Schema matching using Gaussian mixture models with Wasserstein distance

Mixture model is a probabilistic model that is able to infer subpopulations from total population without additional information (within the paradigm of unsupervised learning). Mixture models closely correspond to the mixture distributions of the probabilistic distributions of observations. In general, in the structure of mixture model, we make assumptions over latent variables that evaluate membership of each observation. Given the dataset, we can assume that it is a sample and then mixture model can estimate the parameters of the probability distributions that created points of this dataset, as well as assign each observation vector of probabilities indicating the original distribution. Comparing different mixture models can be considered a generalization of the problem of comparing different distributions. From the viewpoint of optimal transport theory, the Wasserstein distance is an important method for measuring similarities and the maintenance of the explainable nature of mixture models.