Seminars Sorted by Series

I will discuss a proof of the existence of infinitely many solutions for the singular Yamabe problem in spheres using bifurcation theory and the spectral theory of hyperbolic surfaces.

In this talk I will begin by reviewing classical geometric properties of constant mean curvature surfaces, H>0, in R^3. I will then talk about several more recent results for surfaces embedded in R^3 with constant mean curvature, such as curvature...

Abstract: There is a very extensive literature of statistical methods for the analysis of data with missing values. I'll provide a historical overview, including ad-hoc approaches, statistical models and conditions for ignoring the missingness...

Abstract: An abundant literature addresses missing data in an inferential framework: estimating parameters and their variance from incomplete tables. Here, we consider supervised-learning settings: predicting a target when missing values appear in...

Abstract: In today’s data-driven society, human beings still make most critical decisions and yet they are increasingly utilizing recommendations produced by statistical and machine learning methods. Given the prevalence of this approach in many...

Abstract: In many applications, it is of interest to cluster subjects based on very high-dimensional data, often in the presence of missing data. Although discrete mixture models are routinely used, we demonstrate pitfalls in high-dimensional...

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...

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...

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...

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: 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...

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...

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...

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...