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...

Abstract: 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...

Abstract: 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...

Abstract: 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...

Abstract: Cells are the basic biological units of multicellular organisms.  The development of single-cell technologies such as single cell RNA sequencing (scRNA-seq) have enabled us to study the diversity of cell types in tissue and to elucidate the roles of individual...

Abstract: I will give a brief introduction to the technology followed by some exploratory data analysis demonstrating the statistical challenges and how some of these can be considered missing data problems.

Abstract: Recent advances in biotechnology and genomics have generated dizzying amounts of large, noisy, and sparse datasets that require concomitant development of machine learning methods. The analyses of single-cell RNA-seq data have driven the development of...

Abstract: Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled structure to...

Abstract: Causal inference has been widely conducted in various fields and many methods have been proposed for different settings. However, for noisy data with both mismeasurements and missing observations, those methods often break down. In this talk, I will discuss a...