Phylogenetic networks represent reticulate evolutionary histories. Statistical methods for their inference under the multispecies coalescent have recently been developed. A particularly powerful approach uses data that consist of bi-allelic markers (e.g. single nucleotide polymorphism data) and allows for exact likelihood computations of phylogenetic networks while numerically integrating over all possible gene trees per marker. While the approach has good accuracy in terms of estimating the network and its parameters, likelihood computations remain a major computational bottleneck and limit the methods applicability.