9 papers
A Generalized Parallelogram Rule for Proportional Analogies on Riemannian Manifolds
Pierre-Alexandre Murena, Marcelo Hartmann
Analogies are quaternary relations of the form "a is to b as c is to d", usually denoted a : b :: c : d. This notion is formalized in particular with the notion of proportional ana…
Beyond Laplace: Closed-form wrapped Gaussian posterior approximations on statistical manifolds
Marcelo Hartmann, Luu Hoang Phuc Hau, Anton Mallasto +8
In Bayesian statistics, the Laplace approximation provides a computationally efficient approximation to posterior distributions. However, its Gaussian form restricts it to elliptic…
Learning Geometry and Topology via Multi-Chart Flows
Hanlin Yu, Søren Hauberg, Marcelo Hartmann +2
Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the amb…
Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process
Bernardo Williams, Harsha Vardhan Tetali, Arto Klami +1
We propose a conjugate and calibrated Gaussian process (GP) model for multi-class classification by exploiting the geometry of the probability simplex. Our approach uses Aitchison…
Riemannian Laplace Approximation with the Fisher Metric
Hanlin Yu, Marcelo Hartmann, Bernardo Williams +2
Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the…
Simplex-to-Euclidean Bijections for Categorical Flow Matching
Bernardo Williams, Victor M. Yeom-Song, Marcelo Hartmann +1
We propose a method for learning and sampling from probability distributions supported on the simplex. Our approach maps the open simplex to Euclidean space via smooth bijections,…