Distributed Ordinal Regression Over Networks

Many real-world data are labeled with natural orders, i.e., ordinal labels. Examples can be found in a wide variety of fields. Ordinal regression is a problem to predict ordinal labels for given patterns. There are specially developed ordinal regression methods to tackle this type of problems, but they are usually centralized. However, in some scenarios, data are collected distributedly by nodes of a network. For the purpose of privacy protection or due to some practical constraints, it is difficult or impossible to transmit the data to a fusion center for processing. Thus the centralized ordinal regression methods are inapplicable. In this paper, we formulate a distributed generalized ordered logit model for distributed ordinal regression. To estimate parameters in the model, a distributed constrained optimization formulation based on maximum likelihood methods is established. Then, we propose a projected gradient based algorithm to solve the optimization problem. We prove the consensus and the convergence of the proposed distributed algorithm. We also conduct numerical simulations on synthetic and real-world datasets. Simulation results show that the proposed distributed algorithm is comparable to the corresponding centralized algorithm. Even when the data label distribution among nodes is unbalanced, the proposed algorithm still has competitive performance.