Research

My research interests are, generally, in the areas of numerical analysis and computational mathematics. With graduate students, my research group has been working on various questions in data science and machine learning, including the development of efficient algorithms in high dimensional optimization, dimension reduction, mathematical modeling in machine learning (e.g., Variational Autoencoders VAE), and optimization in the context of neural networks/deep learning. We have worked on theory and algorithms for problems of missing data under monotone or non-monotone patterns, optimization and hyper-parameter tuning in general applications and Data Science, as well as Ridge Functions and Active Subspaces for dimension reduction. We have developed theory and application of several new Copulas to model multivariate non-normal distributions, exploring complex margin and tail inter-dependence.

For a detailed list of publications: C.V.