Abstract Two-stage Cumulative Attribute (CA) regression has been found effective in regression problems of computer vision such as facial age and crowd density estimation. The first stage regression maps input features to cumulative attributes that encode correlations between target values. The previous works have dealt with single output regression. In this work, we propose cumulative attribute spaces for 2- and 3-output (multivariate) regression. We show how the original CA space can be generalized to multiple output by the Cartesian product (CartCA). However, for target spaces with more than two outputs the CartCA becomes computationally infeasible and therefore we propose an approximate solution - multi-view CA (MvCA) - where CartCA is applied to output pairs. We experimentally verify improved performance of the CartCA and MvCA spaces in 2D and 3D face pose estimation and three-output (RGB) illuminant estimation for color constancy.