  Positive-confidence (Pconf) classification [Ishida et al., 2018] is a
promising weakly-supervised learning method which trains a binary classifier
only from positive data equipped with confidence. However, in practice, the
confidence may be skewed by bias arising in an annotation process. The Pconf
classifier cannot be properly learned with skewed confidence, and consequently,
the classification performance might be deteriorated. In this paper, we
introduce the parameterized model of the skewed confidence, and propose the
method for selecting the hyperparameter which cancels out the negative impact
of skewed confidence under the assumption that we have the misclassification
rate of positive samples as a prior knowledge. We demonstrate the effectiveness
of the proposed method through a synthetic experiment with simple linear models
and benchmark problems with neural network models. We also apply our method to
drivers' drowsiness prediction to show that it works well with a real-world
problem where confidence is obtained based on manual annotation.
