  Learning multiple tasks across heterogeneous domains is a challenging problem
since the feature space may not be the same for different tasks. We assume the
data in multiple tasks are generated from a latent common domain via sparse
domain transforms and propose a latent probit model (LPM) to jointly learn the
domain transforms, and the shared probit classifier in the common domain. To
learn meaningful task relatedness and avoid over-fitting in classification, we
introduce sparsity in the domain transforms matrices, as well as in the common
classifier. We derive theoretical bounds for the estimation error of the
classifier in terms of the sparsity of domain transforms. An
expectation-maximization algorithm is derived for learning the LPM. The
effectiveness of the approach is demonstrated on several real datasets.
