Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flows
| Autor: | Brendan Leigh Ross, Jesse Cresswell |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Jesse Cresswell |
| DOI: | 10.48550/arxiv.2106.05275 |
| Popis: | 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 estimation. 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. Comment: NeurIPS 2021 Camera-Ready. Code: https://github.com/layer6ai-labs/CEF |
| Databáze: | OpenAIRE |
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