Why my KLqp cannot infer good parameters on simple iris regression task

Follow by the guide in bayesian_linear_regression_implicitklqp I implete a bayesian linear regression here test_klqp

Yet I found klqp and implicit klqp poorly model the iris data on regression task. (i.e. the MSE is much worse than a sklearn linear regression fit.)

Did I miss or misunderstand something? or is the KLqp does not suit for this kind of tasks (But I have no problem in getting good results in Probabilistic Matrix Factorization)