188 citations · 367 across the 31 of their papers we have counts for
15 papers · 1 filter
Identifying latent distances with Finslerian geometry
Alison Pouplin, David Eklund, Carl Henrik Ek +1
Riemannian geometry provides us with powerful tools to explore the latent space of generative models while preserving the underlying structure of the data. The latent space can be…
Is an encoder within reach?
Helene Hauschultz, Rasmus Berg Palm. Pablo Moreno-Muños, Nicki Skafte Detlefsen +2
The encoder network of an autoencoder is an approximation of the nearest point projection onto the manifold spanned by the decoder. A concern with this approximation is that, while…
Mario Plays on a Manifold: Generating Functional Content in Latent Space through Differential Geometry
Miguel González-Duque, Rasmus Berg Palm, Søren Hauberg +1
Deep generative models can automatically create content of diverse types. However, there are no guarantees that such content will satisfy the criteria necessary to present it to en…
Visualizing Riemannian data with Rie-SNE
Andri Bergsson, Søren Hauberg
Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the cla…
Adaptive Cholesky Gaussian Processes
Simon Bartels, Kristoffer Stensbo-Smidt, Pablo Moreno-Muñoz +3
We present a method to approximate Gaussian process regression models for large datasets by considering only a subset of the data. Our approach is novel in that the size of the sub…
Robust uncertainty estimates with out-of-distribution pseudo-inputs training
Pierre Segonne, Yevgen Zainchkovskyy, Søren Hauberg
Probabilistic models often use neural networks to control their predictive uncertainty. However, when making out-of-distribution (OOD)} predictions, the often-uncontrollable extrap…
Bounds all around: training energy-based models with bidirectional bounds
Cong Geng, Jia Wang, Zhiyong Gao +2
Energy-based models (EBMs) provide an elegant framework for density estimation, but they are notoriously difficult to train. Recent work has established links to generative adversa…
Pulling back information geometry
Georgios Arvanitidis, Miguel González-Duque, Alison Pouplin +2
Latent space geometry has shown itself to provide a rich and rigorous framework for interacting with the latent variables of deep generative models. The existing theory, however, r…
Density estimation on smooth manifolds with normalizing flows
Dimitris Kalatzis, Johan Ziruo Ye, Alison Pouplin +2
We present a framework for learning probability distributions on topologically non-trivial manifolds, utilizing normalizing flows. Current methods focus on manifolds that are homeo…
Hierarchical VAEs Know What They Don't Know
Jakob D. Havtorn, Jes Frellsen, Søren Hauberg +1
Deep generative models have been demonstrated as state-of-the-art density estimators. Yet, recent work has found that they often assign a higher likelihood to data from outside the…
Variational Autoencoders with Riemannian Brownian Motion Priors
Dimitris Kalatzis, David Eklund, Georgios Arvanitidis +1
Variational Autoencoders (VAEs) represent the given data in a low-dimensional latent space, which is generally assumed to be Euclidean. This assumption naturally leads to the commo…
Expected path length on random manifolds
David Eklund, Søren Hauberg
Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provi…
Geodesic Clustering in Deep Generative Models
Tao Yang, Georgios Arvanitidis, Dongmei Fu +2
Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much dist…
Intrinsic Grassmann Averages for Online Linear, Robust and Nonlinear Subspace Learning
Rudrasis Chakraborty, Søren Hauberg, Baba C. Vemuri
Principal Component Analysis (PCA) and Kernel Principal Component Analysis (KPCA) are fundamental methods in machine learning for dimensionality reduction. The former is a techniqu…
Geodesic Exponential Kernels: When Curvature and Linearity Conflict
Aasa Feragen, Francois Lauze, Søren Hauberg
We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized t…