A Maximum Entropy Typological Model

Introduction. One of the most contested debates in phonology concerns identifying factors that affect typology. The Analytic Bias approach (AB) claims that biases in learning affect the typology, while the Channel Bias approach (CB) assumes phonetic precursors and transmission of language affect the typology (Moreton 2008). Empirical evidence in favor of both hypotheses exists: processes that are typologically rare have been shown to be underlearned; processes that are the result of phonologized phonetically motivated sound changes are also typologically frequent. An increasing body of work acknowledges both influences (Moreton 2008), but very few attempts have been made to model them together or try to disambiguate the two. This paper aims to fill this gap and proposes a model that unifies the two influences as well as provides grounds for disambiguating AB and CB. Probabilistic typology within CB. A quantified model of CB influences on typology is the first step towards a new typological model. Current proposals for deriving typology within CB are insufficient or do not produce implementable quantitative results (cf. Blevins 2004, Moreton 2008, Yu 2011, Cathcart 2015). We first argue that phonetically unnatural alternations can only arise through a combination of at least three sound changes (Minimal Sound Change Requirement, MSCR). This generalization is backed by a typological study of unnatural alternations as well as by a formal proof (in a given environment, a natural feature value cannot change into an unnatural one with only two sound changes). Then, we propose a new probabilistic model of CB typology and claim that for every synchronic alternation, we can calculate its HISTORICAL PROBABILITY (Pχ ) based on the number of sound changes required for the alternation to arise and the probability of each sound change required. Calculation of Pχ is not a trivial task: we propose a new method of estimating historical probabilities from typological surveys called “bootstrapping sound changes” (BSC). Historical probabilities are bootstrapped (Efron 1979) from a sample of successes (languages in the sample with a sound change S1) and failures (languages in the sample without S1). If an alternation Ax requires n > 1 sound changes to arise, Pχ is bootstrapped from a product of probabilities based on the number of successes and failures (divided by n! to account for the ordering of sound changes). For example, we can estimate Pχ of natural and unnatural alternations (such as post-nasal voicing, PNV vs. post-nasal devoicing, PND). Pχ (PNV) is considerably greater (20.5%, BCa CI = [15%, 26%]) than Pχ (PND) (0.047%, BCa CI = [0.018%, 0.12%]) based on the number of sound changes the two alternations require and their probabilities and using the BSC method on the sample of sound changes in Kümmel (2007). Pχ of the other two unnatural alternations discussed here, final voicing (FV) and intervocalic devoicing (IVD), are also very low (0.0028%, BCa CI = [0.00045%, 0.015%] for FV, and 0.0064%, BCa CI = [0.0013%, 0.027%] for IVD). The BSC method has several implications: it allows us to (i) compare Pχ of different alternations with statistical inference (e.g. Pχ (FV) is significantly lower than Pχ (PND), with the BCa CI of the difference being [0.02%, 0.11%]); (ii) identify historically equiprobable processes for testing learnability; (iii) predict the (un)attestedness of alternations in a given sample; and finally, (iv) BSC provides quantified means for encoding Channel Bias in a typological model. Typology within AB and MaxEnt. Numerous studies experimentally confirm that some alternations are underlearned. The evidence for AB is strongest when testing featurally more vs. less complex alternations (complexity bias, Moreton and Pater 2012). AB is encoded in MaxEnt models of phonological learning in two similar ways: Wilson (2006) sets different variance (σ2), White (2017) sets different weights (μ) in the regularization term of different constraints to encode that some processes require more input data to be learnt. These priors are determined independently, from P-map related perceptual distance measures. While structurally complex alternations are consistently underlearned, much less robust results are obtained when testing alternations that target a single feature value where one direction is phonetically natural and typologically common and the other is unnatural and rare (substantive bias; Moreton and Pater 2012). In fact, two studies specifically tested the learnability of PND and IVD compared to their natural counterparts and found no significant difference between the natural/unnatural pairs (Seidl et al. 2007, Do et al. 2016).