Joint or Conditional Probability in Statistical Word Learning: Why decide?

Joint or Conditional Probability in Statistical Word Learning: Why decide? Krystal Klein (krklein@indiana.edu) and Chen Yu (chenyu@indiana.edu) Department of Psychological and Brain Sciences, 1101 E. 10 th St Bloomington, IN 47401 USA Abstract Three experiments investigated the ability of human learners to concurrently extract and track both joint and conditional probabilities in statistical word learning. In each experiment, participants were briefly trained on novel word– novel object pairs and asked to learn correct mappings by the end of training. Across a series of learning conditions, we systematically manipulated conditional and joint probabilities individually and in combination to determine whether learners are able to encode multiple statistics in various learning contexts. Our results suggest that participants acquired both joint and conditional probabilities of word-referent co- occurrences. Based on the results from these experiments, we propose that learners are capable of utilizing the most reliable statistics that they acquired in training to make correct judgments in various testing tasks. These results suggest that statistical word learning is not only powerful but also adaptive. Keywords: Language acquisition; word learning Introduction A recent trend in cognitive development is to study how human learners rely on statistical information to gradually reduce the uncertainty in the learning environment and ultimately acquire correct linguistic knowledge. The first study of this sort by Saffran, Aslin, Newport (1997) showed that 8-month-old infants can segment continuous speech into words based on statistical information alone. Subsequently, evidence has been mounting that both infant and adult learners can rely on sequential statistics to extract meaningful units from continuous sequences of stimuli in a variety of different sensory modalities (e.g., visual object sequence, action sequences, and tactile sequences) (Conway & Christiansen, 2005; Kirkham, Slemmer, & Johnson, 2002; Newport & Aslin, 2004; Saffran et al., 1999). More recently, Yu & Smith (2007) and Smith & Yu (2008) have extended this line of research to word learning by integrating this idea with a well-established proposal – cross-situational learning (e.g. Gleitman, 1990; Siskind, 1996). By doing so, they proposed a new paradigm – cross- situational statistical learning. The basic idea is that a learner who is exposed to multiple words and multiple referents in a single learning experience need not solve the word-referent mapping problem in this moment; if the learner can instead accumulate co-occurrence statistics of words and referents across multiple temporally distinct learning situations, he or she can ultimately figure out the correct pairings from cross-situational statistics. For example, in one condition reported by Yu and Smith (2007), participants were asked to learn 18 word-referent mappings over a series of learning trials. In each trial, learners viewed four pictures of objects and heard four names in an arbitrary order. Given 16 possible word- referent associations, learners could not have inferred correct pairings from individual trials. However, after being exposed to 27 individually ambiguous trials like this, participants in Yu & Smith (2007) acquired more than 9 out of 18 words. Further, a statistical associative model was developed to explain the underlying learning mechanism that supports cross-situational statistical learning. A set of simulation studies shows that this general associative account can serve as a fundamental framework to incorporate other cues/constraints, such as social cues (Yu & Ballard, 2007), syntactic cues (Yu, 2006), and prior knowledge (Klein, Yu, & Shiffrin, 2009), making statistical learning more efficient and more effective. Although those recent empirical and computational studies have advanced our understanding of statistical learning in general and cross-situational word learning in particular, important questions regarding the mechanistic nature of cross-situational learning remain unanswered. For instance, what word-referent association information do learners track and compute across multiple learning situations? Do learners represent these statistics in terms of joint probabilities of co-occurring events or conditional probabilities? Do they retrieve statistical information they have accumulated in a probabilistic way or a deterministic way? In particular, if they have represented and accumulated statistical information in more than one form, which do they rely on in different contexts of knowledge retrieval? There are two general probabilistic representations of co- occurring statistics in the context of statistical word learning: 1) joint probability of co-occurrence of words and objects p(w,o); 2) conditional probabilities of words given an object p(w|o) or conditional probabilities of objects given a word p(o|w). These two representations are not mutually exclusive, but rather, complementary: they reflect different aspects of co-occurring statistics. Joint probabilities represent overall frequencies of two co-occurring events; and conditional probabilities measure the frequency of one event (e.g. a word) given the presence of the other event (e.g. an object), which has predictive power when encoding sequential statistics. Moreover, one can convert between these two representations given knowledge of the statistical base rate of a single event p(w) or p(o): The role of joint and conditional probabilities has been studied in both statistical speech segmentation (Saffran, Aslin & Newport, 1997) and visual statistical learning (Fiser & Aslin, 2001). For example, Fiser and Aslin demonstrated that learners rely on conditional probabilities of co- occurrences in learning statistical structures of visual scenes. In their study, they controlled the frequency (joint probability) of two sets of visual shape pairs and varied the