The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a penalty (i.e. a function of regression coefficients). The ridge penalty is the sum of squared regression coefficients, giving rise to ridge regression. Here many aspect of ridge regression are reviewed e.g. moments, mean squared error, its equivalence to constrained estimation, and its relation to Bayesian regression. Finally, its behaviour and use are illustrated in simulation and on omics data. Subsequently, ridge regression is generalized to allow for a more general penalty. The ridge penalization framework is then translated to logistic regression and its properties are shown to carry over. To contrast ridge penalized estimation, the final chapters introduce its lasso counterpart and generalizations thereof.

翻译：线性回归模型无法适用于高维数据，因为高维性会导致经验不可识别性。惩罚回归通过对损失函数添加惩罚项（即回归系数的函数）来克服这种不可识别性。岭惩罚项是回归系数的平方和，由此形成了岭回归。本文回顾了岭回归的多个方面，例如矩、均方误差、其与约束估计的等价性以及与贝叶斯回归的关系。最后，通过模拟和组学数据展示了其行为和应用。随后，对岭回归进行推广以允许更一般的惩罚项。接着，将岭惩罚框架应用于逻辑回归，并证明其性质得以延续。为了与岭惩罚估计形成对比，最后章节介绍了LASSO及其推广形式。