfortunately, nave modeling with aggregated data may signicantly diminish the accuracy of inferences at the individ- ual level. This paper addresses the scenario where features are provided at the individual level, but the target variables are only avail- able as histogram aggregates or order statis- tics. We consider a limiting case of gener- alized linear modeling when the target vari- ables are only known up to permutation, and explore how this relates to permutation test- ing; a standard technique for assessing statis- tical dependency. Based on this relationship, we propose a simple algorithm to estimate the model parameters and individual level in- ferences via alternating imputation and stan- dard generalized linear model tting. Our re-