Regression Models Beyond the Mean – A BayesianApproach to Machine Learning

计算机科学的最新进展导致许多科学研究中数据结构的规模、细节和复杂性不断增加。特别是在如今，这种大数据应用不仅允许而且需要更大的灵活性来克服可能导致模型错误规范和有偏差推理的建模限制，因此进一步了解更准确的模型和适当的推理方法非常重要。因此，该研究小组将为单变量和多变量回归模型开发统计工具，这些模型是可解释的，并且可以非常快速和准确地估计。具体来说，我们的目标是为机器学习的最新创新开发概率方法，以便估计大型数据集的模型。为了获得更精确的整个分布的回归模型，我们构建了新的分布模型，可以用于单变量和多变量响应。在所有模型中，我们将解决收缩和自动变量选择的问题，以应对大量的预测因子，以及捕获任何类型的协变量效应的可能性。该建议还包括软件开发以及在自然科学和社会科学（如收入分配、市场营销、天气预报、慢性病等）方面的应用，突出了其在现代统计和数据科学的重要方面成功作出贡献的潜力。

Recent progress in computer science has led to data structures of increasing size, detail and complexity in many scientific studies. In particular nowadays, where such big data applications do not only allow but also require more flexibility to overcome modelling restrictions that may result in model misspecification and biased inference, further insight in more accurate models and appropriate inferential methods is of enormous importance. This research group will therefore develop statistical tools for both univariate and multivariate regression models that are interpretable and that can be estimated extremely fast and accurate. Specifically, we aim to develop probabilistic approaches to recent innovations in machine learning in order to estimate models for huge data sets. To obtain more accurate regression models for the entire distribution we construct new distributional models that can be used for both univariate and multivariate responses. In all models we will address the issues of shrinkage and automatic variable selection to cope with a huge number of predictors, and the possibility to capture any type of covariate effect. This proposal also includes software development as well as applications in natural and social sciences (such as income distributions, marketing, weather forecasting, chronic diseases and others), highlighting its potential to successfully contribute to important facets in modern statistics and data science.