  Conventional predictive Artificial Neural Networks (ANNs) commonly employ
deterministic weight matrices; therefore, their prediction is a point estimate.
Such a deterministic nature in ANNs causes the limitations of using ANNs for
medical diagnosis, law problems, and portfolio management, in which discovering
not only the prediction but also the uncertainty of the prediction is
essentially required. To address such a problem, we propose a predictive
probabilistic neural network model, which corresponds to a different manner of
using the generator in conditional Generative Adversarial Network (cGAN) that
has been routinely used for conditional sample generation. By reversing the
input and output of ordinary cGAN, the model can be successfully used as a
predictive model; besides, the model is robust against noises since adversarial
training is employed. In addition, to measure the uncertainty of predictions,
we introduce the entropy and relative entropy for regression problems and
classification problems, respectively. The proposed framework is applied to
stock market data and an image classification task. As a result, the proposed
framework shows superior estimation performance, especially on noisy data;
moreover, it is demonstrated that the proposed framework can properly estimate
the uncertainty of predictions.
