A distinctive characteristic of the causal pairwise classification problem compared to the traditional classification problem is the nature of the samples points. In a regular classification problem a sample is a vector representing the position of the example in the feature space $\mathbb{R}^d$, where $d$ represents the number of features. In our pairwise classification problem, a sample is an empirical distribution, a set of points $\{ x_i,y_i \}_{i=1}^{n_j}$. Therefore, a feature construction step is added between the data and the learning algorithm.