publications

2025

1. Stochastic Variance-Reduced Gaussian Variational Inference on the Bures-Wasserstein Manifold

   Hoang Phuc Hau Luu, Hanlin Yu, Bernardo Williams, and 2 more authors

   In The Thirteenth International Conference on Learning Representations, 2025
2. Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature

   Bernardo Williams, Hanlin Yu, Hoang Phuc Hau Luu, and 2 more authors

   In The 41st Conference on Uncertainty in Artificial Intelligence, 2025
3. Conditional Noise-Contrastive Estimation of Energy-Based Models by Jumping between Modes

   Hanlin Yu, Michael U. Gutmann, Arto Klami, and 1 more author

   In EurIPS 2025 Workshop on Principles of Generative Modeling (PriGM), 2025
4. Connecting Neural Models Latent Geometries with Relative Geodesic Representations

   Hanlin Yu, Berfin Inal, Georgios Arvanitidis, and 3 more authors

   In The Thirty-Ninth Annual Conference on Neural Information Processing Systems, 2025
5. Density Ratio Estimation with Conditional Probability Paths

   Hanlin Yu, Arto Klami, Aapo Hyvarinen, and 2 more authors

   In Forty-Second International Conference on Machine Learning, 2025
6. Learning Geometry and Topology via Multi-Chart Flows

   Hanlin Yu, Søren Hauberg, Marcelo Hartmann, and 2 more authors

   2025

2024

1. Non-Geodesically-Convex Optimization in the Wasserstein Space

   Hoang Phuc Hau Luu, Hanlin Yu, Bernardo Williams, and 4 more authors

   In The Thirty-Eighth Annual Conference on Neural Information Processing Systems, 2024
2. Geometric No-U-Turn Samplers: Concepts and Evaluation

   Bernardo Williams, Hanlin Yu, Marcelo Hartmann, and 1 more author

   In Proceedings of The 12th International Conference on Probabilistic Graphical Models, Sep 2024

   Abs

   We enhance geometric Markov Chain Monte Carlo methods, in particular making them easier to use by providing better tools for choosing the metric and various tuning parameters. We extend the No-U-Turn criterion for automatic choice of integration length for Lagrangian Monte Carlo and propose a modification to the computationally efficient Monge metric, as well as summarizing several previously proposed metric choices. Through extensive experimentation, including synthetic examples and posteriordb benchmarks, we demonstrate that Riemannian metrics can outperform Euclidean counterparts, particularly in scenarios with high curvature, while highlighting how the optimal choice of metric is problem-specific.

3. Riemannian Laplace Approximation with the Fisher Metric

   Hanlin Yu, Marcelo Hartmann, Bernardo Williams Moreno Sanchez, and 2 more authors

   In Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, May 2024

   Abs

   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 Bernstein-von Mises theorem, but for complex targets and finite-data posteriors it is often too crude an approximation. A recent generalization of the Laplace Approximation transforms the Gaussian approximation according to a chosen Riemannian geometry providing a richer approximation family, while still retaining computational efficiency. However, as shown here, its properties depend heavily on the chosen metric, indeed the metric adopted in previous work results in approximations that are overly narrow as well as being biased even at the limit of infinite data. We correct this shortcoming by developing the approximation family further, deriving two alternative variants that are exact at the limit of infinite data, extending the theoretical analysis of the method, and demonstrating practical improvements in a range of experiments.

2023

1. Warped Geometric Information on the Optimisation of Euclidean Functions

   Marcelo Hartmann, Bernardo Williams, Hanlin Yu, and 3 more authors

   May 2023
2. Scalable Stochastic Gradient Riemannian Langevin Dynamics in Non-Diagonal Metrics

   Hanlin Yu, Marcelo Hartmann, Bernardo Williams, and 1 more author

   Transactions on Machine Learning Research, May 2023