Review for NeurIPS paper: Improving Local Identifiability in Probabilistic Box Embeddings

Summary and Contributions: This paper is concerned with the mitigating local identifiability issues in probabilistic box embeddings. Probabilistic box embedding model is used to represent the probabilities of binary variables in terms of volumes of axis-aligned hyperrectangles. These probability distributions can be used to express specific relations between entities such as hierarchies, partial orders, and lattice structures. Learning box embeddings using gradient-based methods are not straightforward due to unidentifiability of such models. Non-identifiability means that the likelihood is not affected for whatever infinitesimal change in parameter space is made, hence relaxation of the boxes is required.