Summary of Computational-statistical Trade-off in Kernel Two-sample Testing with Random Fourier Features, by Ikjun Choi and Ilmun Kim
Computational-Statistical Trade-off in Kernel Two-Sample Testing with Random Fourier Features
by Ikjun Choi, Ilmun Kim
First submitted to arxiv on: 12 Jul 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper proposes an approach to improve the computational efficiency of the Maximum Mean Discrepancy (MMD) test, a popular method for two-sample testing in high-dimensional data. The MMD test has quadratic-time complexity, which can be challenging for large-scale analysis. To address this limitation, the authors revisit the approximated MMD test using random Fourier features and investigate its computational-statistical trade-off. They show that by carefully choosing the number of random features, it is possible to attain the same minimax separation rates as the MMD test within sub-quadratic time, while maintaining pointwise consistency in power. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper helps make a popular testing method faster and more efficient for big data. The Maximum Mean Discrepancy (MMD) test is used to compare two groups of data points. While it’s been very effective, it has one major problem: it takes a long time to do many calculations. To fix this, the authors look at a simpler version of the MMD test that uses random numbers and mathematical techniques called Fourier features. They find that by using the right number of these features, they can make the test faster without losing its power. |
