  In representation learning, there has been recent interest in developing
algorithms to disentangle the ground-truth generative factors behind data, and
metrics to quantify how fully this occurs. However, these algorithms and
metrics often assume that both representations and ground-truth factors are
flat, continuous, and factorized, whereas many real-world generative processes
involve rich hierarchical structure, mixtures of discrete and continuous
variables with dependence between them, and even varying intrinsic
dimensionality. In this work, we develop benchmarks, algorithms, and metrics
for learning such hierarchical representations.
