What about the middle ground of structured probabilistic/statistical models? By introducing strong assumptions and prior information you create models that still have great flexibility, but have meaningful parameters which can be interpreted theoretically. These appear to me to solve both Chomsky's apparent non-interpretive model complaint and the technical problem of training a model with a large number of parameters.
On one end of the continuum, n-gram models for large n with infinite training data estimate the empirical distribution of language and thus are the best you can possibly do. On the other end, rule based grammars directly transcribe intelligible "rules" of language generation and comprehension. Both ends are clearly fraught with problems.
In the middle we have topic models, recursive grammars, decision trees, various ad-hoc smoothing methods, each of which both allowing for more tractable training and introducing more meaning to the parameters of the trained model.
I feel like effort here provides (somewhat unsatisfactory) answers to both criticisms. I think it's fair to say that probabilistic/statistical models deserve more attention in a lot of fields in order to overcome a history of neglect, however.
On one end of the continuum, n-gram models for large n with infinite training data estimate the empirical distribution of language and thus are the best you can possibly do. On the other end, rule based grammars directly transcribe intelligible "rules" of language generation and comprehension. Both ends are clearly fraught with problems.
In the middle we have topic models, recursive grammars, decision trees, various ad-hoc smoothing methods, each of which both allowing for more tractable training and introducing more meaning to the parameters of the trained model.
I feel like effort here provides (somewhat unsatisfactory) answers to both criticisms. I think it's fair to say that probabilistic/statistical models deserve more attention in a lot of fields in order to overcome a history of neglect, however.