Fig. 2From: Measuring Edge Importance: A Quantitative Analysis of the Stochastic Shielding Approximation for Random Processes on GraphsDeficiency between the full and approximate processes for the 3-state chain. Comparison of the deficiency U ( i , j ) (t)= X ( i , j ) (t)−X(t) projected onto each component of the system of trajectories of an OU process on R 3 . Top panel: U ( 3 , 4 ) is essentially zero which shows that reduced process X ( 3 , 4 ) is optimal for preserving the accuracy of the first component. Second panel: no reduced process is optimal for preserving the accuracy of the second component. Third panel: U ( 1 , 2 ) is essentially zero which shows that X ( 1 , 2 ) is optimal for preserving the accuracy of the third component (the conducting state in our 3-state example). Bottom panel: squared norm of the deficiency ∥ U ( i , j ) ∥ 2 = ∥ X ( i , j ) − X ∥ 2 Back to article page