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的数据结构变得越来越大、越来越详细和越来越复杂。尤其是在这样的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指定和偏颇推理的建模限制的今天，进一步了解更准确的模型和适当的推理方法具有极其重要的意义。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，这些工具是可解释的，可以非常快速和准确地进行估计。具体地说，我们的目标是为机器学习中最近的创新开发概率方法，以便估计巨大数据集的模型。为了得到更准确的整体分布回归模型，我们构造了既可用于单变量响应又可用于多变量响应的新的分布模型。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素，以及捕捉任何类型的协变量效应的可能性。该提案还包括软件开发以及在自然科学和社会科学中的应用(如收入分配、营销、天气预报、慢性病和其他)，突出了其对现代统计和数据科学的重要方面作出成功贡献的潜力。

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.