Iterated learning in populations

1. Iterated learning in populations Learning and evolving expectations about linguistic heterogeneity Kenny Smith, Bill Thompson d d d h h h h Iterated Bayesian learning Tool for testing link between learner biases and universals Language universals Languages do not differ arbitrarily: certain properties recur across languages Two possibleexplanations Universals reflect biases of language learners? Universals result from other pressures inherent in language transmission and use? , sample from posterior How does stable distribution of languages reflect bias, P(h)? Results for Iterated Bayesian learning Single parent Griffiths & Kalish (2007) Convergence to the prior Distribution of languages reflects learner biases only Multiple parents Burkett & Griffiths (2010) If learners expect heterogeneous input: convergence to prior If learners expect homogeneous input: other factors influence stable distribution of languages Learning α Gamma prior over α, k=1 Learner learns distribution over languages and α(Gibbs sampler from Escobar & West, 1995) Evolving α Dual-transmission model Reproduction proportional to communicative accuracy Genes encode α, gamma-distributed mutations (shape = k, scale = θ) • Summary of results • High-α convergence to the prior in multiple-teacher model predicts wrong type of universal • There are regimes under which low α is favoured (selection for communication, learning with strong prior for low α) • Conclusions and implications • We expect the relationship between learner biases and language universals to be modulated by other factors • Initial conditions, bottleneck, population structure, language use, … • How can we disentangle these effects when inferring causes of universals? References Burkett, D., & Griffiths, T. L. (2010). Iterated learning of multiple languages from multiple teachers. In A. D. M. Smith, M.Schouwstra, B. de Boer, & K. Smith (Eds.), The Evolution of Language (pp. 58-65). Singapore: Word Scientific. Escobar, M. D., & West, M. (1995). Bayesian Density Estimation and Inference Using Mixtures. Journal of the American Statistical Association, 90, 577-588. Griffiths, T. L., & Kalish, M. L. (2007). Language evolution by iterated learning with Bayesian agents. Cognitive Science, 31, 441-480.