At a high level, this is a robust optimization formulation which seeks to minimize worst case cut values, and can be cast as a Mixed Integer Programming (MIP) problem.
for a bipartite graph G = (U, V, E) Algorithm 1 Structured-output causal rationalizer 1: procedure SOCRAT(x, y, F ) 2: (µ, σ) ← ENCODE(x) 3: end for 8: Ex →y ← BIPARTITION(G) 10: Ex →y ← SORT(Ex →y ) By cut capacity 11: return Ex →y 12: end procedure with edge weights given as uncertainty intervals θ ij ±θ ij , the partitioning problem is given by where x u ik , x v jk are binary variables indicating subset belonging for elements of U and V respectively, y ij are binary auxiliary variables indicating whether i and j are in different partitions, and Y is a set of constraints that ensure the K-partition is valid.