Metrics for Deep Generative Models

Nutan Chen, Alexej Klushyn, Richard Kurle, Xueyan Jiang, Justin Bayer, Patrick Smagt
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1540-1550, 2018.

Abstract

Neural samplers such as variational autoencoders (VAEs) or generative adversarial networks (GANs) approximate distributions by transforming samples from a simple random source—the latent space—to samples from a more complex distribution represented by a dataset. While the manifold hypothesis implies that a dataset contains large regions of low density, the training criterions of VAEs and GANs will make the latent space densely covered. Consequently points that are separated by low-density regions in observation space will be pushed together in latent space, making stationary distances poor proxies for similarity. We transfer ideas from Riemannian geometry to this setting, letting the distance between two points be the shortest path on a Riemannian manifold induced by the transformation. The method yields a principled distance measure, provides a tool for visual inspection of deep generative models, and an alternative to linear interpolation in latent space. In addition, it can be applied for robot movement generalization using previously learned skills. The method is evaluated on a synthetic dataset with known ground truth; on a simulated robot arm dataset; on human motion capture data; and on a generative model of handwritten digits.

Cite this Paper


BibTeX
@InProceedings{pmlr-v84-chen18e, title = {Metrics for Deep Generative Models}, author = {Nutan Chen and Alexej Klushyn and Richard Kurle and Xueyan Jiang and Justin Bayer and Patrick Smagt}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {1540--1550}, year = {2018}, editor = {Amos Storkey and Fernando Perez-Cruz}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/chen18e/chen18e.pdf}, url = { http://proceedings.mlr.press/v84/chen18e.html }, abstract = {Neural samplers such as variational autoencoders (VAEs) or generative adversarial networks (GANs) approximate distributions by transforming samples from a simple random source—the latent space—to samples from a more complex distribution represented by a dataset. While the manifold hypothesis implies that a dataset contains large regions of low density, the training criterions of VAEs and GANs will make the latent space densely covered. Consequently points that are separated by low-density regions in observation space will be pushed together in latent space, making stationary distances poor proxies for similarity. We transfer ideas from Riemannian geometry to this setting, letting the distance between two points be the shortest path on a Riemannian manifold induced by the transformation. The method yields a principled distance measure, provides a tool for visual inspection of deep generative models, and an alternative to linear interpolation in latent space. In addition, it can be applied for robot movement generalization using previously learned skills. The method is evaluated on a synthetic dataset with known ground truth; on a simulated robot arm dataset; on human motion capture data; and on a generative model of handwritten digits.} }
Endnote
%0 Conference Paper %T Metrics for Deep Generative Models %A Nutan Chen %A Alexej Klushyn %A Richard Kurle %A Xueyan Jiang %A Justin Bayer %A Patrick Smagt %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-chen18e %I PMLR %P 1540--1550 %U http://proceedings.mlr.press/v84/chen18e.html %V 84 %X Neural samplers such as variational autoencoders (VAEs) or generative adversarial networks (GANs) approximate distributions by transforming samples from a simple random source—the latent space—to samples from a more complex distribution represented by a dataset. While the manifold hypothesis implies that a dataset contains large regions of low density, the training criterions of VAEs and GANs will make the latent space densely covered. Consequently points that are separated by low-density regions in observation space will be pushed together in latent space, making stationary distances poor proxies for similarity. We transfer ideas from Riemannian geometry to this setting, letting the distance between two points be the shortest path on a Riemannian manifold induced by the transformation. The method yields a principled distance measure, provides a tool for visual inspection of deep generative models, and an alternative to linear interpolation in latent space. In addition, it can be applied for robot movement generalization using previously learned skills. The method is evaluated on a synthetic dataset with known ground truth; on a simulated robot arm dataset; on human motion capture data; and on a generative model of handwritten digits.
APA
Chen, N., Klushyn, A., Kurle, R., Jiang, X., Bayer, J. & Smagt, P.. (2018). Metrics for Deep Generative Models. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:1540-1550 Available from http://proceedings.mlr.press/v84/chen18e.html .

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