Earth mover distance12/24/2023 ![]() The EMD highlights the fact that the tail of \(F\) contains a significant amount of data. Contrast this with \(\KS(D, E) = 0.08\) and \(\KS(D, F) = 0.17\), which is only twice as high. Looking at histograms of their values makes it seem like they’re similarly distributed. These are all features of their empirical distributions.įor example, these two data sets seem to have similar spread, and both are centered around 0. Given two different sets of data, a quick visual inspection is often sufficient to compare their minimum and maximum values, their average values, and their spread. Statistical distances, as distances between samples, are an interesting answer to that problem. However, there are cases where, rather than deciding whether to reject a statistical hypothesis, you want to measure how similar or far apart the data sets are without any assumptions. When comparing data sets, statistical tests can tell you whether or not two data samples are likely to be generated by the same process or if they are related in some way. This post explores how to compare distributions using both visual tools and robust statistical distances. Statistical distances are distances between distributions or samples, which are used in a variety of machine learning applications, such as anomaly and outlier detection, ordinal regression, and in generative adversarial networks (GANs). Normal distributions Uniform distributions Beta distributions Gamma distributions Distribution with bump Distribution with farther bump Distributions with long tails Distributions with longer tails Normal(0, 1) vs.
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