Taking the Lasso method as its starting point this book describes the main ingredients needed
to study general loss functions and sparsity-inducing regularizers. It also provides a
semi-parametric approach to establishing confidence intervals and tests. Sparsity-inducing
methods have proven to be very useful in the analysis of high-dimensional data. Examples
include the Lasso and group Lasso methods and the least squares method with other
norm-penalties such as the nuclear norm. The illustrations provided include generalized linear
models density estimation matrix completion and sparse principal components. Each chapter
ends with a problem section. The book can be used as a textbook for a graduate or PhD course.
