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.

由于它们的灵活性和预测性能，基于机器学习的回归方法已成为预测建模和预测的重要工具。但是，大多数方法着重于估计目标数量的条件均值或特定分位数，而没有提供完整的条件分布，其中包含不确定性信息，这些信息可能对决策至关重要。通用解决方案包括将条件分布估计问题转换为约束的多类分类问题，其中可以应用诸如深度神经网络之类的工具。提出了一种新颖的联合二元交叉熵损失函数来实现这一目标。通过模拟将其性能与当前的最新技术进行比较。