This paper presents a discovery that the length of the entities in various datasets follows a family of scale-free power law distributions. The concept of entity here broadly includes the named entity, entity mention, time expression, aspect term, and domain-specific entity that are well investigated in natural language processing and related areas. The entity length denotes the number of words in an entity. The power law distributions in entity length possess the scale-free property and have well-defined means and finite variances. We explain the phenomenon of power laws in entity length by the principle of least effort in communication and the preferential mechanism.
Our work is related to Zipf's law and the distributions of word length and sentence length. Power laws have been observed to appear in numerous natural and man-made systems @cite_62 , we here concern them in language.
@cite_62
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When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, forest fires, solar flares, moon craters and people's personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them. Standard statistical models of language fail to capture one of the most striking properties of natural languages: the power-law distribution in the frequencies of word tokens. We present a framework for developing statistical models that generically produce power-laws, augmenting standard generative models with an adaptor that produces the appropriate pattern of token frequencies. We show that taking a particular stochastic process - the Pitman-Yor process - as an adaptor justifies the appearance of type frequencies in formal analyses of natural language, and improves the performance of a model for unsupervised learning of morphology. A single statistical framework, comprising power law distributions and scale-free networks, seems to fit a wide variety of phenomena. There is evidence that power laws appear in software at the class and function level. We show that distributions with long, fat tails in software are much more pervasive than previously established, appearing at various levels of abstraction, in diverse systems and languages. The implications of this phenomenon cover various aspects of software engineering research and practice. Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out. We investigated long-range correlations in two literary texts, "Moby Dyck" by H. Melville and Grimm's tales. The analysis is based on the calculation of entropylike quantities as the mutual information for pairs of letters and the entropy, the mean uncertainty, per letter. We further estimate the number of different subwords of a given length n. Filtering out the contributions due to the effects of the finite length of the texts, we find correlations ranging to a few hundred letters. Scaling laws for the mutual information (decay with a power law), for the entropy per letter (decay with the inverse square root of n) and for the word numbers (stretched exponential growth with n and with a power law of the text length) were found. Power-law distributions have been observed in a wide variety of areas. To our knowledge however, there has been no systematic observation of power-law distributions in chemoinformatics. Here, we present several examples of power-law distributions arising from the features of small, organic molecules. The distributions of rigid segments and ring systems, the distributions of molecular paths and circular substructures, and the sizes of molecular similarity clusters all show linear trends on log-log rank frequency plots, suggesting underlying power-law distributions. The number of unique features also follow Heaps'-like laws. The characteristic exponents of the power-laws lie in the 1.5-3 range, consistently with the exponents observed in other power-law phenomena. The power-law nature of these distributions leads to several applications including the prediction of the growth of available data through Heaps' law and the optimal allocation of experimental or computational resources via the 80 20 rule. More importantly, we also show how the power-laws can be leveraged to efficiently compress chemical fingerprints in a lossless manner, useful for the improved storage and retrieval of molecules in large chemical databases. We show that the largest eigenvalues of graphs whose highest degrees are Zipf-like distributed with slope a are distributed according to a power law with slope α 2. This follows as a direct and almost certain corollary of the degree power law. Our result has implications for the singular value decomposition method in information retrieval. We present a generative distributional model for the unsupervised induction of natural language syntax which explicitly models constituent yields and contexts. Parameter search with EM produces higher quality analyses than previously exhibited by unsupervised systems, giving the best published un-supervised parsing results on the ATIS corpus. Experiments on Penn treebank sentences of comparable length show an even higher F1 of 71 on non-trivial brackets. We compare distributionally induced and actual part-of-speech tags as input data, and examine extensions to the basic model. We discuss errors made by the system, compare the system to previous models, and discuss upper bounds, lower bounds, and stability for this task. We propose a plausible explanation of the power law distributions of degrees observed in the graphs arising in the Internet topology [Faloutsos, Faloutsos, and Faloutsos, SIGCOMM 1999] based on a toy model of Internet growth in which two objectives are optimized simultaneously: "last mile" connection costs, and transmission delays measured in hops. We also point out a similar phenomenon, anticipated in [Carlson and Doyle, Physics Review E 1999], in the distribution of file sizes. Our results seem to suggest that power laws tend to arise as a result of complex, multi-objective optimization. Words in natural language follow a Zipfian distribution whereby some words are frequent but most are rare. Learning representations for words in the long tail'' of this distribution requires enormous amounts of data. Representations of rare words trained directly on end tasks are usually poor, requiring us to pre-train embeddings on external data, or treat all rare words as out-of-vocabulary words with a unique representation. We provide a method for predicting embeddings of rare words on the fly from small amounts of auxiliary data with a network trained end-to-end for the downstream task. We show that this improves results against baselines where embeddings are trained on the end task for reading comprehension, recognizing textual entailment and language modeling. Even though people in our contemporary technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in 2 social Internet communities in search of statistical laws in human interaction activity. This research reveals that human communication networks dynamically follow scaling laws that may also explain the observed trends in economic growth. Specifically, we identify a generalized version of Gibrat's law of social activity expressed as a scaling law between the fluctuations in the number of messages sent by members and their level of activity. Gibrat's law has been essential in understanding economic growth patterns, yet without an underlying general principle for its origin. We attribute this scaling law to long-term correlation patterns in human activity, which surprisingly span from days to the entire period of the available data of more than 1 year. Further, we provide a mathematical framework