Gaussian Process Based Dual Latent Function Approach to Ordinal Regression

The Gaussian process prior formulation introduced by us in this paper learns a mapping for ordinal regression task using dual sets of latent functions. In this formulation one set of latent functions are associated with data items and the other set of latent functions are associated with entities. An entity is a term introduced by us in this work to refer to the object responsible for assigning ordinal labels to data items. For example in the collaborative filtering problem an entity corresponds to a user. In our work we assume that the entities cluster, and we use latent functions to having a Gaussian process prior to model these clusters. Similarly we also assume that the data items cluster and use latent functions having a Gaussian process prior to model these clusters. We learn the parameters of these Gaussian processes in a discriminative learning framework by minimizing a loss function using an alternating minimization procedure. The purpose of introducing dual sets of latent functions is to overcome the deficiency in the predictive nature of discriminative models for ordinal regression tasks while learning from less training data unlike generative models which have a good performance even while learning from less training data. Thus we evaluate the performance of our model on two problems, collaborative filtering and image annotation, by comparing with well known baseline methods using a generative model approach so as to understand the efficacy of our model on less training data.