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Enhancing Unsupervised Probabilistic Grammar Learning with Unambiguity Regularization

This paper presents a novel framework for unsupervised grammar learning through unambiguity regularization, focusing on the observation that natural languages are remarkably unambiguous despite being commonly ambiguous. By leveraging this unambiguity, we propose new algorithms, including EM, Viterbi-EM, and softmax-EM. The framework is validated through experiments on probabilistic grammar induction, demonstrating improved accuracy using unambiguity bias and variational inference. Our approach aims to mitigate ambiguities in language processing, ultimately enhancing performance in various NLP tasks.

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Enhancing Unsupervised Probabilistic Grammar Learning with Unambiguity Regularization

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  1. Unambiguity Regularization for Unsupervised Learning of Probabilistic Grammars

  2. Overview • Unambiguity Regularization • A novel approach for unsupervised natural language grammar learning • Based on the observation that natural language is remarkably unambiguous • Includes standard EM, Viterbi EM and so-called softmax-EM as special cases

  3. Outline • Background • Motivation • Formulation and algorithms • Experimental results

  4. Background • Unsupervised learning of probabilistic grammars • Learning a probabilistic grammar from unannotated sentences Training Corpus Probabilistic Grammar Induction S ® NP VP NP ®Det N VP ®Vt NP (0.3) | Vi PP (0.2) | rolls (0.2) | bounces(0.1) …… A square is above the triangle. A triangle rolls. The square rolls. A triangle is above the square. A circle touches a square. ……

  5. Background • Unsupervised learning of probabilistic grammars • Typically done by assuming a fixed set of grammar rules and optimizing the rule probabilities • Various prior information can be incorporated into the objective function to improve learning • e.g., rule sparsity, symbol correlation, etc. • Our approach: Unambiguity regularization • Utilizes a novel type of prior information: the unambiguity of natural languages

  6. The Ambiguity of Natural Language • Ambiguities are ubiquitous in natural languages • NL sentences can often be parsed in more than one way • Example [Manning and Schutze (1999)] The post office will hold out discounts and service concessions as incentives. Noun? Verb? Modifies “hold out” or “concessions”? Given a complete CNF grammar of 26 nonterminals, the total number of possible parses is              .

  7. The Unambiguity of Natural Language • Although each NL sentence has a large number of possible parses, the probability mass is concentrated on a very small number of parses

  8. Comparison with non-NL grammars NL Grammar Max-Likelihood Grammar Learned by EM Random Grammar

  9. Incorporate Unambiguity Bias into Learning • How to measure the ambiguity • Entropy of the parse given the sentence and the grammar • How to add it into the objective function • Use a prior distribution that prefers low ambiguity Intractable Learning

  10. Incorporate Unambiguity Bias into Learning • How to measure the ambiguity • Entropy of the parse given the sentence and the grammar • How to add it into the objective function • Use posterior regularization [Ganchev et al. (2010)] Entropy of the parses based on q KL-divergence between q and the posterior distribution of the parses Log posterior of the grammar given the training sentences A constant that controls the strength of regularization An auxiliary distribution

  11. Optimization • Coordinate Ascent • Fix    and optimize    • Exactly the M-step of EM • Fix    and optimize    • Depends on the value of     p q

  12. Optimization • Coordinate Ascent • Fix    and optimize    • Exactly the M-step of EM • Fix    and optimize    • Depends on the value of     p q

  13. Optimization • Coordinate Ascent • Fix    and optimize    • Exactly the M-step of EM • Fix    and optimize    • Depends on the value of     p q Softmax-EM

  14. Softmax-EM • Implementation • Simply exponentiate all the grammar rule probabilities before the E-step of EM • Does not increase the computational complexity of the E-step

  15. The value of     • Choosing a fixed value of     • Too small: not enough to induce unambiguity • Too large: the learned grammar might be excessively unambiguous • Annealing • Start with a large value of     • Strongly push the learner away from the highly ambiguous initial grammar • Gradually reduce the value of     • Avoid inducing excessive unambiguity

  16. Mean-field Variational Inference • So far: maximum a posteriori estimation (MAP) • Variational inference approximates the posterior of the grammar • Leads to more accurate predictions than MAP • Can accommodate prior distributions that MAP cannot • We have also derived a mean-field variational inference version of unambiguity regularization • Very similar to the derivation of the MAP version

  17. Experiments • Unsupervised learning of the dependency model with valence (DMV) [Klein and Manning, 2004] • Data: WSJ (sect 2-21 for training, sect 23 for testing) • Trained on the gold-standard POS tags of the sentences of length ≤ 10 with punctuation stripped off

  18. Experiments with Different Values of     • Viterbi EM leads to high accuracy on short sentences • Softmax-EM (              ) leads to the best accuracy over all sentences

  19. Experiments with Annealing and Prior • Annealing the value of     from 1 to 0 in 100 iterations • Adding Dirichlet priors (              ) over rule probabilities using variational inference • Compared with the best results previously published for learning DMV

  20. Experiments on Extended Models • Applying unambiguity regularization on E-DMV, an extension of DMV [Gillenwater et al., 2010] • Compared with the best results previously published for learning extended dependency models

  21. Experiments on More Languages • Examining the effect of unambiguity regularization with the DMV model on the corpora of eight additional languages. • Unambiguity regularization improves learning on eight out of the nine languages, but with different optimal values of . • Annealing the value of leads to better average performance than using any fixed value of .

  22. Related Work • Some previous work also manipulates the entropy of hidden variables • Deterministic annealing [Rose, 1998; Smith and Eisner, 2004] • Minimum entropy regularization [Grandvalet and Bengio, 2005; Smith and Eisner, 2007] • Unambiguity regularization differs from them in • Motivation: the unambiguity of NL grammars • Algorithm: • a simple extension of EM • exponent >1 in the E-step • decreasing the exponent in annealing

  23. Conclusion • Unambiguity regularization • Motivation • The unambiguity of natural languages • Formulation • Regularize the entropy of the parses of training sentences • Algorithms • Standard EM, Viterbi EM, softmax-EM • Annealing the value of • Experiments • Unambiguity regularization is beneficial to learning • By incorporating annealing, it outperforms the current state-of-the-art

  24. Thank you! Q&A

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