  This paper addresses a regression problem in which output label values are
the results of sensing the magnitude of a phenomenon. A low value of such
labels can mean either that the actual magnitude of the phenomenon was low or
that the sensor made an incomplete observation. This leads to a bias toward
lower values in labels and the resultant learning because labels may have lower
values due to incomplete observations, even if the actual magnitude of the
phenomenon was high. Moreover, because an incomplete observation does not
provide any tags indicating incompleteness, we cannot eliminate or impute them.
To address this issue, we propose a learning algorithm that explicitly models
incomplete observations corrupted with an asymmetric noise that always has a
negative value. We show that our algorithm is unbiased as if it were learned
from uncorrupted data that does not involve incomplete observations. We
demonstrate the advantages of our algorithm through numerical experiments.
