We study a regression problem where for some part of the data we observe both label variable (Y) and predictors (X), while other only are given. Such arises, example, when observations costly may require skilled human agent. When conditional expectation E[Y|X] is not exactly linear, one can consider best linear approximation to expectation, which be estimated consistently by least-square estima...

In multi-label classification tasks, labels are commonly related with each other. It has been well recognized that utilizing label relationship is essential to multi-label learning. One way to utilizing label relationship is to map labels to a lower-dimensional space of uncorrelated labels, where the relationship could be encoded in the mapping. Previous linear mapping methods commonly result i...