Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flows [article]

Brendan Leigh Ross, Jesse C. Cresswell
2021 arXiv   pre-print
Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data supported on an unknown low-dimensional manifold, a common occurrence in real-world domains such as image data. Recent attempts to remedy this limitation have introduced geometric complications that defeat a central benefit of normalizing flows: exact density
more » ... on. We recover this benefit with Conformal Embedding Flows, a framework for designing flows that learn manifolds with tractable densities. We argue that composing a standard flow with a trainable conformal embedding is the most natural way to model manifold-supported data. To this end, we present a series of conformal building blocks and apply them in experiments with synthetic and real-world data to demonstrate that flows can model manifold-supported distributions without sacrificing tractable likelihoods.
arXiv:2106.05275v2 fatcat:j4lrysqoobbetbwkd5pa4dxssu