In this paper we consider the reduced rank regression problem min rank ¯ L=n,L 3 det Y α − ¯ LP β − L 3 U α Y α − ¯ LP β − L 3 U α T solved by maximum-likelihood-inspired State-Space Subspace System Identification algorithms. We conclude that the determinant criterion is, due to potential rank-deficiencies, not general enough to handle all problem instances. The main part of the paper analyzes ...

There is growing evidence in the epidemiologic literature of the relationship between air pollution and adverse health outcomes. Prediction of individual air pollution exposure in the Environmental Protection Agency (EPA) funded Multi-Ethnic Study of Atheroscelerosis and Air Pollution (MESA Air) study relies on a flexible spatio-temporal prediction model that integrates land-use regression with...

Output kernel learning techniques allow to simultaneously learn a vector-valued function and a positive semidefinite matrix which describes the relationships between the outputs. In this paper, we introduce a new formulation that imposes a low-rank constraint on the output kernel and operates directly on a factor of the kernel matrix. First, we investigate the connection between output kernel l...

Isotonic regression is a shape-constrained nonparametric regression in which the ordinate is a nondecreasing function of the abscissa. The regression outcome is an increasing step function. For an initial set of n points, the number of steps in the isotonic regression, m, may be as large as n. As a result, the full isotonic regression has been criticized as overfitting the data or making the re...