Bernardo WilliaMS

Helsinki, Finland

I am a PhD student in Computer Science at the University of Helsinki, working in the Probabilistic Machine Learning Lab. My supervisors are Arto Klami and Marcelo Hartmann.

My research focuses on developing statistical methods inspired by Riemannian geometry. My main interests include Bayesian inference and discrete generative models, see some selected publications below!

news

Jun 08, 2026	💬 We were invited to MCQMC 2026 in Edinburgh, where I will give a talk in the session Advances in Slice Sampling.
Jun 01, 2026	🎉 Our paper Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process was accepted at UAI 2026.
Jan 22, 2026	🎉 Spotlight acceptance at AISTATS 2026! Our paper Simplex-to-Euclidean Bijections for Categorical Flow Matching was accepted as a spotlight paper (top 3%).
Dec 02, 2025	💬 Presenting Categorical Flow Matching via Simplex-to-Euclidean Bijections at the NeurIPS 2025 FPI workshop!
Sep 07, 2025	💬 I will attend GenU workshop in Copenhagen, see you there!

selected publications

UAI

Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process

Bernardo Williams, Harsha Vardhan Tetali, Arto Klami, and 1 more author

In The 42nd Conference on Uncertainty in Artificial Intelligence, 2026

arXiv Bib

@inproceedings{williams2026simplexgp,
  title = {Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process},
  author = {Williams, Bernardo and Tetali, Harsha Vardhan and Klami, Arto and Hartmann, Marcelo},
  booktitle = {The 42nd Conference on Uncertainty in Artificial Intelligence},
  year = {2026},
}

AISTATS

Simplex-to-Euclidean Bijections for Categorical Flow Matching

Bernardo Williams, Victor M Yeom-Song, Marcelo Hartmann, and 1 more author

2026

arXiv Bib

@article{williams2025simplex,
  title = {Simplex-to-Euclidean Bijections for Categorical Flow Matching},
  author = {Williams, Bernardo and Yeom-Song, Victor M and Hartmann, Marcelo and Klami, Arto},
  booktitle = {International Conference on Artificial Intelligence and Statistics},
  year = {2026},
}

UAI

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

arXiv Bib

@inproceedings{williamsgeodesic,
  title = {Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature},
  author = {Williams, Bernardo and Yu, Hanlin and Luu, Hoang Phuc Hau and Arvanitidis, Georgios and Klami, Arto},
  booktitle = {The 41st Conference on Uncertainty in Artificial Intelligence},
  year = {2025},
}

AISTATS

Riemannian Laplace Approximation with the Fisher Metric

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

In International Conference on Artificial Intelligence and Statistics, 2024

arXiv Bib

@inproceedings{yu2024riemannian,
  title = {Riemannian Laplace Approximation with the Fisher Metric},
  author = {Yu, Hanlin and Hartmann, Marcelo and Williams, Bernardo and Girolami, Mark and Klami, Arto},
  booktitle = {International Conference on Artificial Intelligence and Statistics},
  year = {2024},
}