We develop in this manuscript a new method for performing dimension reduction when probabilistic graphical models are being used to perform estimation of 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 and (ii) D the number of projection vectors can be larger than H − 1, where H is the number of slices. We develop the methodology for the case of sliced inverse regression model and sliced average variance estimation, but extensions to other dimension reduction techniques are straightforward. Theoretical properties of the methodology are developed for the case without a restriction on the relationship between n and p and computational advantages are demonstrated by simulated and real data experiments.