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...

ML are algos not models (estimators to be precise). This model could be fit by many of them. However, fitting the model directly with the linear model will be advantageous for computational reasons.