Statistical Models: The Learning and Inference of various Graphical Models as well as their applications, including generative model like HMM, Bayesian Net, MRF, and discriminative models like SVM, Fisher linear discriminant etc.
Optimization Problems: The theory and practice of various probability inference algorithm, such as EM algorithm, particle filters in the continuous domain, as well as graph cut algorithm, belief propagation algorithm in the discrete domain.
Algorithms: Efficient Algorithms and Data Structures.