Emile Mathieu
now a Research Scientist at Xaira
Publications
Sampling and inference for discrete random probability measures in probabilistic programs
Ben Bloem-Reddy, Emile Mathieu, Adam Foster, Tom Rainforth, Hong Ge, Maria Lomeli, Zoubin Ghahramani, December 2017. (In NIPS workshop on Advances in Approximate Inference). California, United States.
Abstract▼ URL
We consider the problem of sampling a sequence from a discrete random prob- ability measure (RPM) with countable support, under (probabilistic) constraints of finite memory and computation. A canonical example is sampling from the Dirichlet Process, which can be accomplished using its well-known stick-breaking representation and lazy initialization of its atoms. We show that efficiently lazy initialization is possible if and only if a size-biased representation of the discrete RPM is known. For models constructed from such discrete RPMs, we consider the implications for generic particle-based inference methods in probabilistic program- ming systems. To demonstrate, we implement posterior inference for Normalized Inverse Gaussian Process mixture models in Turing.
Spectral Diffusion Processes
Angus Phillips, Thomas Seror, Michael Hutchinson, Valentin De Bortoli, Arnaud Doucet, Emile Mathieu, 2022. (In NeurIPS workshop on Score-Based Methods).
Abstract▼ URL
Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. In this work we propose to extend this methodology to learn generative models over functional spaces. To do so, we represent functional data in spectral space to dissociate the stochastic part of the processes from their space-time part. Using dimensionality reduction techniques we then sample from their stochastic component using finite dimensional SGM. We demonstrate our method’s effectiveness for modelling various multimodal datasets.