Isometric Gaussian Process Latent Variable Model for Dissimilarity Data

Abstract

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 generated manifold to endow the latent space with a well-defined stochastic distance measure, which is modeled locally as Nakagami distributions. These stochastic distances are sought to be as similar as possible to observed distances along a neighborhood graph through a censoring process. The model is inferred by variational inference based on observations of pairwise distances. We demonstrate how the new model can encode invariances in the learned manifolds.

ICML 2021

References in corpus (10)

• UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction
• Semi-supervised Learning with GANs: Manifold Invariance with Improved Inference
• Metrics for Probabilistic Geometries
• Matérn Gaussian processes on Riemannian manifolds
• Only Bayes should learn a manifold (on the estimation of differential geometric structure from data)
• Invariant Gaussian Process Latent Variable Models and Application in Causal Discovery
• A more globally accurate dimensionality reduction method using triplets
• Probabilistic Riemannian submanifold learning with wrapped Gaussian process latent variable models
• Lexicographic metric spaces: basic properties and the metric dimension
• Distribution of Gaussian Process Arc Lengths