|
Kneser–Ney Smoothing
Kneser–Ney smoothing, also known as Kneser-Essen-Ney smoothing, is a method primarily used to calculate the probability distribution of ''n''-grams in a document based on their histories. It is widely considered the most effective method of smoothing due to its use of absolute discounting by subtracting a fixed value from the probability's lower order terms to omit ''n''-grams with lower frequencies. This approach has been considered equally effective for both higher and lower order ''n''-grams. The method was proposed in a 1994 paper by Reinhard Kneser, Ute Essen and . A common example that illustrates the concept behind this method is the frequency of the bigram "San Francisco". If it appears several times in a training corpus, the frequency of the unigram "Francisco" will also be high. Relying on only the unigram frequency to predict the frequencies of ''n''-grams leads to skewed results; however, Kneser–Ney smoothing corrects this by considering the frequency of the unigra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-gram
An ''n''-gram is a sequence of ''n'' adjacent symbols in particular order. The symbols may be ''n'' adjacent letter (alphabet), letters (including punctuation marks and blanks), syllables, or rarely whole words found in a language dataset; or adjacent phonemes extracted from a speech-recording dataset, or adjacent base pairs extracted from a genome. They are collected from a text corpus or speech corpus. If Latin numerical prefixes are used, then ''n''-gram of size 1 is called a "unigram", size 2 a "bigram" (or, less commonly, a "digram") etc. If, instead of the Latin ones, the Cardinal number (linguistics), English cardinal numbers are furtherly used, then they are called "four-gram", "five-gram", etc. Similarly, using Greek numerical prefixes such as "monomer", "dimer", "trimer", "tetramer", "pentamer", etc., or English cardinal numbers, "one-mer", "two-mer", "three-mer", etc. are used in computational biology, for polymers or oligomers of a known size, called k-mer, ''k'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Document
A document is a writing, written, drawing, drawn, presented, or memorialized representation of thought, often the manifestation of nonfiction, non-fictional, as well as fictional, content. The word originates from the Latin ', which denotes a "teaching" or "lesson": the verb ' denotes "to teach". In the past, the word was usually used to denote written proof useful as evidence of a truth or fact. In the computer age, Computer Age, "document" usually denotes a primarily textual computer file, including its structure and format, e.g. fonts, colors, and Computer-generated imagery, images. Contemporarily, "document" is not defined by its transmission medium, e.g., paper, given the existence of electronic documents. "Documentation" is distinct because it has more denotations than "document". Documents are also distinguished from "Realia (library science), realia", which are three-dimensional objects that would otherwise satisfy the definition of "document" because they memorialize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smoothing
In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points higher than the adjacent points (presumably because of noise) are reduced, and points that are lower than the adjacent points are increased leading to a smoother signal. Smoothing may be used in two important ways that can aid in data analysis (1) by being able to extract more information from the data as long as the assumption of smoothing is reasonable and (2) by being able to provide analyses that are both flexible and robust. Many different algorithms are used in smoothing. Compared to curve fitting Smoothing may be distinguished from the related and partially overlapping concept of curve fitting in the following ways: * curve fitting often involves the use of an explicit functio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bigram
A bigram or digram is a sequence of two adjacent elements from a string of tokens, which are typically letters, syllables, or words. A bigram is an ''n''-gram for ''n''=2. The frequency distribution of every bigram in a string is commonly used for simple statistical analysis of text in many applications, including in computational linguistics, cryptography, and speech recognition. ''Gappy bigrams'' or ''skipping bigrams'' are word pairs which allow gaps (perhaps avoiding connecting words, or allowing some simulation of dependencies, as in a dependency grammar). Applications Bigrams, along with other n-grams, are used in most successful language models for speech recognition. Bigram frequency attacks can be used in cryptography to solve cryptograms. See frequency analysis. Bigram frequency is one approach to statistical language identification. Some activities in logology or recreational linguistics involve bigrams. These include attempts to find English words beginning wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
San Francisco
