Calibrated Multivariate Regression Networks.

In this paper, we propose a new multi-layer learning architecture, the calibrated multivariate regression network (CMRN). Compared to previous multivariate models, the CMRN is able to simultaneously handle major challenges in multivariate regression including highly nonlinear input-output relationships, underlying inter-output correlations and calibration of multiple outputs within one single framework. The CMRN is comprised of a nonlinear module with cosine activations and a linear module with the low-rank expansion, which establishes a compact multivariate regression network. By seamlessly working with the $\ell _{2,1}$ loss, the CMRN automatically calibrates multiple outputs with distinct noise levels to achieve improved performance. Being succinctly formulated but theoretically well-founded, the CMRN offers a compact multi-layer learning architecture that can be efficiently trained to scale up with massive datasets. We conduct extensive experimental evaluation on two representative large multivariate regression tasks for both machine learning and computer vision. The proposed CMRN can produce high performance on all tasks, which is better or competitive to state-of-the-art models. Extensive ablation studies offer deep insights into the effectiveness of the proposed CMRN. [ABSTRACT FROM AUTHOR]