Fast and Cheap Krylov-Based Covariance Smoothing

2025/01/14 by Yun, Ho, Panaretos, Victor M.
#65D10 (Primary) 62G05 (Secondary) #Applications (stat.AP) #Computation (stat.CO) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.2501.08265

Abstract

We introduce the Tensorized-and-Restricted Krylov (TReK) method, a simple and efficient algorithm for estimating covariance tensors with large observational sizes. TReK extends the conjugate gradient method to incorporate range restrictions, enabling its use in a variety of covariance smoothing applications. By leveraging matrix-level operations, it achieves significant improvements in both computational speed and memory cost, improving over existing methods by an order of magnitude. TReK ensures finite-step convergence in the absence of rounding errors and converges fast in practice, making it well-suited for large-scale problems. The algorithm is also highly flexible, supporting a wide range of forward and projection tensors.

Related

• Tucker Tensor analysis of Matern functions in spatial statistics
• Kriging in Tensor Train data format
• Dimension-free Bounds for Covariance Estimation with Tensor-Train Structure
• Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurements
• Fast multidimensional convolution in low-rank formats via cross approximation