Statistical universals of language : mathematical chance vs. human choice / / Kumiko Tanaka-Ishii

• Autore: Tanaka-Ishii Kumiko
• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (226 pages) : illustrations
• Disciplina: 410.151
• Soggetto topico: Mathematical linguistics; Computational linguistics; Lingüística matemàtica; Lingüística computacional
• Soggetto genere / forma: Llibres electrònics
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Contents -- Part I Language as a Complex System -- 1 Introduction -- 1.1 Aims -- 1.2 Structure of This Book -- 1.3 Position of This Book -- 1.3.1 Statistical Universals as Computational Properties of Natural Language -- 1.3.2 A Holistic Approach to Language via Complex Systems Theory -- 1.4 Prospectus -- 2 Universals -- 2.1 Language Universals -- 2.2 Layers of Universals -- 2.3 Universal, Stylized Hypothesis, and Law -- 3 Language as a Complex System -- 3.1 Sequence and Corpus -- 3.1.1 Definition of Corpus -- 3.1.2 On Meaning -- 3.1.3 On Infinity -- 3.1.4 On Randomness -- 3.2 Power Functions -- 3.3 Scale-Free Property: Statistical Self-Similarity -- 3.4 Complex Systems -- 3.5 Two Basic Random Processes -- Part II Property of Population -- 4 Relation Between Rank and Frequency -- 4.1 Zipf's Law -- 4.2 Scale-Free Property and Hapax Legomena -- 4.3 Monkey Text -- 4.4 Power Law of n-grams -- 4.5 Relative Rank-Frequency Distribution -- 5 Bias in Rank-Frequency Relation -- 5.1 Literary Texts -- 5.2 Speech, Music, Programs, and More -- 5.3 Deviations from Power Law -- 5.3.1 Scale -- 5.3.2 Speaker Maturity -- 5.3.3 Characters vs. Words -- 5.4 Nature of Deviations -- 6 Related Statistical Universals -- 6.1 Density Function -- 6.2 Vocabulary Growth -- Part III Property of Sequences -- 7 Returns -- 7.1 Word Returns -- 7.2 Distribution of Return Interval Lengths -- 7.3 Exceedance Probability -- 7.4 Bias Underlying Return Intervals -- 7.5 Rare Words as a Set -- 7.6 Behavior of Rare Words -- 8 Long-Range Correlation -- 8.1 Long-Range Correlation Analysis -- 8.2 Mutual Information -- 8.3 Autocorrelation Function -- 8.4 Correlation of Word Intervals -- 8.5 Nonstationarity of Language -- 8.6 Weak Long-Range Correlation -- 9 Fluctuation -- 9.1 Fluctuation Analysis -- 9.2 Taylor Analysis -- 9.3 Differences Between the Two Fluctuation Analyses. ; 9.4 Dimensions of Linguistic Fluctuation -- 9.5 Relations Among Methods -- 10 Complexity -- 10.1 Complexity of Sequence -- 10.2 Entropy Rate -- 10.3 Hilberg's Ansatz -- 10.4 Computing Entropy Rate of Human Language -- 10.5 Reconsidering the Question of Entropy Rate -- Part IV Relation to Linguistic Elements and Structure -- 11 Articulation of Elements -- 11.1 Harris's Hypothesis -- 11.2 Information-Theoretic Reformulation -- 11.3 Accuracy of Articulation by Harris's Scheme -- 12 Word Meaning and Value -- 12.1 Meaning as Use and Distributional Semantics -- 12.2 Weber-Fechner Law -- 12.3 Word Frequency and Familiarity -- 12.4 Vector Representation of Words -- 12.5 Compositionality of Meaning -- 12.6 Statistical Universals and Meaning -- 13 Size and Frequency -- 13.1 Zipf Abbreviation of Words -- 13.2 Compound Length and Frequency -- 14 Grammatical Structure and Long Memory -- 14.1 Simple Grammatical Framework -- 14.2 Phrase Structure Grammar -- 14.3 Long-Range Dependence in Sentences -- 14.4 Grammatical Structure and Long-Range Correlation -- 14.5 Nature of Long Memory Underlying Language -- Part V Mathematical Models -- 15 Theories Behind Zipf's Law -- 15.1 Communication Optimization -- 15.2 A Limit Theorem -- 15.3 Significance of Statistical Universals -- 16 Mathematical Generative Models -- 16.1 Criteria for Statistical Universals -- 16.2 Independent and Identically Distributed Sequences -- 16.3 Simon Model and Variants -- 16.4 Random Walk Models -- 17 Language Models -- 17.1 Language Models and Statistical Universals -- 17.2 Building Language Models -- 17.3 N-Gram Models -- 17.4 Grammatical Models -- 17.5 Neural Models -- 17.6 Future Directions for Generative Models -- Part VI Ending Remarks -- 18 Conclusion -- 19 Acknowledgments -- Part VII Appendix -- 20 Glossary and Notations -- 20.1 Glossary -- 20.2 Mathematical Notation. ; 20.3 Other Conventions -- 21 Mathematical Details -- 21.1 Fitting Functions -- 21.2 Proof that Monkey Typing Follows a Power Law -- 21.3 Relation Between η and ζ -- 21.4 Relation Between η and ξ -- 21.5 Proof That Interval Lengths of I.I.D. Process Follow Exponential Distribution -- 21.6 Proof of α=0.5 and ν=1.0 for I.I.D. Process -- 21.7 Summary of Shannon's Method to Estimate Entropy Rate -- 21.8 Relation of h, Perplexity, and Cross Entropy -- 21.9 Type Counts, Shannon Entropy, and Yule's K, via Generalized Entropy -- 21.10 Upper Bound of Compositional Distance -- 21.11 Rough Summary of Mandelbrot's Communication Optimization Rationale to Deduce a Power Law -- 21.12 Rough Definition of Central Limit Theorem -- 21.13 Definition of Simon Model -- 22 Data -- 22.1 Literary Texts -- 22.2 Large Corpora -- 22.3 Other Kinds of Data Related to Language -- 22.4 Corpora for Scripts -- References -- Index.
• Titolo autorizzato: Statistical universals of language
• ISBN: 3-030-59377-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910484715103321
• Lo trovi qui: Univ. Federico II
• Serie: Mathematics in Mind