  Multi-task learning (MTL) aims to improve generalization performance by
learning multiple related tasks simultaneously. While sometimes the underlying
task relationship structure is known, often the structure needs to be estimated
from data at hand. In this paper, we present a novel family of models for MTL,
applicable to regression and classification problems, capable of learning the
structure of task relationships. In particular, we consider a joint estimation
problem of the task relationship structure and the individual task parameters,
which is solved using alternating minimization. The task relationship structure
learning component builds on recent advances in structure learning of Gaussian
graphical models based on sparse estimators of the precision (inverse
covariance) matrix. We illustrate the effectiveness of the proposed model on a
variety of synthetic and benchmark datasets for regression and classification.
We also consider the problem of combining climate model outputs for better
projections of future climate, with focus on temperature in South America, and
show that the proposed model outperforms several existing methods for the
problem.
