  Estimating the mixing density of a latent mixture model is an important task
in signal processing. Nonparametric maximum likelihood estimation is one
popular approach to this problem. If the latent variable distribution is
assumed to be continuous, then bootstrapping can be used to approximate it.
However, traditional bootstrapping requires repeated evaluations on resampled
data and is not scalable. In this letter, we construct a generative process to
rapidly produce nonparametric maximum likelihood bootstrap estimates. Our
method requires only a single evaluation of a novel two-stage optimization
algorithm. Simulations and real data analyses demonstrate that our procedure
accurately estimates the mixing density with little computational cost even
when there are a hundred thousand observations.
