Latent Supervised Learning

This article introduces a new machine learning task, called latent supervised learning, where the goal is to learn a binary classifier from continuous training labels that serve as surrogates for the unobserved class labels. We investigate a specific model where the surrogate variable arises from a two-component Gaussian mixture with unknown means and variances, and the component membership is determined by a hyperplane in the covariate space. The estimation of the separating hyperplane and the Gaussian mixture parameters forms what shall be referred to as the change-line classification problem. We propose a data-driven sieve maximum likelihood estimator for the hyperplane, which in turn can be used to estimate the parameters of the Gaussian mixture. The estimator is shown to be consistent. Simulations as well as empirical data show the estimator has high classification accuracy.