Latent Space Non-Linear Statistics

By Line Kühnel, Tom Fletcher, Sarang C. Joshi, S. Sommer. 2018

35 citations recorded by the source corpus.

Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back to a nonlinear Riemannian geometry on the latent space. The latent space thus provides a low-dimensional nonlinear representation of data and classical linear statistical techniques are no longer applicable. In this paper we show how statistics of data in their latent space representation can be performed using techniques from the field of nonlinear manifold statistics. Nonlinear manifold statistics provide generalizations of Euclidean statistical notions including means, principal component analysis, and maximum likelihood fits of parametric probability distributions. We develop new techniques for maximum likelihood inference in latent space, and adress the computational complexity of using geometric algorithms with high-dimensional data by training a separate neural network to approximate the Riemannian metric and cometric tensor capturing the shape of the learned data manifold.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Geometry and Topology, Statistics and Probability, Representation & Self-Supervised Learning

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Yujun Shen
2. Ceyuan Yang
3. Jinjin Gu
4. Bolei Zhou
5. Xiaoou Tang
6. Ling Xie
7. Ruiyang Liu
8. Jingyi Yu

In Computer Vision and Pattern Recognition

1. Bolei Zhou
2. Yujun Shen
3. Luc Van Gool
4. Chen Change Loy
5. Ming-Hsuan Yang
6. Eli Shechtman
7. Daniel Cohen-Or
8. Xiaoou Tang

In Geometry and Topology

1. Xiaoou Tang

In Statistics and Probability

1. Bolei Zhou
2. Jingyi Yu
3. Jinjin Gu
4. Xiaoou Tang

In Representation & Self-Supervised Learning

1. Bolei Zhou
2. Yujun Shen
3. Ceyuan Yang
4. Xiaoou Tang
5. Antonio Torralba
6. Andrea Vedaldi
7. James R. Glass
8. Bernt Schiele

Citations in the corpus

• Interpreting the Latent Space of GANs for Semantic Face Editing (2019, background): “Latent space of GANs is generally treated as Riemannian manifold [9, 2, 21].”
• InterFaceGAN: Interpreting the Disentangled Face Representation Learned by GANs (2020, background): “Latent space of GANs is generally treated as Riemannian manifold [20], [21], [22].”
• A Free Viewpoint Portrait Generator with Dynamic Styling (2020, background): “Since the disentangled representation is discovered[34, 27, 15] in common VAE, GANs[11, 12] architecture, many studies on latent space[33, 28, 24] that observes the vector arithmetic phenomenon have been engaged in changing the attributes of output images.”