1 citations · 1 across the 8 of their papers we have counts for
8 papers
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…
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,…
Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature
Bernardo Williams, Hanlin Yu, Hoang Phuc Hau Luu +2
Traditional Markov Chain Monte Carlo sampling methods often struggle with sharp curvatures, intricate geometries, and multimodal distributions. Slice sampling can resolve local exp…
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…
Warped geometric information on the optimisation of Euclidean functions
Marcelo Hartmann, Bernardo Williams, Hanlin Yu +3
We consider the fundamental task of optimising a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning…
Scalable Stochastic Gradient Riemannian Langevin Dynamics in Non-Diagonal Metrics
Hanlin Yu, Marcelo Hartmann, Bernardo Williams +1
Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometr…