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Multivariate Regression with Calibration
Han Liu · Lie Wang · Tuo Zhao

Thu Dec 11 11:00 AM -- 03:00 PM (PST) @ Level 2, room 210D
We propose a new method named calibrated multivariate regression (CMR) for fitting high dimensional multivariate regression models. Compared to existing methods, CMR calibrates the regularization for each regression task with respect to its noise level so that it is simultaneously tuning insensitive and achieves an improved finite-sample performance. Computationally, we develop an efficient smoothed proximal gradient algorithm which has a worst-case iteration complexity $O(1/\epsilon)$, where $\epsilon$ is a pre-specified numerical accuracy. Theoretically, we prove that CMR achieves the optimal rate of convergence in parameter estimation. We illustrate the usefulness of CMR by thorough numerical simulations and show that CMR consistently outperforms other high dimensional multivariate regression methods. We also apply CMR on a brain activity prediction problem and find that CMR is as competitive as the handcrafted model created by human experts.

Author Information

Han Liu (Tencent AI Lab)
Lie Wang (Massachusetts Institute of Technology)
Tuo Zhao (Johns Hopkins University Princeton University)

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