  Feature allocation models generalize species sampling models by allowing
every observation to belong to more than one species, now called features.
Under the popular Bernoulli product model for feature allocation, given $n$
samples, we study the problem of estimating the missing mass $M_{n}$, namely
the expected number hitherto unseen features that would be observed if one
additional individual was sampled. This is motivated by numerous applied
problems where the sampling procedure is expensive, in terms of time and/or
financial resources allocated, and further samples can be only motivated by the
possibility of recording new unobserved features. We introduce a simple, robust
and theoretically sound nonparametric estimator $\hat{M}_{n}$ of $M_{n}$.
$\hat{M}_{n}$ turns out to have the same analytic form of the popular
Good-Turing estimator of the missing mass in species sampling models, with the
difference that the two estimators have different ranges. We show that
$\hat{M}_{n}$ admits a natural interpretation both as a jackknife estimator and
as a nonparametric empirical Bayes estimator, we give provable guarantees for
the performance of $\hat{M}_{n}$ in terms of minimax rate optimality, and we
provide with an interesting connection between $\hat{M}_{n}$ and the
Good-Turing estimator for species sampling. Finally, we derive non-asymptotic
confidence intervals for $\hat{M}_{n}$, which are easily computable and do not
rely on any asymptotic approximation. Our approach is illustrated with
synthetic data and SNP data from the ENCODE sequencing genome project.
