Special year - math workshop

Low rank matrix completion (LRMC) has received tremendous attention in recent years.  The low rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear variety.  This work extends this thinking to cases where the columns are points on...

Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and one encounters the problem of recovering the matrix...

Low rank is a popular prior in matrix and tensor completion. The set of matrices or tensors of a given rank forms a smooth manifold. Estimating the full data under the low-rank prior then turns into an optimization problem over a manifold of fixed-rank objects. What is the worst-case complexity...

We have seen the rise of high-dimensional omics data, e.g., genome, transcriptome, microbiome, and proteome in recent decades. The different types of missingness in modern omics data bring up significant biological and statistical challenges. In this talk, we focus on two problems in modern...

For many applications in healthcare, econometrics, financial forecasting, and climate science, data can only be obtained as aggregates. This begs the question, can one construct accurate models using only aggregates? I will present two vignettes outlining recent work towards an answer. First,...

For many machine learning tasks, the input data lie on a low-dimensional manifold embedded in a high-dimensional space and, because of this high-dimensional structure, most algorithms inefficient. The typical solution is to reduce the dimension of the input data using a standard dimension...