In training, We expect this is possible when we have prior knowledge that Y 1 depends only on X 1 and Y 2 depends only on X 2 .
with chain rule, Since P (Y 1 |X 1 ) and P (Y 2 |X 2 ) are both high in training, if they generalize well, they should also be high in test, so that their product should be high in test.