This paper reports the results of a Blinder-Oaxaca style decomposition analysis on Hungarian matched employer-employee data to study the gender pay-gap. We carry out the decomposition by Random Forest regressions. The raw gap in our horizon (2008-2016) is increasing, but we find that the wage structure effects are rather stable, thus the rise in the gap is due to the disappearance of the formerly negative composition effects. Graphical analysis sheds light on interesting non-linear relationships; some of them can be readily interpreted by the previous literature. A Classification and Regression Tree analysis suggests that complicated interaction patterns exist in the data. We identify segments of the Hungarian labour market that are most and least exposed to gender-dependent wage determination. Our findings lend support to the idea that an important part of the gender wage gap is attributable to monopsonistic competition with gender-dependent supply elasticities.