Uncertainty in Artificial Intelligence
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Adaptive Monotone Shrinkage for Regression
Zhuang Ma, Dean Foster, Robert Stine
We develop an adaptive monotone shrinkage es- timator for regression models with the following characteristics: i) dense coefficients with small but important effects; ii) a priori ordering that in- dicates the probable predictive importance of the features. We capture both properties with an em- pirical Bayes estimator that shrinks coefficients monotonically with respect to their anticipated importance. This estimator can be rapidly com- puted using a version of Pool-Adjacent-Violators algorithm. We show that the proposed monotone shrinkage approach is competitive with the class of all Bayesian estimators that share the prior in- formation. We further observe that the estima- tor also minimizes Steinā??s unbiased risk estimate. Along with our key result that the estimator mim- ics the oracle Bayes rule under an order assump- tion, we also prove that the estimator is robust. Even without the order assumption, our estima- tor mimics the best performance of a large family of estimators that includes the least squares es- timator, constant-Ī» ridge estimator, James-Stein estimator, etc. All the theoretical results are non- asymptotic. Simulation results and data analysis from a model for text processing are provided to support the theory.
Pages: 533-542
PS Link:
PDF Link: /papers/14/p533-ma.pdf
AUTHOR = "Zhuang Ma and Dean Foster and Robert Stine",
TITLE = "Adaptive Monotone Shrinkage for Regression",
BOOKTITLE = "Proceedings of the Thirtieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-14)",
ADDRESS = "Corvallis, Oregon",
YEAR = "2014",
PAGES = "533--542"

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