Probabilistic machine learning is still machine learning. If you're referring to one of the popular tensor frameworks, pretty much all of them have probabilistic features or add-ons [1][2][3]. There are also frameworks developed specifically for this kind of work [4][5].

This [6] is a more in depth look at hierarchical / multi-level modeling. The prediction section [7] specifically goes over cross validation and inference.

[1] https://www.tensorflow.org/probability/examples/Multilevel_M... [2] https://pyro.ai/examples/forecasting_iii.html [3] http://edwardlib.org/ [4] https://mc-stan.org/ [5] https://docs.pymc.io/ [6] https://docs.pymc.io/notebooks/multilevel_modeling.html [7] https://docs.pymc.io/notebooks/multilevel_modeling.html#Pred...