2023/01/14 by Domingo-Enrich, Carles, Dwivedi, Raaz, Mackey, Lester · 4 citations
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2301.05974
Kernel two-sample testing provides a powerful framework for distinguishing any pair of distributions based on n sample points. However, existing kernel tests either run in n2 time or sacrifice undue power to improve runtime. To address these shortcomings, we introduce Compress Then Test (CTT), a new framework for high-powered kernel testing based on sample compression. CTT cheaply approximates an expensive test by compressing each n point sample into a small but provably high-fidelity coreset. For standard kernels and subexponential distributions, CTT inherits the statistical behavior of a quadratic-time test -- recovering the same optimal detection boundary -- while running in near-linear time. We couple these advances with cheaper permutation testing, justified by new power analyses; improved time-vs.-quality guarantees for low-rank approximation; and a fast aggregation procedure for identifying especially discriminating kernels. In our experiments with real and simulated data, CTT and its extensions provide 20--200x speed-ups over state-of-the-art approximate MMD tests with no loss of power.