Efficient Sampling Algorithms for Approximate Computation of High-Dimensional Data in Scientific Computing

Abstract

As the dimensionality of high-dimensional data increases, scientific computing faces many challenges. There is an urgent need for high-quality approximation methods. To address the high-dimensional data approximation problems frequently encountered in fields such as environmental monitoring, genomics, and remote sensing, this paper introduces a new class of efficient sampling algorithms. In order to improve the speed and reliability of data-based statistics, the aforementioned two methods were chosen. A large number of experiments have shown that the above methods perform well in synthesizing Gaussian fields, hyperspectral images, and single-cell gene expression matrices. According to the results, the proposed algorithm achieved an average approximation error of less than 0.018, even with a sampling ratio of only 5%. It outperforms traditional importance sampling (0.043) and uniform random sampling (0.071), and exhibits linear scalability in terms of computation time and memory. To demonstrate that reliable and accurate estimators can still be used under adaptive weighting and feedback mechanisms, ablation experiments and sensitivity analyzes were also conducted. These findings provide new standards for the sample economy and accuracy of data-intensive scientific processes. The study provides the scientific community with a reproducible and open workflow to help accelerate research and gain deeper insights into high-dimensional data.