We propose a framework to shrink a user-specified characteristic of a precision matrix estimator that is needed to fit a predictive model. Estimators in our framework minimize the Gaussian negative loglikelihood plus an L1 penalty on a linear or affine function evaluated at the optimization variable corresponding to the precision matrix. We establish convergence rate bounds for these estimators and propose an alternating direction method of multipliers algorithm for their computation. Our simulation studies showthat our estimators can perform better than competitors when they are used to fit predictive models. In particular, we illustrate cases where our precision matrix estimators perform worse at estimating the population precision matrix but better at prediction.
Bibliographical noteFunding Information:
We thank the associate editor and two referees for helpful comments. A. J. Molstad’s research was supported in part by a Doctoral Dissertation Fellowship from the University of Minnesota. A. J. Rothman’s research was supported in part by the U.S. National Science Foundation.
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- Alternating direction method of multipliers
- Linear discriminant analysis
- Precision matrix estimation