Computational-Statistical Trade-off in Kernel Two-Sample Testing with Random Fourier Features
arXiv:2407.08976v2 Announce Type: replace-cross Abstract: Recent years have seen a surge in methods for two-sample testing, among which the Maximum Mean Discrepancy (MMD) test has emerged as an effective tool for handling complex and high-dimensional data. Despite its success and widespread adoption, the primary limitation of the MMD test has been its quadratic-time complexity, which poses challenges for large-scale analysis. While various approaches have been proposed to expedite the procedure, it has been unclear whether it is possible to attain the same power guarantee as the MMD test at su
This paper addresses a known limitation in a widely used statistical method (MMD) by proposing a solution for its quadratic-time complexity, which is crucial for handling the large-scale datasets prevalent in current AI research.
Improving the computational efficiency of fundamental statistical tests like MMD can accelerate advancements in machine learning, particularly in areas requiring robust comparison of high-dimensional data, thereby enhancing the rigor and scalability of AI research.
The proposed method could allow the Maximum Mean Discrepancy test to maintain its power guarantees while significantly reducing computational demands, making it practical for larger and more complex datasets.
- · AI researchers
- · Machine learning engineers
- · Developers of large-scale data analysis tools
More efficient and scalable two-sample testing becomes possible for large AI datasets.
Faster development and validation of new machine learning models and algorithms.
Potentially enables new applications of kernel methods that were previously computationally infeasible due to data size.
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Read at arXiv cs.LG