Graph informed sliced inverse regression

A new method is developed for performing sufficient dimension reduction when probabilistic graphical models are being used to estimate parameters. The procedure enriches the domain of application of dimension reduction techniques to settings where (i) p the number of variables 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 and (iii) D the number of projection vectors can be larger than the number of slices H. The methodology is developed for the case of the sliced inverse regression model, but extensions to other dimension reduction techniques such as sliced average variance estimation or other methods are straightforward.