6 papers
Convergence Rates for Learning Pseudo-Differential Operators
Jiaheng Chen, Daniel Sanz-Alonso
This paper establishes convergence rates for learning elliptic pseudo-differential operators, a fundamental operator class in partial differential equations and mathematical physic…
High-Dimensional Quasi-Monte Carlo via Combinatorial Discrepancy
Jiaheng Chen, Haotian Jiang, Nathan Kirk
Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods are classical approaches for the numerical integration of functions over . While QMC methods can achieve faster co…
On the Estimation of Gaussian Moment Tensors
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso
This paper studies two estimators for Gaussian moment tensors: the standard sample moment estimator and a plug-in estimator based on Isserlis's theorem. We establish dimension-free…
VAMO: Efficient Zeroth-Order Variance Reduction for SGD with Faster Convergence
Jiahe Chen, Ziye Ma
Optimizing large-scale nonconvex problems, common in deep learning, demands balancing rapid convergence with computational efficiency. First-order (FO) optimizers, which serve as t…
Sharp Concentration of Simple Random Tensors
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso
This paper establishes sharp dimension-free concentration inequalities and expectation bounds for the deviation of the sum of simple random tensors from its expectation. As part of…
Precision and Cholesky Factor Estimation for Gaussian Processes
Jiaheng Chen, Daniel Sanz-Alonso
This paper studies the estimation of large precision matrices and Cholesky factors obtained by observing a Gaussian process at many locations. Under general assumptions on the prec…