The goal is to develop a family of provable stochastic algorithms for e.g. large scale optimization and training deep neural networks. The provability is established by probabilistic weak approximation and the ordinary differential equation theory. 
My goal is to develop methods that can be smoothly implemented in the ecosystem of data science, and perform provabiy accurate statistical analysis including hypothesis testing on statistical models and causal effect.
I develop quantile regression methods for economic and financial datasets that allow nonparametric modeling and/or high dimensionality $p>n$. 
Clinicians rely on medical imaging to make diagonosis. I develop machine learning methods that discover subtle patterns in brain fRMI and lung MRI. 