The predictability of letters in written english

We show that the predictability of letters in written English texts depends strongly on their position in the word. The first letters are usually the least easy to predict. This agrees with the intuitive notion that words are well defined subunits in written languages, with much weaker correlations across these units than within them. It implies that the average entropy of a letter deep inside a word is roughly 4 times smaller than the entropy of the first letter.Comment: 3 pages, 4 figure

Towards the quantification of the semantic information encoded in written language

Written language is a complex communication signal capable of conveying information encoded in the form of ordered sequences of words. Beyond the local order ruled by grammar, semantic and thematic structures affect long-range patterns in word usage. Here, we show that a direct application of information theory quantifies the relationship between the statistical distribution of words and the semantic content of the text. We show that there is a characteristic scale, roughly around a few thousand words, which establishes the typical size of the most informative segments in written language. Moreover, we find that the words whose contributions to the overall information is larger, are the ones more closely associated with the main subjects and topics of the text. This scenario can be explained by a model of word usage that assumes that words are distributed along the text in domains of a characteristic size where their frequency is higher than elsewhere. Our conclusions are based on the analysis of a large database of written language, diverse in subjects and styles, and thus are likely to be applicable to general language sequences encoding complex information.Comment: 19 pages, 4 figure

The entropy of words-learnability and expressivity across more than 1000 languages

The choice associated with words is a fundamental property of natural languages. It lies at the heart of quantitative linguistics, computational linguistics and language sciences more generally. Information theory gives us tools at hand to measure precisely the average amount of choice associated with words: the word entropy. Here, we use three parallel corpora, encompassing ca. 450 million words in 1916 texts and 1259 languages, to tackle some of the major conceptual and practical problems of word entropy estimation: dependence on text size, register, style and estimation method, as well as non-independence of words in co-text. We present two main findings: Firstly, word entropies display relatively narrow, unimodal distributions. There is no language in our sample with a unigram entropy of less than six bits/word. We argue that this is in line with information-theoretic models of communication. Languages are held in a narrow range by two fundamental pressures: word learnability and word expressivity, with a potential bias towards expressivity. Secondly, there is a strong linear relationship between unigram entropies and entropy rates. The entropy difference between words with and without co-textual information is narrowly distributed around ca. three bits/word. In other words, knowing the preceding text reduces the uncertainty of words by roughly the same amount across languages of the world.Peer ReviewedPostprint (published version

Token-based typology and word order entropy: A study based on universal dependencies

The present paper discusses the benefits and challenges of token-based typology, which takes into account the frequencies of words and constructions in language use. This approach makes it possible to introduce new criteria for language classification, which would be difficult or impossible to achieve with the traditional, type-based approach. This point is illustrated by several quantitative studies of word order variation, which can be measured as entropy at different levels of granularity. I argue that this variation can be explained by general functional mechanisms and pressures, which manifest themselves in language use, such as optimization of processing (including avoidance of ambiguity) and grammaticalization of predictable units occurring in chunks. The case studies are based on multilingual corpora, which have been parsed using the Universal Dependencies annotation scheme

Artificial Sequences and Complexity Measures

In this paper we exploit concepts of information theory to address the fundamental problem of identifying and defining the most suitable tools to extract, in a automatic and agnostic way, information from a generic string of characters. We introduce in particular a class of methods which use in a crucial way data compression techniques in order to define a measure of remoteness and distance between pairs of sequences of characters (e.g. texts) based on their relative information content. We also discuss in detail how specific features of data compression techniques could be used to introduce the notion of dictionary of a given sequence and of Artificial Text and we show how these new tools can be used for information extraction purposes. We point out the versatility and generality of our method that applies to any kind of corpora of character strings independently of the type of coding behind them. We consider as a case study linguistic motivated problems and we present results for automatic language recognition, authorship attribution and self consistent-classification.Comment: Revised version, with major changes, of previous "Data Compression approach to Information Extraction and Classification" by A. Baronchelli and V. Loreto. 15 pages; 5 figure

Constant conditional entropy and related hypotheses

Constant entropy rate (conditional entropies must remain constant as the sequence length increases) and uniform information density (conditional probabilities must remain constant as the sequence length increases) are two information theoretic principles that are argued to underlie a wide range of linguistic phenomena. Here we revise the predictions of these principles in the light of Hilberg's law on the scaling of conditional entropy in language and related laws. We show that constant entropy rate (CER) and two interpretations for uniform information density (UID), full UID and strong UID, are inconsistent with these laws. Strong UID implies CER but the reverse is not true. Full UID, a particular case of UID, leads to costly uncorrelated sequences that are totally unrealistic. We conclude that CER and its particular cases are incomplete hypotheses about the scaling of conditional entropies.Peer ReviewedPostprint (author's final draft