We present neural mixture distributional regression (NMDR), a holistic framework to estimate complex finite mixtures of distributional regressions defined by flexible additive predictors. Our framework is able to handle a large number of mixtures of potentially different distributions in high-dimensional settings, allows for efficient and scalable optimization and can be applied to recent concepts that combine structured regression models with deep neural networks. While many existing approaches for mixture models address challenges in optimization of such and provide results for convergence under specific model assumptions, our approach is assumption-free and instead makes use of optimizers well-established in deep learning. Through extensive numerical experiments and a high-dimensional deep learning application we provide evidence that the proposed approach is competitive to existing approaches and works well in more complex scenarios.

翻译：我们提出了神经混合物分布回归(NMDR),这是一个全面框架,用以估计由灵活添加剂预测器界定的分布回归的复杂有限混合物。我们的框架能够处理大量高维环境中可能不同分布的混合物,从而实现高效和可扩缩的优化,并可用于将结构回归模型与深神经网络相结合的近期概念。虽然许多混合模型的现有方法应对优化此类模型方面的挑战,并在具体模型假设下为趋同提供结果,但我们的方法是没有假设的,而是在深层次学习中充分利用优化。通过广泛的数字实验和高维深学习应用,我们提供了证据,证明拟议方法对现有方法具有竞争力,在更为复杂的情景下运作良好。