Title: Graph informed sliced inverse regression
Authors: Eugen Pircalabelu - Université catholique de Louvain (Belgium) [presenting]
Andreas Artemiou - Cardiff University (United Kingdom)
Abstract: A new method is considered for performing dimension reduction when probabilistic graphical models are being used to perform the estimation of parameters. The procedure enriches the domain of application of dimension reduction techniques to settings where (i) the number of variables $p$ in the model is much larger than the available sample size $n$, (ii) $p$ is much larger than the number of slices $H$ the model uses. The number of projection vectors $D$ can be larger than $n$. The methodology is developed for the case of the sliced inverse regression model. Still, extensions to other dimension reduction techniques such as sliced average variance estimation or other methods are straightforward. The application on simulated data reveals that there is a substantial gain to be made by using the graph informed versions even for low dimensional settings. Theoretical derivations and algorithmic implementations are also illustrated.