mlsanityData to 14 Oct 2026

Metrics for Probabilistic Geometries

arXiv 1411.7432 ↗First posted 27 Nov 2014stat.ML cs.LGcited by 28

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Abstract (arXiv)

We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where the distribution over mappings is given by a Gaussian process. We treat the corresponding latent variable model as a Riemannian manifold and we use the expectation of the metric under the Gaussian process prior to define interpolating paths and measure distance between latent points. We show how distances that respect the expected metric lead to more appropriate generation of new data.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). First posted on arXiv 27 Nov 2014.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 6; 2022: 4; 2023: 5; 2024: 3; 2025: 6; 2026: 4.

28 papers.

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  1. 2021Fast Adaptation with Linearized Neural Networkscited by 32
  2. 2021Pulling back information geometrycited by 23
  3. 2023Riemannian Laplace approximations for Bayesian neural networkscited by 15
  4. 2021A prior-based approximate latent Riemannian metriccited by 11
  5. 2023Data Representations' Study of Latent Image Manifoldscited by 11
  6. 2021Exploring the Latent Space of Autoencoders with Interventional Assayscited by 10
  7. 2022Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifoldscited by 10
  8. 2024Pulling back symmetric Riemannian geometry for data analysiscited by 8
  9. 2023Intrinsic Gaussian Process on Unknown Manifolds with Probabilistic Metricscited by 6
  10. 2024Decoder ensembling for learned latent geometriescited by 6
  11. 2025Riemann2: Learning Riemannian Submanifolds from Riemannian Datacited by 6
  12. 2021Bayesian Quadrature on Riemannian Data Manifoldscited by 5
16 more
  1. 2022Mario Plays on a Manifold: Generating Functional Content in Latent Space through Differential Geometrycited by 5
  2. 2025Connecting Neural Models Latent Geometries with Relative Geodesic Representationscited by 4
  3. 2022Identifying latent distances with Finslerian geometrycited by 3
  4. 2023Warped geometric information on the optimisation of Euclidean functionscited by 3
  5. 2025Identifying Metric Structures of Deep Latent Variable Modelscited by 3
  6. 2021Geometry and Generalization: Eigenvalues as predictors of where a network will fail to generalizecited by 2
  7. 2025Geodesic Calculus on Implicitly Defined Latent Manifoldscited by 2
  8. 2022Geometric instability of out of distribution data across autoencoder architecturecited by 1
  9. 2024On Probabilistic Pullback Metrics for Latent Hyperbolic Manifoldscited by 1
  10. 2023Modeling Barrett's Esophagus Progression using Geometric Variational Autoencoderscited by 0
  11. 2025Taxonomy-aware Dynamic Motion Generation on Hyperbolic Manifoldscited by 0
  12. 2025A Likely Geometry of Generative Modelscited by 0
  13. 2026Aligning the Unseen in Attributed Graphs: Interplay between Graph Geometry and Node Attributes Manifoldcited by 0
  14. 2026Intrinsic-Hybrid Latent Diffusion Models for Generative Modeling on Unknown Manifoldscited by 0
  15. 2026Bayesian Optimization with Fisher Information Geometry: Gradient Bounds and Trust-Region Methodscited by 0
  16. 2026Beyond Local Linearity: Scale-Resolved Geometry of Learned Image Encoderscited by 0