Abstract: Domain Adaptation methods can be classified into two basic families of approaches: non-parametric and parametric. Non-parametric approaches depend on statistical indicators such as feature covariances to minimize the domain shift. Non-parametric approaches tend to be fast to compute and require no additional parameters, but they are unable to leverage probability density functions with complex internal structures. Parametric approaches, on the other hand, use models of the probability distributions as surrogates in minimizing the domain shift, but they require additional trainable parameters to model these distributions. In this work, we propose a new statistical approach to minimizing the domain shift based on stochastically projecting and evaluating the cumulative density function in both domains. As with non-parametric approaches, there are no additional trainable parameters. As with parametric approaches, the internal structure of both domains’ probability distributions is considered, thus leveraging a higher amount of information when reducing the domain shift. Evaluation on standard datasets used for Domain Adaptation shows better performance of the proposed model compared to non-parametric approaches while being competitive with parametric ones. (Code available at: https://github.com/moliusimon/mca).