Regularization with Categorical Covariates: Generalizations and Extensions

分类变量的统计建模的挑战是涉及大量的参数。即使考虑的变量数量不多，指定模型所需的参数数量也可能很高，特别是如果所研究的离散变量具有许多不同的级别。这样的高维参数空间在估计模型和解释结果时造成了问题。为了解决这些问题，提出了具体的正则化技术。然而，到目前为止，这些方法仅适用于具有非常严格假设的简单设置，即（近似）正态分布的结果和统计独立的观察结果。由于这些假设在实践中经常被违反，因此预期项目的目标是推广和扩展分类协变量的正则化方法，以确保这些有前途的方法可以用于应用科学中有趣的应用。

The challenge in statistical modelling of categorical variables is the high number of parameters involved. Even if the number of variables considered is only modest the number of parameters that are necessary to specify a model can be high in particular, if the investigated discrete variables have many different levels. Such high-dimensional parameter spaces cause problems when estimating the model and interpreting the results. To attack these problems, specific regularization techniques have been proposed. So far, however, these methods only work for rather simple settings with very restrictive assumptions, as (approximately) normally distributed outcomes and statistically independent observations. Since these assumptions are often violated in practice, the goal of the intended project is to generalize and extend regularization approaches for categorical covariates to make sure that these promising methods can be used in interesting applications in the applied sciences.