%0 Journal Article %1 brehmer2020flows %A Brehmer, Johann %A Cranmer, Kyle %D 2020 %K flows generative-models %T Flows for simultaneous manifold learning and density estimation %U http://arxiv.org/abs/2003.13913 %X We introduce manifold-modeling flows (MFMFs), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs, autoencoders, and energy-based models, they have the potential to represent data sets with a manifold structure more faithfully and provide handles on dimensionality reduction, denoising, and out-of-distribution detection. We argue why such models should not be trained by maximum likelihood alone and present a new training algorithm that separates manifold and density updates. With two pedagogical examples we demonstrate how manifold-modeling flows let us learn the data manifold and allow for better inference than standard flows in the ambient data space.

@article{brehmer2020flows, abstract = {We introduce manifold-modeling flows (MFMFs), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs, autoencoders, and energy-based models, they have the potential to represent data sets with a manifold structure more faithfully and provide handles on dimensionality reduction, denoising, and out-of-distribution detection. We argue why such models should not be trained by maximum likelihood alone and present a new training algorithm that separates manifold and density updates. With two pedagogical examples we demonstrate how manifold-modeling flows let us learn the data manifold and allow for better inference than standard flows in the ambient data space.}, added-at = {2020-04-01T18:53:10.000+0200}, author = {Brehmer, Johann and Cranmer, Kyle}, biburl = {https://www.bibsonomy.org/bibtex/268902625444f7a769261b02975fc980a/kirk86}, description = {[2003.13913] Flows for simultaneous manifold learning and density estimation}, interhash = {e90c140579995af1b76c083315f1a83e}, intrahash = {68902625444f7a769261b02975fc980a}, keywords = {flows generative-models}, note = {cite arxiv:2003.13913Comment: Code at https://github.com/johannbrehmer/manifold-flow}, timestamp = {2020-04-01T18:53:10.000+0200}, title = {Flows for simultaneous manifold learning and density estimation}, url = {http://arxiv.org/abs/2003.13913}, year = 2020 }