Modeling the Development of Determiner Productivity in Children's Early Speech

Modeling the Development of Determiner Productivity in Children’s Early Speech Stephan Meylan Michael C. Frank Roger Levy smeylan@berkeley.edu Department of Psychology University of California, Berkeley mcfrank@stanford.edu Department of Psychology Stanford University rlevy@ucsd.edu Department of Linguistics University of California, San Diego Noun Phrase Abstract The English definite and indefinite articles (also known as de- terminers) are a useful index of early morphosyntactic pro- ductivity in children’s speech, and give evidence about chil- dren’s representation of syntactic abstractions. Previous work (i.e. Pine & Lieven, 1997) used a measure of productivity that shows a strong sensitivity to sample size and does not account for the relationship between adult input and children’s learn- ing. In this paper, we develop a more robust metric by em- ploying a hierarchical Bayesian model to characterize the de- gree of generalization implicit in observed determiner usage. By inferring parameters for a generative model over longitudi- nal corpora, we measure the trajectory of grammatical category abstraction. Our results are consistent with the hypothesis that child learners exhibit adult-like patterns of generalization quite early in the acquisition of determiners. Keywords: grammatical productivity; development; syntax; morphosyntax; modeling Introduction How do children begin to use the rich combinatorial struc- ture of language to express novel thoughts? Nativist accounts propose an innate specification of syntactic categories that al- low the child learner to exploit regularities in language struc- ture from birth (Valian, 1986). Constructivist theories, on the other hand, contend that abstract categorical knowledge is built up over time as the child learner generalizes from spe- cific usages to form broader combinatorial rules (Tomasello, 2003). The indefinite determiner “a” and the definite deter- miner “the”—the shortest and most frequent words in the En- glish language—are a locus of interest for both theoretical viewpoints. Because they are both frequent and obligatory, determiners are an early index of morphosyntactic 1 produc- tivity that can be observed cross-linguistically. A context-free grammar production rule (Figure 1) cap- tures the intuition that a noun phrase can be created by choos- ing a determiner from the abstract DET category and a noun from the abstract N category. This noun phrase in turn com- bines with other phrase structures, like a verb phrase or prepo- sition, to form higher-order structures. For most singular nouns, a grammatical NP can be formed using either deter- miner. Furthermore, hearing a novel word with one deter- miner suggests that use with the the other is also likely gram- matical. Hearing someone introduce “a blickmoo” for the first time, you would not hesitate to request “the blickmoo” even if you had never heard that sequence of words before. 1 In English, determiners and nouns are separate words by lin- guistic criteria (e.g. an adjective may come between a determiner and a noun). Many other languages use determiners that are mor- phologically integrated with the noun (see Kramsky, 1972 for an overview). Determiner {a, the} Noun {cat, dog, baby, ground, dialectic, tuxedo, [. . .] } Figure 1: Many noun phrases can be created by combin- ing a word from the abstract categories determiner and noun (NP→DET+N). It is an open question whether children’s early representations are organized around these abstractions. When do children share that same judgment? Valian (1986) showed that children between 2;0 and 2;6 demonstrate a variety of productive syntactic categories, including deter- miners. Using a distributional analysis of children’s speech, she found that determiners were used in a fashion consistent with an adult-like grammar. Determiners were never used as the sole content of an utterance, never appeared in a sentence- final position, and were always sequenced correctly with re- spect to adjectives and nouns in noun phrases. Pine & Lieven (1997) challenged Valian’s assertion of adult-like grammatical productivity in children’s speech by citing an apparent limit to productivity in determiner use. As a quantitative metric, Pine and Lieven presented the over- lap measure for determiners: the number of nouns used with both determiners (in some sample), divided by the number of nouns used with either (in the same sample). For 11 chil- dren from 1;0 to 3;0 this proportion ranged from 0 to .23, which Pine and Lieven interpreted as being extremely low for a speaker with productive determiner syntax. Rather than making full use of the combinatorial productivity of nouns and determiners, on this metric children thus seemed to be very conservative in their productions and to show a strong tendency to use nouns with only a single determiner. Pine and Lieven interpreted this finding as supporting item-based theories of learning in which there is only gradual generaliza- tion from individual instances to abstractions like DET. Valian et al. (2009) objected that Pine & Lieven (1997) failed to take noun frequency into account in considering de- terminer use. Because the overlap measure is necessarily 0 for all nouns that appear only once, Valian and colleagues argued that the overlap measure, especially when calculated over small datasets, under-represents productivity. Highly frequent nouns were much more likely to be used with both determiners: more than 80% of nouns used at least 6 times were used with both “a” and “the.” Our own analyses of the Providence corpus (Demuth & McCullough, 2009) confirm