Fabien Mathieu

Dohy Hong, Fabien Mathieu, Gérard Burnside

In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We show how this can be applied to prove and improve the convergence of a fixed point problem associated to the matrix iteration scheme, including for distributed computation framework. The approach can be understood as a decomposition of the matrix-vector product operation in elementary operations at the vector entry level.

Theo Delemazure, François Durand, Fabien Mathieu

Many decision problems cannot be solved exactly and use several estimation algorithms that assign scores to the different available options. The estimation errors can have various correlations, from low (e.g. between two very different approaches) to high (e.g. when using a given algorithm with different hyperparameters). Most aggregation rules would suffer from this diversity of correlations. In this article, we propose different aggregation rules that take correlations into account, and we compare them to naive rules in various experiments based on synthetic data. Our results show that when sufficient information is known about the correlations between errors, a maximum likelihood aggregation should be preferred. Otherwise, typically with limited training data, we recommend a method that we call Embedded Voting (EV).