that relates the generalized version of Gibrat's law to the long-term correlated dynamics, which suggests that the same underlying mechanism could be the source of Gibrat's law in economics, ranging from large firms, research and development expenditures, gross domestic product of countries, to city population growth. These findings are also of importance for designing communication networks and for the understanding of the dynamics of social systems in which communication plays a role, such as economic markets and political systems. Word usage is influenced by diverse factors, including topic, genre and various speaker author characteristics. To characterize these aspects of language, we introduce the “Multi-Factor Sparse Plus Low Rank” exponential language model, which allows supervised joint training of arbitrary overlapping factor-specific model components. This flexible architecture has the advantage of being highly interpretable. The elements of sparse parameter matrices can be viewed as factor-dependent corrections (e.g. topic- or speaker-dependent phenomena). In topic modeling experiments on conversational telephone speech, we obtain modest perplexity reductions over an n-gram baseline and demonstrate topic-dependent keyword extraction that leads to a 13 (absolute) improvement in precision over TFIDF. We also show how keywords can be jointly learned for speakers, roles and topics in a study of Supreme Court oral arguments. Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the exponent are a mathematically sound alternative to graphical methods. A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential attachment and copying mechanisms that existing evolving graph processes fail to model due to technical obstacles. The result also serves as a further cautionary note reinforcing the point of view that a power law degree distribution should not be regarded as the only important characteristic of a complex network, as has been previously argued [D. Achlioptas, A. Clauset, D. Kempe, C. Moore, On the bias of traceroute sampling, or power-law degree distribution in regular graphs, in: Proceedings of the 37th ACM Symposium on Theory of Computing, STOC'05, 2005, pp. 694-703; L. Li, D. Alderson, J. Doyle, W. Willinger, Towards a theory of scale-free graphs: Definition, properties, and implications, Internet Mathematics 2 (4) (2005) 431-523; M. Mitzenmacher, The future of power law research, Internet Mathematics, 2 (4) (2005) 525-534]. This paper presents a model-based, unsupervised algorithm for recovering word boundaries in a natural-language text from which they have been deleted. The algorithm is derived from a probability model of the source that generated the text. The fundamental structure of the model is specified abstractly so that the detailed component models of phonology, word-order, and word frequency can be replaced in a modular fashion. The model yields a language-independent, prior probability distribution on all possible sequences of all possible words over a given alphabet, based on the assumption that the input was generated by concatenating words from a fixed but unknown lexicon. The model is unusual in that it treats the generation of a complete corpus, regardless of length, as a single event in the probability space. Accordingly, the algorithm does not estimate a probability distribution on wordss instead, it attempts to calculate the prior probabilities of various word sequences that could underlie the observed text. Experiments on phonemic transcripts of spontaneous speech by parents to young children suggest that our algorithm is more effective than other proposed algorithms, at least when utterance boundaries are given and the text includes a substantial number of short utterances. Understanding how words change their meanings over time is key to models of language and cultural evolution, but historical data on meaning is scarce, making theories hard to develop and test. Word embeddings show promise as a diachronic tool, but have not been carefully evaluated. We develop a robust methodology for quantifying semantic change by evaluating word embeddings (PPMI, SVD, word2vec) against known historical changes. We then use this methodology to reveal statistical laws of semantic evolution. Using six historical corpora spanning four languages and two centuries, we propose two quantitative laws of semantic change: (i) the law of conformity---the rate of semantic change scales with an inverse power-law of word frequency; (ii) the law of innovation---independent of frequency, words that are more polysemous have higher rates of semantic change. Abstract In this study, word length distributions are investigated in Old Icelandic songs and prose texts. Although Old Icelandic is separated from the other languages studied so far within the framework of the Gottingen word length project, the same model, viz. the hyper‐Poisson distribution, can successfully be fitted to the data. Using human evaluation of 100,000 words spread across 24 corpora in 10 languages diverse in origin and culture, we present evidence of a deep imprint of human sociality in language, observing that (i) the words of natural human language possess a universal positivity bias, (ii) the estimated emotional content of words is consistent between languages under translation, and (iii) this positivity bias is strongly independent of frequency of word use. Alongside these general regularities, we describe interlanguage variations in the emotional spectrum of languages that allow us to rank corpora. We also show how our word evaluations can be used to construct physical-like instruments for both real-time and offline measurement of the emotional content of large-scale texts. SemEval 2016 task 11 involved determining whether words in a sentence were complex or simple for a cohort of people with English as a second language. Training data consisted of 200 annotated sentences, representing the combined judgements of 20 human annota- tors, such that if any annotator of the group labelled a word as complex, then it was con- sidered to be complex. Testing was based on single annotator judgements. Our system used a random forest classifier with a variety of features, the most important of which were term frequency statistics garnered from four large corpora, and style lexicons built on two large corpora. Minor features in the final system include the presence or absence of words in various readability word lists; many other features we tried were not successful. Our rank- ing amongst submitted systems did not reflect the strength of our system, due to submitting a far from optimal weighting between complex and simple, but we show that when a more ap- propriate weighting is used, our system ranks amongst the best submitted systems. Despite the apparent randomness of the Internet, we discover some surprisingly simple power-laws of the Internet topology. These power-laws hold for three snapshots of the Internet, between November 1997 and December 1998, despite a 45 growth of its size during that period. We show that our power-laws fit the real data very well resulting in correlation coefficients of 96 or higher.Our observations provide a novel perspective of the structure of the Internet. The power-laws describe concisely skewed distributions of graph properties such as the node outdegree. In addition, these power-laws can be used to estimate important parameters such as the average neighborhood size, and facilitate the design and the performance analysis of protocols. Furthermore, we can use them to generate and select realistic topologies for simulation purposes.