Professor William Leeb

This group performs research on new statistical and computational methods for high-dimensional statistical analysis. The first pillar of the proposed methodology is principal component analysis (PCA). The researchers extend the use of PCA to the setting of high-dimensional observations with corrupted observations, non-Gaussian noise, and low signal-to-noise ratios. These kinds of datasets arise in problems such as cryo-electron microscopy and X-ray free electron laser imaging. This work will provide robust tools for exploratory data analysis for these problems. The second pillar of the research program is the method of moments, a classical technique for parameter estimation that are repurposed for new problems. The researchers extend the range of applicability of the method of moments to many big data problems that exhibit certain algebraic structure. For these problems, the method of moments enables scalable and near-optimal statistical inference. Finally, the novel extensions of PCA and the method moments will be combined together to derive new near-optimal and scalable statistical inference procedures for high-dimensional problems.