12.4 Classical Two-Sample Test
The classical and quantum kernels considered above can be used to calculate the closeness of two samples from the given dataset. We can even do it systematically for all pairs of samples in the dataset. However, in many situations, we are interested in comparing the closeness of (or the distance between) whole datasets rather than individual samples.
In other words, given two datasets A and B, with samples drawn from some unknown multivariate probability distributions, the task is to measure the distance between these datasets in order to decide whether the null hypothesis of both sets of samples being drawn from the same probability distribution can be rejected or not. This is a two-sample test problem, which we consider below. We start with describing a popular classical two-sample test before introducing its quantum counterpart.
When it comes to the multivariate distribution classification problem, one of the most widely used measures of similarity is...
