Obtaining a suitable distance measure between two pronunciations is important, not only for dialectologists who are interested in finding the relationship between different dialects (e.g., [1]), but also for sociolinguists investigating the effect of political borders on vernacular speech [2], language researchers investigating the typological and genealogical relationships among the world's languages (e.g., [3]), applied linguists attempting to gauge the degree of comprehensibility among related languages [4], and researchers measuring the atypicality of the speech of the bearers of cochlear implants [5]. Furthermore, having a distance measure between word pronunciations enables quantitative analyses in which the integrated effect of geography and sociolinguistic factors can be investigated (e.g., [6]). Standard sociolinguistic analyses focus on whether specific categorical differences are present in the speech of people from different social groups. By using a measure of pronunciation difference, we allow more powerful numerical analysis techniques to be used. For these analyses to be meaningful, however, the measurements of pronunciation distance need to match perceptual distances as closely as possible.

There are various computational methods to measure word or pronunciation distance (or similarity), of which the Levenshtein distance has been the most popular [1], [7], [8], [9], [10]. The Levenshtein distance determines the pronunciation distance between two transcribed strings by calculating the number of substitutions, insertions and deletions to transform one string into the other [11]. For example, the Levenshtein distance between two accented pronunciations of the word Wednesday, [wεnzdeI] and [wεnsde] is 3 as illustrated by the alignment in Table 1.

A clear drawback of this variant of the Levenshtein distance is that it does not distinguish the substitution of similar sounds (such as [o] and [u]) from more different sounds (such as [o] and [i]). Consequently, effort has been made to integrate more sensitive segment distances in the Levenshtein distance algorithm [1], [12]. As manually determining sensitive segment distances is time-consuming and language-dependent, Wieling and colleagues [13] developed an automatic method to determine sensitive segment distances. Their method calculated the pointwise mutual information between two segments, assigning lower distances between segments which aligned relatively frequently and higher distances between segments which aligned relatively infrequently. Results indicated that the obtained segment distances were acoustically sensible and resulted in improved alignments [14]. Applying the adapted method to the example alignment shown above yields the associated costs shown in Table 2.

While Levenshtein distances correlate well (r = 0.67) with perceptual dialect distances between Norwegian dialects [15], there is no cognitive basis to link the Levenshtein distance to perceptual distances (but see [16] for an attempt to adapt the Levenshtein algorithm in line with theories about spoken word recognition). This is also exemplified by the fact that the Levenshtein distance is symmetrical (i.e. the distance between speaker A and B is the same as the other way around), while perceptual dialect distances may also show an asymmetrical pattern [15].

As exposure to language shapes expectations and affects what is judged similar to one's own pronunciation and what is different, we turn to one of the most influential theories about animal and human (discrimination) learning: the model of Rescorla and Wagner [17]. The basic assumption of this model is that a learner predicts an outcome (e.g., the meaning of a word) based on the set of available cues (e.g., the sounds of a word). Depending on the correctness of the prediction, the association strengths between the outcome and the cues are adjusted so that future prediction accuracy improves. Concretely, if an outcome is present together with a certain cue, its association strength increases, while the association strength between an absent outcome and that cue decreases. When an outcome is found together with multiple cues (i.e. when there is cue competition), the adjustments are more conservative (depending on the number of cues). The learning theory of Rescorla and Wagner is formalized in a set of recurrence equations which specify the association strength of cue with outcome O at time as , where the change in association strength is defined as:In this definition, denotes the presence of cue X at time t and its absence at time t. Whenever the cue occurs without the outcome being present, the association strength is decreased, whereas it is increased when both the cue and outcome are present. The adjustment of the association strength depends on the number of cues present together with the outcome. The standard settings for the parameters are , all equal, and .

The Rescorla-Wagner model has been used to explain findings in animal learning and cognitive psychology [18] and more recently, Ramscar and colleagues [19], [20], [21] have successfully used this model in the context of children's language acquisition. For example, Ramscar and colleagues [21] showed that the Rescorla-Wagner model clearly predicted that exposure to regular plurals (such as rats) decreases children's tendency to over-regularize irregular plurals (such as mouses) at a certain stage in their development.

Danks [22] proposed parameter-free equilibrium equations (i.e. where ) for the recurrence equations presented above: , where represents the conditional probability of cue given cue , and the conditional probability of outcome O given cue . Consequently, it is possible to directly calculate the association strength between cues and outcomes in the stable (i.e. adult) state where further learning does not substantially change the association weights. Baayen and colleagues [23] have proposed an extension to estimate multiple outcomes in parallel. Their ‘naive discriminative learning’ (NDL) approach (implementing the Danks equations [22]) lends itself for efficient computation and is readily available via their R package ‘ndl’. More details about the underlying computations can also be found in [23].

After all association strengths of the adult state are determined, the activation (i.e. activation strength) of an outcome given a set of cues can be calculated by summing the corresponding association strengths. Especially these activations are important for prediction. For example, Baayen and colleagues [23] found that the estimated activation of words correlated well with experimental reaction times to those words.

Here we propose to use naive discriminative learning to determine pronunciation distances. The intuition behind our approach is that a speaker of a certain dialect or language variety is predominantly exposed to speakers who speak similarly, and this input shapes the network of association strengths between cues (in our case, sequences of three sound segments representing the pronunciation, i.e. substrings of the phonetic transcription) and outcomes (in our case, the meaning of the pronounced word) for the speaker. The use of sequences of three segments, so-called trigrams, allows the measure to become sensitive to the adjustments sounds undergo in the context of other sounds, and trigrams have been experimented with in dialectology before [24]. (For comparison, we will also report results when using unigram and bigram cues.) By exposing the speaker to a new pronunciation (in the form of its associated cues) we can measure how well the speaker is likely to understand that pronunciation by inspecting the activation strength of the corresponding outcome. The activation strength of the outcome will depend on the association strengths between the outcome and the cues involved in the pronunciation. If only cues are present which have a high association strength with the outcome, the activation of the outcome will be high, whereas the activation of the outcome will be somewhat lower if one of the cues has a low association strength with the outcome. By calculating the activation strength difference for two different pronunciations of the same word, we obtain a (gradual) measure of pronunciation distance. For example, the word ‘with’ would be highly activated when a native English listener hears []. However, when a Mandarin speaker would incorrectly pronounce ‘with’ as [], this would result in a somewhat lower activation.

