3 research outputs found
Role of Bootstrap Averaging in Generalized Approximate Message Passing
Generalized approximate message passing (GAMP) is a computationally efficient
algorithm for estimating an unknown signal from a random
linear measurement , where
is a known measurement matrix and is
the noise vector. The salient feature of GAMP is that it can provide an
unbiased estimator , which
can be used for various hypothesis-testing methods. In this study, we consider
the bootstrap average of an unbiased estimator of GAMP for the elastic net. By
numerically analyzing the state evolution of \emph{approximate message passing
with resampling}, which has been proposed for computing bootstrap statistics of
the elastic net estimator, we investigate when the bootstrap averaging reduces
the variance of the unbiased estimator and the effect of optimizing the size of
each bootstrap sample and hyperparameter of the elastic net regularization in
the asymptotic setting . The results
indicate that bootstrap averaging effectively reduces the variance of the
unbiased estimator when the actual data generation process is inconsistent with
the sparsity assumption of the regularization and the sample size is small.
Furthermore, we find that when is less sparse, and the data size is
small, the system undergoes a phase transition. The phase transition indicates
the existence of the region where the ensemble average of unbiased estimators
of GAMP for the elastic net norm minimization problem yields the unbiased
estimator with the minimum variance.Comment: 6 pages, 5 figure