  In this paper, we study the accuracy of values aggregated over classes
predicted by a classification algorithm. The problem is that the resulting
aggregates (e.g., sums of a variable) are known to be biased. The bias can be
large even for highly accurate classification algorithms, in particular when
dealing with class-imbalanced data. To correct this bias, the algorithm's
classification error rates have to be estimated. In this estimation, two issues
arise when applying existing bias correction methods. First, inaccuracies in
estimating classification error rates have to be taken into account. Second,
impermissible estimates, such as a negative estimate for a positive value, have
to be dismissed. We show that both issues are relevant in applications where
the true labels are known only for a small set of data points. We propose a
novel bias correction method using Bayesian inference. The novelty of our
method is that it imposes constraints on the model parameters. We show that our
method solves the problem of biased classification-based aggregates as well as
the two issues above, in the general setting of multi-class classification. In
the empirical evaluation, using a binary classifier on a real-world dataset of
company tax returns, we show that our method outperforms existing methods in
terms of mean squared error.
