Abstract
The previous two parts of this book considered statistical universals of language. Sequences were input to specific analysis methods to examine the behavior of words or characters. The resulting phenomena were studied from the two viewpoints of the poplulation and sequence. As shown by the thick rightward arrow in Fig. 1.1, Parts II and III studied language corpora to reveal the statistical universals.
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Notes
- 1.
The description of pronunciation here follows that appearing in (Harris 1955).
- 2.
Note that there are other, far less common possibilities such as “The United States of Tara,” the name of a television series, and misspelled words (see Sect. 17.3).
- 3.
Section 21.9 explains the relations of various measures of complexity through the notion of generalized entropy , including the successor count and the Shannon entropy.
- 4.
\(g(c_i^{i+n-1}\)) in this chapter is designed to follow Harris’s concept closely. Another way is instead to use \({\mathrm{H}}(X_{i+n}|X_i^{i+n-1} = c_i^{i+n-1})\), whose relation with \({\mathrm{H}}(X_n|X_1^{n-1})\) is clearer. The overall experimental result should not be different.
- 5.
This maximum value was chosen after testing with some larger values in the original work (Tanaka-Ishii and Jin, 2008). Language has long memory, as reported in Part III, but when limited to this specific task of articulation using Harris’s scheme, n = 10 was deemed sufficient to obtain maximum performance.
- 6.
This figure appeared in Tanaka-Ishii and Jin (2008). For clarity, the figure only shows part of the experimental results. In the experiment, an entropy shift was verified starting from every phoneme for a length of 10, as mentiond in the main text.
- 7.
The denotation of phonemes by capital letters here follows the CMU Pronouncing Dictionary (The Speech Group at CMU, 1998).
- 8.
The experiment involved a threshold parameter k such that candidate points at j > i were regarded as borders when \(g(c_i^{j}) - g(c_i^{j-1}) \geq k\). This k value was then varied, and f-scores were acquired for all thresholds. The value k = 1.6 gave the best results.
- 9.
This figure also appeared in Tanaka-Ishii and Jin (2008). As detailed in the original paper, the rightmost point has slightly different precision and recall values from those given in the text. The reason is that the threshold value k was varied as mentioned in the previous footnote, and this graph shows the result for another slightly different k.
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Tanaka-Ishii, K. (2021). Articulation of Elements. In: Statistical Universals of Language. Mathematics in Mind. Springer, Cham. https://doi.org/10.1007/978-3-030-59377-3_11
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