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Calibrated Multivariate Regression with Application to Neural Semantic Basis Discovery
We propose a calibrated multivariate regression method named CMR for fitting
high dimensional multivariate regression models. Compared with existing
methods, CMR calibrates regularization for each regression task with respect to
its noise level so that it simultaneously attains improved finite-sample
performance and tuning insensitiveness. Theoretically, we provide sufficient
conditions under which CMR achieves the optimal rate of convergence in
parameter estimation. Computationally, we propose an efficient smoothed
proximal gradient algorithm with a worst-case numerical rate of convergence
\cO(1/\epsilon), where is a pre-specified accuracy of the
objective function value. We conduct thorough numerical simulations to
illustrate that CMR consistently outperforms other high dimensional
multivariate regression methods. We also apply CMR to solve a brain activity
prediction problem and find that it is as competitive as a handcrafted model
created by human experts. The R package \texttt{camel} implementing the
proposed method is available on the Comprehensive R Archive Network
\url{http://cran.r-project.org/web/packages/camel/}.Comment: Journal of Machine Learning Research, 201
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