High Dimensional
High-dimensional data analysis focuses on extracting meaningful information and building predictive models from datasets with numerous variables, often exceeding the number of observations. Current research emphasizes developing computationally efficient algorithms, such as stochastic gradient descent and its variants, and novel model architectures like graph neural networks and deep learning approaches tailored to handle the unique challenges posed by high dimensionality, including issues of sparsity and missing data. These advancements are crucial for addressing complex problems across diverse fields, including scientific modeling, robotics, and financial risk assessment, where high-dimensional data are increasingly prevalent.
Papers
Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities
Matthew T. C. Li, Tiangang Cui, Fengyi Li, Youssef Marzouk, Olivier Zahm
A variational Bayes approach to debiased inference for low-dimensional parameters in high-dimensional linear regression
Ismaël Castillo, Alice L'Huillier, Kolyan Ray, Luke Travis