We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across groups, and a sparse linear combination of the dictionary elements is estimated to form a model within each group. We refer to the method as conditional spa...

We introduce a learning technique for regression between highdimensional spaces. Standard methods typically reduce this task to many onedimensional problems, with each output dimension considered independently. By contrast, in our approach the feature construction and the regression estimation are performed jointly, directly minimizing a loss function that we specify, subject to a rank constrai...

We present self-modeling regression models for flexible nonparametric modeling of multiple outcomes measured longitudinally. Based on penalized regression splines, the models borrow strength across multiple outcomes by specifying a global time profile, thereby yielding a means of dimension reduction and estimates of trend more precise than those based on univariate regressions. The proposed mod...

This paper deals with multivariate regression chain graphs, which were introduced by Cox and Wermuth (1993, 1996) to represent linear causal models with correlated errors. Specifically, we present a constraint based algorithm for learning a chain graph a given probability distribution is faithful to. We also show that for each Markov equivalence class of multivariate regression chain graphs the...