Francois Caron

Francois Caron, Fadhel Ayed, Paul Jung et al.

We consider gradient-based optimisation of wide, shallow neural networks, where the output of each hidden node is scaled by a positive parameter. The scaling parameters are non-identical, differing from the classical Neural Tangent Kernel (NTK) parameterisation. We prove that for large such neural networks, with high probability, gradient flow and gradient descent converge to a global minimum and can learn features in some sense, unlike in the NTK parameterisation. We perform experiments illustrating our theoretical results and discuss the benefits of such scaling in terms of prunability and transfer learning.

Cian Naik, Francois Caron, Judith Rousseau et al.

In this paper we propose a Bayesian nonparametric approach to modelling sparse time-varying networks. A positive parameter is associated to each node of a network, which models the sociability of that node. Sociabilities are assumed to evolve over time, and are modelled via a dynamic point process model. The model is able to capture long term evolution of the sociabilities. Moreover, it yields sparse graphs, where the number of edges grows subquadratically with the number of nodes. The evolution of the sociabilities is described by a tractable time-varying generalised gamma process. We provide some theoretical insights into the model and apply it to three datasets: a simulated network, a network of hyperlinks between communities on Reddit, and a network of co-occurences of words in Reuters news articles after the September 11th attacks.

Richard Yi Da Xu, Francois Caron, Arnaud Doucet

Unsupervised image segmentation aims at clustering the set of pixels of an image into spatially homogeneous regions. We introduce here a class of Bayesian nonparametric models to address this problem. These models are based on a combination of a Potts-like spatial smoothness component and a prior on partitions which is used to control both the number and size of clusters. This class of models is flexible enough to include the standard Potts model and the more recent Potts-Dirichlet Process model \cite{Orbanz2008}. More importantly, any prior on partitions can be introduced to control the global clustering structure so that it is possible to penalize small or large clusters if necessary. Bayesian computation is carried out using an original generalized Swendsen-Wang algorithm. Experiments demonstrate that our method is competitive in terms of RAND\ index compared to popular image segmentation methods, such as mean-shift, and recent alternative Bayesian nonparametric models.