  Resampling techniques are widely used in statistical inference and ensemble
learning, in which estimators' statistical properties are essential. However,
existing methods are computationally demanding, because repetitions of
estimation/learning via numerical optimization/integral for each resampled data
are required. In this study, we introduce a computationally efficient method to
resolve such problem: replicated vector approximate message passing. This is
based on a combination of the replica method of statistical physics and an
accurate approximate inference algorithm, namely the vector approximate message
passing of information theory. The method provides tractable densities without
repeating estimation/learning, and the densities approximately offer an
arbitrary degree of the estimators' moment in practical time. In the
experiment, we apply the proposed method to the stability selection method,
which is commonly used in variable selection problems. The numerical results
show its fast convergence and high approximation accuracy for problems
involving both synthetic and real-world datasets.
