Parametrization Cookbook: A set of Bijective Parametrizations for using Machine Learning methods in Statistical Inference

We present in this paper a way to transform a constrained statistical inference problem into an unconstrained one in order to be able to use modern computational methods, such as those based on automatic differentiation, GPU computing, stochastic gradients with mini-batch. Unlike the parametrizations classically used in Machine Learning, the parametrizations introduced here are all bijective and are even diffeomorphisms, thus allowing to keep the important properties from a statistical inference point of view, first of all identifiability. This cookbook presents a set of recipes to use to transform a constrained problem into a unconstrained one. For an easy use of parametrizations, this paper is at the same time a cookbook, and a Python package allowing the use of parametrizations with numpy, but also JAX and PyTorch, as well as a high level and expressive interface allowing to easily describe a parametrization to transform a difficult problem of statistical inference into an easier problem addressable with modern optimization tools

The impact of compaction, moisture content, particle size and type of bulking agent on initial physical properties of sludge-bulking agent mixtures before composting

This study aimed to experimentally acquire evolution profiles between depth, bulk density, Free Air Space (FAS), air permeability and thermal conductivity in initial composting materials. The impact of two different moisture content, two particle size and two types of bulking agent on these four parameters was also evaluated. Bulk density and thermal conductivity both increased with depth while FAS and air permeability both decreased with it. Moreover, depth and moisture content had a significant impact on almost all the four physical parameters contrary to particle size and the type of bulking agent