San Francisco, officially the City and County of San Francisco, is a commercial, Financial District, San Francisco, financial, and Culture of San Francisco, cultural center of Northern California. With a population of 827,526 residents as of 2024, San Francisco is the List of California cities by population, fourth-most populous city in the U.S. state of California and the List of United States cities by population, 17th-most populous in the United States. San Francisco has a land area of at the upper end of the San Francisco Peninsula and is the County statistics of the United States, fifth-most densely populated U.S. county. Among U.S. cities proper with over 250,000 residents, San Francisco is ranked first by per capita income and sixth by aggregate income as of 2023. San Francisco anchors the Metropolitan statistical area#United States, 13th-most populous metropolitan statistical area in the U.S., with almost 4.6 million residents in 2023. The larger San Francisco Bay Area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Text Corpus
In linguistics and natural language processing, a corpus (: corpora) or text corpus is a dataset, consisting of natively digital and older, digitalized, language resources, either annotated or unannotated. Annotated, they have been used in corpus linguistics for statistical statistical hypothesis testing, hypothesis testing, checking occurrences or validating linguistic rules within a specific language territory. Overview A corpus may contain texts in a single language (''monolingual corpus'') or text data in multiple languages (''multilingual corpus''). In order to make the corpora more useful for doing linguistic research, they are often subjected to a process known as annotation. An example of annotating a corpus is part-of-speech tagging, or ''POS-tagging'', in which information about each word's part of speech (verb, noun, adjective, etc.) is added to the corpus in the form of ''tags''. Another example is indicating the Lemma (morphology), lemma (base) form of each word ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unigram
An ''n''-gram is a sequence of ''n'' adjacent symbols in particular order. The symbols may be ''n'' adjacent letters (including punctuation marks and blanks), syllables, or rarely whole words found in a language dataset; or adjacent phonemes extracted from a speech-recording dataset, or adjacent base pairs extracted from a genome. They are collected from a text corpus or speech corpus. If Latin numerical prefixes are used, then ''n''-gram of size 1 is called a "unigram", size 2 a "bigram" (or, less commonly, a "digram") etc. If, instead of the Latin ones, the English cardinal numbers are furtherly used, then they are called "four-gram", "five-gram", etc. Similarly, using Greek numerical prefixes such as "monomer", "dimer", "trimer", "tetramer", "pentamer", etc., or English cardinal numbers, "one-mer", "two-mer", "three-mer", etc. are used in computational biology, for polymers or oligomers of a known size, called ''k''-mers. When the items are words, -grams may also be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Translate
Google Translate is a multilingualism, multilingual neural machine translation, neural machine translation service developed by Google to translation, translate text, documents and websites from one language into another. It offers a web application, website interface, a mobile app for Android (operating system), Android and iOS, as well as an API that helps developers build browser extensions and application software, software applications. As of , Google Translate supports languages and language varieties at various levels. It served over 200 million people daily in May 2013, and over 500 million total users , with more than 100 billion words translated daily. Launched in April 2006 as a statistical machine translation service, it originally used United Nations and European Parliament documents and transcripts to gather linguistic data. Rather than translating languages directly, it first translated text to English and then pivoted to the target language in most of the langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MapReduce
MapReduce is a programming model and an associated implementation for processing and generating big data sets with a parallel and distributed algorithm on a cluster. A MapReduce program is composed of a ''map'' procedure, which performs filtering and sorting (such as sorting students by first name into queues, one queue for each name), and a '' reduce'' method, which performs a summary operation (such as counting the number of students in each queue, yielding name frequencies). The "MapReduce System" (also called "infrastructure" or "framework") orchestrates the processing by marshalling the distributed servers, running the various tasks in parallel, managing all communications and data transfers between the various parts of the system, and providing for redundancy and fault tolerance. The model is a specialization of the ''split-apply-combine'' strategy for data analysis. It is inspired by the map and reduce functions commonly used in functional programming,"Our abstracti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Methods
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
