188 citations · 367 across the 31 of their papers we have counts for
35 papers
Beyond Laplace: Closed-form wrapped Gaussian posterior approximations on statistical manifolds
Marcelo Hartmann, Luu Hoang Phuc Hau, Anton Mallasto +5
In Bayesian statistics, the Laplace approximation provides a computationally efficient approximation to posterior distributions. However, its Gaussian form restricts it to elliptic…
Variational Autoencoding of Dental Point Clouds
Johan Ziruo Ye, Thomas Ørkild, Peter Lempel Søndergaard +1
Digital dentistry has made significant advancements, yet numerous challenges remain. This paper introduces the FDI 16 dataset, an extensive collection of tooth meshes and point clo…
Riemannian Laplace approximations for Bayesian neural networks
Federico Bergamin, Pablo Moreno-Muñoz, Søren Hauberg +1
Bayesian neural networks often approximate the weight-posterior with a Gaussian distribution. However, practical posteriors are often, even locally, highly non-Gaussian, and empiri…
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…
ICLR 2022 Challenge for Computational Geometry and Topology: Design and Results
Adele Myers, Saiteja Utpala, Shubham Talbar +25
This paper presents the computational challenge on differential geometry and topology that was hosted within the ICLR 2022 workshop ``Geometric and Topological Representation Learn…
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…
Model-agnostic out-of-distribution detection using combined statistical tests
Federico Bergamin, Pierre-Alexandre Mattei, Jakob D. Havtorn +5
We present simple methods for out-of-distribution detection using a trained generative model. These techniques, based on classical statistical tests, are model-agnostic in the sens…
Reactive Motion Generation on Learned Riemannian Manifolds
Hadi Beik-Mohammadi, Søren Hauberg, Georgios Arvanitidis +2
In recent decades, advancements in motion learning have enabled robots to acquire new skills and adapt to unseen conditions in both structured and unstructured environments. In pra…
Benchmarking Generative Latent Variable Models for Speech
Jakob D. Havtorn, Lasse Borgholt, Søren Hauberg +2
Stochastic latent variable models (LVMs) achieve state-of-the-art performance on natural image generation but are still inferior to deterministic models on speech. In this paper, w…
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…
Learning Riemannian Manifolds for Geodesic Motion Skills
Hadi Beik-Mohammadi, Søren Hauberg, Georgios Arvanitidis +2
For robots to work alongside humans and perform in unstructured environments, they must learn new motion skills and adapt them to unseen situations on the fly. This demands learnin…
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…
What is a meaningful representation of protein sequences?
Nicki Skafte Detlefsen, Søren Hauberg, Wouter Boomsma
How we choose to represent our data has a fundamental impact on our ability to subsequently extract information from them. Machine learning promises to automatically determine effi…
Reparametrization Invariance in non-parametric Causal Discovery
Martin Jørgensen, Søren Hauberg
Causal discovery estimates the underlying physical process that generates the observed data: does X cause Y or does Y cause X? Current methodologies use structural conditions to tu…
Geometrically Enriched Latent Spaces
Georgios Arvanitidis, Søren Hauberg, Bernhard Schölkopf
A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space. Instead, we consider the ambient space to be a Riemannian m…
Isometric Gaussian Process Latent Variable Model for Dissimilarity Data
Martin Jørgensen, Søren Hauberg
We present a probabilistic model where the latent variable respects both the distances and the topology of the modeled data. The model leverages the Riemannian geometry of the gene…
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…