  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.
