This course introduces how to use regularized regression methods (such as ridge, LASSO, adaptive LASSO, SCAD, etc.) and feature screening approaches (for example, overlapping group screening and Kendall/Pearson partial correlation) to construct statistical prediction models under an ultra-high-dimensional data structure, where the response variable may be continuous, discrete, or right-censored. Ultra-high dimensionality refers to situations in which the number of predictors is far larger than the sample size, making traditional statistical regression methods inapplicable.

The course will use genomic data from The Cancer Genome Atlas (TCGA) for real data analysis and will introduce related R programming. Students will also be required to conduct hands-on implementations and give in-class presentations, with the aim of improving their ability to handle relevant big data problems as well as their oral presentation and communication skills.

The prerequisite for this course is Statistical Learning (SL). In the SL course, students learn fundamental statistical methods, including concepts of statistical modeling, common models such as linear regression, classification, and survival models, as well as techniques like cross-validation, bootstrapping, and regularization. This high-dimensional statistical learning course builds on those concepts and focuses specifically on modeling for high-dimensional data. These foundational methods will not be taught here, so prior knowledge is essential. It is strongly recommended that students complete a statistical learning course before enrolling to ensure they can fully engage with the material and avoid difficulties.