Parent annotation is a node-splitting technique for improving Probabilistic Context-Free Grammars (PCFGs) by annotating each node in a parse tree with the label of its parent node. This incorporates local context into the treebank grammar, relaxing independence assumptions and allowing the model to capture vertical structural dependencies.

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We can split NP non-terminals into two versions: one for subjects, and one for objects. Having two nodes ($$NP_{subject}$$ and $$NP_{object}$$) allows us to correctly model their different distributional properties since we can have different probabilities for the rules $$NP_{subject} \to PRP$$ and $$NP_{object} \to PRP$$. The intuition of splits can be implemented by doing parent annotation, in which we annotate each node with its parent in the parse tree. A PCFG can also be improved by splitting pre-terminal POS nodes, as adding specific tags for parts of speech improves PCFG modeling.

Improving PCFGs by splitting NP non-terminals

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

Node-splitting increases the size of the grammar and reduces the amount of training data available for each grammar rule. This leads to overfitting, so it is important to arrive at a correct level of granularity for a particular training set. The split and merge algorithm starts with a simple X-bar grammar and alternately splits and merges non-terminals to find the set of annotates nodes that maximizes the likelihood of training set treebank. 

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