Research
Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science.…
Gradient Boosting Decision Tree (GBDT) is a popular machine learning algorithm, and has quite a few effective implementations. Although many engineering optimizations have been adopted in these implementations, the efficiency and scalability are still unsatisfactory…
This talk will be centered on partial verification results. Software model checkers can be used both to find bugs and to prove certain properties hold. However, due to resource bounds or tool limitations, many times…
Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science.…
Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science.…
We prove that any random distribution satisfying conformal invariance and a form of domain Markov property and having a finite moment condition must be the Gaussian free field. We also present some open problems regarding…
Optimal matching problems are random variational problems widely investigated in the mathematics and physics literature. We discuss here the optimal matching problem of an empirical measure on a sample of iid random variables to the…
Consider the fractional Brownian motions on the real line. What should we expect if we replace the real line by a manifold M? We will provide an answer to this question, extending work begun by…
