  Commonly used objective functions (losses) for a supervised optimization of
discriminative neural network classifiers were either distribution-based or
metric-based. The distribution-based losses could compromise the generalization
or cause classification biases towards the dominant classes of an imbalanced
class-sample distribution. The metric-based losses could make the network model
independent of any distribution and thus improve its generalization. However,
they could still be biased towards the dominant classes and could suffer from
discrepancies when a class was absent in both the reference (ground truth) and
the predicted labels. In this paper, we proposed a novel optimization process
which not only tackled the unbalancedness of the class-sample distribution of
the training samples but also provided a mechanism to tackle errors in the
reference labels of the training samples. This was achieved by proposing a
novel algorithm to find candidate classification labels of the training samples
from their prior probabilities and the currently estimated posteriors on the
network and a novel objective function for the optimizations. The algorithm was
the result of casting the generalized Kelly criterion for optimal betting into
a multiclass classification problem. The proposed objective function was the
expected free energy of a prospective active inference and could incorporate
the candidate labels, the original reference labels, and the priors of the
training samples while still being distribution-based. The incorporation of the
priors into the optimization not only helped to tackle errors in the reference
labels but also allowed to reduce classification biases towards the dominant
classes by focusing the attention of the neural network on important but
minority foreground classes.
