On the High Dimensional Power of a Linear-Time Two Sample Test under Mean-shift Alternatives

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Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “There are some recent studies on high-dimensional analysis of MMD and related tests: see Reddi et al. (2015), Ramdas et al. (2015b;a) for example.”
Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, background): “The most popular choice of bandwidth is the “median heuristic” where it is chosen as the median Euclidean distance between all pairs of points (see Schölkopf and Smola [2002]).”
Wasserstein Auto-Encoders (2017, methodology): “These methods have been criticised to require larger mini-batches during training: estimating MMDk(PX , PG) requires number of samples roughly proportional to the dimensionality of the input space X [23] which is typically larger than 103.”
Revisiting Classifier Two-Sample Tests (2016, background): “The power bound in Theorem 1 has an optimal order of magnitude for multi-dimensional problems (Bai & Saranadasa, 1996; Gretton et al., 2012a; Reddi et al., 2015).”
Deep Transfer Learning with Joint Adaptation Networks (2016, background): “Moreover, it may be possible that some widely-used kernels are unable to capture very complex distances in high dimensional spaces such as natural images (Reddi et al., 2015; Arjovsky et al., 2017).”