Deep distribution regression

Due to their flexibility and predictive performance, machine-learning based regression methods have become an important tool for predictive modeling and forecasting. However, most methods focus on estimating the conditional mean or specific quantiles of the target quantity and do not provide the full conditional distribution, which contains uncertainty information that might be crucial for decision making. A general solution consists of transforming a conditional distribution estimation problem into a constrained multi-class classification problem, in which tools such as deep neural networks can be applied. A novel joint binary cross-entropy loss function is proposed to accomplish this goal. Its performance is compared to current state-of-the-art methods via simulation. The approach also shows improved accuracy in a probabilistic solar energy forecasting problem.