  The problem of estimating the support of a distribution is of great
importance in many areas of machine learning, computer science, physics and
biology. Most of the existing work in this domain has focused on settings that
assume perfectly accurate sampling approaches, which is seldom true in
practical data science. Here we introduce the first known approach to support
estimation in the presence of sampling artifacts and errors where each sample
is assumed to arise from a Poisson repeat channel which simultaneously captures
repetitions and deletions of samples. The proposed estimator is based on
regularized weighted Chebyshev approximations, with weights governed by
evaluations of so-called Touchard (Bell) polynomials. The supports in the
presence of sampling artifacts are calculated using discretized semi-infite
programming methods. The estimation approach is tested on synthetic and textual
data, as well as on GISAID data collected to address a new problem in
computational biology: mutational support estimation in genes of the SARS-Cov-2
virus. In the later setting, the Poisson channel captures the fact that many
individuals are tested multiple times for the presence of viral RNA, thereby
leading to repeated samples, while other individual's results are not recorded
due to test errors. For all experiments performed, we observed significant
improvements of our integrated methods compared to those obtained through
adequate modifications of state-of-the-art noiseless support estimation
methods.
