We consider the problem of assessing the importance of multiple variables or factors from a dataset when side information is available.

Online Robust Matrix Factorization (ORMF) algorithms seek to learn a reduced number of latent features as well as outliers from streaming data sets.

We study robust PCA for the fully observed setting, which is about separating a low rank matrix L and a sparse matrix S from their sum D=L+S.

Latent variable models lay the statistical foundation for data science problems with unstructured, incomplete and heterogeneous information. Spectral methods extract low-dimensional geometric structures for downstream tasks in a computationally efficient way.