Of course, using an adult state with fixed association weights between cues and outcomes is a clear simplification. Language change is a continuous process and the experience of a listener (i.e. the association weights between cues and outcomes) will obviously be affected by this. However, as the new language experience only makes up a small part of the total language experience of a listener, the effect of the past experience is most important in determining the association weights. As a consequence, and in line with the results of Labov's ([25]: Ch. 4) Cross-Dialectal Comprehension (CDC) studies (which evaluated how well American English speakers understand speakers from their own and other regions), our model will yield lower meaning activations (i.e. more misunderstandings) when sound change is in progress (i.e. the original sound segments will have a higher association strength with the meaning than the new sound segments). In similar fashion, our model predicts higher meaning activations for pronunciations closer to one's own pronunciation variant (i.e. the “local advantage”). We also emphasize that our model is able to capture differences in understandability per word (as each word has its own frequency of occurrence) – which might explain Labov's finding that certain sounds are not always correctly identified, even if they are characteristic of local speakers ([25]: pp. 84–85).

Furthermore, the model we propose is general, as it does not focus on a selection of linguistic features (such as vowels), but takes into account all sound (sequences) in determining the understandability of a certain pronunciation.

Besides being grounded in cognitive theory of competitive reinforcement learning, a clear benefit of this approach is that the pronunciation distances obtained do not need to be symmetrical, as they depend on the association strengths between cues and outcomes, which are different for every speaker. This is illustrated in Section 2.2 below.

To evaluate the effectiveness of this approach, we conducted two experiments. The first experiment focused on investigating foreignness ratings given by native American English (AE) speakers when judging accented English speech, while the second experiment focused on the asymmetric perceptual distances of Norwegian dialect speakers.

As we noted in the introduction, the Levenshtein distance has been applied to pronunciation transcriptions to assay the degree to which non-local pronunciations sound “different” from local ones (in dialectology, see [1]), but also to predict the comprehensibility of other language varieties (in applied sociolinguistics, see [4]). Since pronunciations may sound non-native or non-local without suffering in comprehensibility, one might suspect that the two notions are not the same, even if they are clearly related. In the present paper we construct a model of an artificial listener to discriminate well enough between words given sound trigrams, which is essentially a comprehension task. But we shall evaluate the same model on how well it predicts human judgments of how similar the speech is to one's own pronunciation (i.e. how native-like foreign accents sound, or how close a pronunciation is to one's own dialect). To the degree to which these experiments succeed, we may conclude that the degree of comprehensibility is largely the same as the degree of nativeness (or localness).

In the present paper we have shown that pronunciation distances derived from naive discriminative learning match perceptual accent and dialect distances quite well. While the results were on par with those on the basis of the Levenshtein distance, the advantage of the present approach is that it is grounded in cognitive theory of comprehension based on fundamental principles of human discrimination learning. Furthermore, the Levenshtein distance is theoretically less suitable for modeling the degrees of difference in the perception of non-local and non-native speech because it is a true distance, i.e. always symmetric, while perceptions of similarity may also be asymmetric [15]. The NDL-based approach naturally generates asymmetrical distances.

We noted above that the task of recognizing words based on phonetic cues is essentially a comprehensibility task. A second contribution of the present paper is therefore to demonstrate that models constructed to comprehend local speech automatically assign scores of non-nativeness (or of non-localness among dialects) in a way that models native speakers judgments.

One may wonder why the NDL-based method only slightly improved upon the results of the Levenshtein distance for the Norwegian dataset, especially since that dataset is characterized by asymmetric perceptual distances. We note here that the 15 NDL models (one for each listener) are only based on the pronunciation of a single speaker. Consequently, it does not take into account the variation within each dialect (taken into account by listeners living in the dialect area), which would have allowed for more precise estimates of the association weights. A general limitation is that Gooskens and Heeringa [15] already indicated that intonation is one of the most important characteristics in Norwegian dialects, and no such cues have been used here (as these were not available to us), thereby limiting the ability to detect relevant asymmetries. Nerbonne and Heeringa ([28]: 563–564), on the other hand, speculate that there is a limit to the accuracy of validating pronunciation difference measures on the basis of aggregate judgments of varietal distance. If one supposes that poorer measures are noisier – but not more biased – than better ones, then the noise will simply be eliminated in examining large aggregates. If this is right, we cannot expect to change mean differences by adopting more accurate measurements. They suggest that improved validation will therefore have to focus on smaller units such as individual words.

While we have not explored this in the present paper, another important advantage of the NDL approach is that cues are not only restricted to phonetic segments. Cues with respect to pronunciation speed or other acoustic characteristics (such as intonation) can be readily integrated in an NDL model (e.g., linking cues representing different intonation patterns to the individual meanings). A problem of the NDL method, however, is that it only accepts discrete cues. A continuous measurement therefore needs to be discretized to separate cues, and this introduces a subjective element in an otherwise parameter-free procedure.

As our datasets only consisted of a few dozen words, our model was highly simplified compared to the cognitive model of a human listener who will have access to thousands of words. It is nevertheless promising that pronunciation distances on the basis of our simplified models match perceptual distances at least as well as current gold standards.