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The phase segregation behavior of three key refractory high entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr) is studied using first-principles calculations. Several linear and non-linear methods are utilized to generate surrogate models for three key refractory high entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr) via the cluster expansion formalism. The characteristics of each of the generated models is explored and the regression methods are compared. Finally, these surrogate models are utilized to generate Monte Carlo trajectories in order to explore the link between phase segregation and previously documented mechanical degradation in these materials. Phase segregation and intermetallic phases documented in the experimental literature are reproduced in all three high entropy alloys. NbTiVZr forms vanadium and zirconium clusters at lower temperatures (250 K) which disperse into the single-phase matrix by 1000 K. HfNbTaTiZr forms HfZr, NbTa, and possibly TiZr intermetallic phases at lower temperatures (250 K). Unlike the other HEAs studied here, HfNbTaTiZr does not lose short-range ordering in the solid state until around 3500 K, which is above its melting temperature. AlHfNbTaTiZr forms NbTa and AlHfTiZr phases at lower temperatures (250 K), which are not observed at higher temperatures (1000 K).