A Reconstruction Error Formulation for Semi-Supervised Multi-task and Multi-view Learning

A significant challenge to make learning techniques more sui table for general purpose use is to move beyond i) complete supervision, ii) low dimensional data, iii) a single t ask and single view per instance. Solving these challenges a llows working with "Big Data" problems that are typically high dim ensional with multiple (but possibly incomplete) labeling s and views. While other work has addressed each of these probl ems separately, in this paper we show how to address them together, namelysemi-supervised dimension reduction for multi-task and multi-view learning (SSDR-MML), which performs optimization for dimension reduction and label inference in semi-supervised setting. The proposed framework is designed to handle both multi-task and multi-view learning settings, and can be easily adapted to many useful applications. Inform ation obtained from all tasks and views is combined via reconstruction errors in a linear fashion that can be efficiently solvedusing an alternating optimization scheme. Our formulation has a number of advantages. W e explicitly model the information combining mechanism as a data structure (a weight/nearest-nei ghbor matrix) which allows investigating fundamental ques tions in multi-task and multi-view learning. W e address one such question by presenting a general measure to quantify the success of simultaneous learning of multiple tasks or from multiple views. W e show that our SSDR-MML approach can outperform many state-of-the-art baseline methods and demonstrate the effectiveness of connecting dimension reduction and learning.