1 citations · 1 across the 9 of their papers we have counts for
10 papers
Posterior sampling by source-space MCMC via prior-based few-step transport maps
Hoang Phuc Hau Luu, Marcelo Hartmann, Zhongjian Wang
Bayesian inference increasingly uses informative but implicit priors represented only by samples, such as historical ensembles, simulator outputs, and pretrained generative models.…
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…
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…
Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification
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…
Geometric Moment Alignment for Domain Adaptation via Siegel Embeddings
Shayan Gharib, Marcelo Hartmann, Arto Klami
We address the problem of distribution shift in unsupervised domain adaptation with a moment-matching approach. Existing methods typically align low-order statistical moments of th…
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,…
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…
Stochastic variance-reduced Gaussian variational inference on the Bures-Wasserstein manifold
Hoang Phuc Hau Luu, Hanlin Yu, Bernardo Williams +2
Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein g…
Non-geodesically-convex optimization in the Wasserstein space
Hoang Phuc Hau Luu, Hanlin Yu, Bernardo Williams +4
We study a class of optimization problems in the Wasserstein space (the space of probability measures) where the objective function is nonconvex along generalized geodesics. Specif…
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…