B-test: A Non-parametric, Low Variance Kernel Two-sample Test
We propose a family of maximum mean discrepancy (MMD) kernel two-sample tests that have low sample complexity and are consistent. The test has a hyper-parameter that allows one to control the tradeoff between sample complexity and computational time. Our family of tests, which we denote as B-tests, is both computationally and statistically efficient, combining favorable properties of pre-viously proposed MMD two-sample tests. It does so by better leveraging sam-ples to produce low variance estimates in the finite sample case, while avoiding a quadratic number of kernel evaluations and complex null-hypothesis approxima-tion as would be required by tests relying on one sample U-statistics. The B-test uses a smaller than quadratic number of kernel evaluations and avoids completely the computational burden of complex null-hypothesis approximation, while main-taining consistency and probabilistically conservative thresholds on Type I error. Finally, recent results of combining multiple kernels transfer seamlessly to our hypothesis test, allowing a further increase in discriminative power and decrease in sample complexity. 1
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