Is the whole greater than the sum of its parts?

The PART-WHOLE relationship routinely finds itself in many disciplines, ranging from collaborative teams, crowdsourcing, autonomous systems to networked systems. From the algorithmic perspective, the existing work has primarily focused on predicting the outcomes of the whole and parts, by either separate models or linear joint models, which assume the outcome of the parts has a linear and independent effect on the outcome of the whole. In this paper, we propose a joint predictive method named PAROLE to simultaneously and mutually predict the part and whole outcomes. The proposed method offers two distinct advantages over the existing work. First (Model Generality), we formulate joint PART-WHOLE outcome prediction as a generic optimization problem, which is able to encode a variety of complex relationships between the outcome of the whole and parts, beyond the linear independence assumption. Second (Algorithm Efficacy), we propose an effective and efficient block coordinate descent algorithm, which is able to find the coordinate-wise optimum with a linear complexity in both time and space. Extensive empirical evaluations on real-world datasets demonstrate that the proposed PAROLE (1) leads to consistent prediction performance improvement by modeling the non-linear part-whole relationship as well as part-part interdependency, and (2) scales linearly in terms of the size of the training dataset.