We are interested in building collaborative filtering models for recommendation systems where users interact with slates instead of individual items. These slates can be hierarchical in nature. The central idea of our approach is to learn low dimensional embeddings of these slates. We present a novel way to learn these embeddings by making use of the (unknown) statistics of the underlying distribution generating the hierarchical data. Our representation learning algorithm can be viewed as a simple composition rule that can be applied recursively in a bottom-up fashion to represent arbitrarily complex hierarchical structures in terms of the representations of its constituent components. We demonstrate our ideas on two real world recommendation systems datasets including the one used for the RecSys 2019 challenge. For that dataset, we improve upon the performance achieved by the winning team's model by incorporating embeddings as features generated by our approach in their solution.