The majority of all commonly used machine learning methods can not be applied directly to data sets with missing values. However, most such meth- ods only depend on the relative di erences between samples instead of their particular values, and thus one useful approach is to directly estimate the pairwise distances between all samples in the data set. This is accomplished by tting a Gaussian mixture model to the data, and using it to derive estimates for the distances. Experimental simulations con rm that the pro- posed method provides accurate estimates compared to alternative methods for estimating distances.