The topic is flexible and depends on student's background, previous experience and mathematical skill. Specifically, in the topic, students will explore basic statistical model or problems for different types of data in the differential privacy or fairness model. For statistical model , topics include component analysis, supervised learning, mixture model , et al. For data, topics include survival data, functional data, network analysis. Students will design new algorithms to solve these problems and provide theoretical guarantees on the utility-privacy or utility-fairness tradeoff. Moreover, they will implement these algorithms on some sensitive data such as healthcare and biomedical data.