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| {{Distinguish|engram}}
| | Singapore has increased a tax on foreign property patrons as part of new temporary measures to cool its residential housing market which has seen continued robust demand regardless of previous efforts to curb costs.<br><br>There is no such thing as a double taxation here. Property tax is imposed primarily based on property ownership. It is different from income tax on the rental earnings, which [http://god-i.es/blog/view/66733/new-launch-apartmentnew-apartmentnew-launch-properties-new-launchlanded god-i.es] is a tax on the earnings which an individual earns. It's free, and you will robotically obtain property market updates, the most recent real property developments, new pointers and insurance policies, and many extra. Find out more At the identical time, monetary institutions have been lengthening the tenures of residential property loans. Over the last three years, the typical tenure for brand new residential property loans has increased from 25 to 29 years. Greater than forty five% of latest residential property loans granted by financial institutions have tenures exceeding 30 years. Pasir Ris, Simei, Tampines Rent Property District 19 Related Articles<br><br>One of the pitfalls is that the heir, who is probably not a surviving co-tenant, could also be disinterested in holding on to the property. The remaining co-tenants might object to the property being bought off and drive the heir to file a partition motion whereby the court docket is entrusted with the duty of distributing the proceeds of the property that is offered as per courtroom orders. Submitting a partition action or shopping for out tenants will result in dissolution of the present arrangement of holding property.<br><br>Additionally notice that your lender could ask you to pay off some of the excellent mortgage ought to the worth of your property fall and the original mortgage to value ratio is exceeded. You might have to be prepared to dip into your financial savings for this purpose. Nevertheless, in case you are 55 years and above when the Valuation Restrict is reached, it's possible you'll use the surplus CPF Atypical Account financial savings to repay the housing loan after setting apart your Minimum Sum money part shortfall. Do check with the HDB Website to understand how CPF guidelines will have an effect on your skill to make the mortgage repayments when you turn fifty five. Frank Hu, an agent listed in Soufun.com's U.S. web site, focuses on promoting land in Colorado and Hawaii because the entry-level funding is much decrease at $10,000 to $20,000.<br><br>Mortgages can be obtained for buy of all freehold properties and a few leasehold properties relying upon the usage and the unexpired lease term. New leasehold residential properties which generally come with ninety nine years leasehold should not be a problem. Banks could also be unwilling to give loans for residential properties with less than 60 years unexpired lease. Condominiums are a well-liked alternative with each expatriates and locals. The huge vary of amenities, from swimming pool and fitness center to round-the-clock safety and scenic surroundings, present for a snug life-style, particularly for households. For an inventory of condominiums, click right here Signal a list itemizing of all the gadgets supplied by the owner, together with their condition. Housing loan repayments<br><br>Finally, homeowners at the moment are left with a choice of holding onto the property and paying significantly increased interest rates or promoting their unit. Taking a look at how way more an proprietor should pay to take care of his unit, it is positively conceivable that those that had stretched themselves will contemplate promoting their units to minimise their monetary pressure. Naturally, the subsequent question is whether there are nonetheless property buyers in the market and what number of there are.<br><br>To reply that question, allow us to check out the house possession fee for Singaporeans and Singapore Residents. Based on knowledge from the department of statistics, it can be seen that the house possession charge in 2012 is 90.1%. In different words, 9 out of 10 Singaporeans and Singapore residents personal at the least one property (i.e. their house). Only one out of 10 do not presently own their house and can potentially still purchase properties with out much restrictions. |
| {{For|Google phrase-usage graphs|Google Ngram Viewer}}
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| {{More footnotes|date=February 2011}}
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| {{DISPLAYTITLE:''n''-gram}}
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| In the fields of [[computational linguistics]] and [[probability]], an '''''n''-gram''' is a contiguous sequence of ''n'' items from a given [[sequence]] of text or speech. The items can be [[phoneme]]s, [[syllable]]s, [[letter (alphabet)|letter]]s, [[word]]s or [[base pairs]] according to the application. The ''n''-grams typically are collected from a [[text corpus|text]] or [[speech corpus]].
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| An ''n''-gram of size 1 is referred to as a "unigram"; size 2 is a "[[bigram]]" (or, less commonly, a "digram"); size 3 is a "[[trigram]]". Larger sizes are sometimes referred to by the value of ''n'', e.g., "four-gram", "five-gram", and so on.
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| == Applications ==
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| An '''''n''-gram model''' is a type of probabilistic [[language model]] for predicting the next item in such a sequence in the form of a <math>(n - 1)</math>–order [[Markov chain|Markov model]]. ''n''-gram models are now widely used in [[probability]], [[communication theory]], [[computational linguistics]] (for instance, statistical [[natural language processing]]), [[computational biology]] (for instance, biological [[sequence analysis]]), and [[data compression]]. The two core advantages{{Compared to?|date=November 2011}} of ''n''-gram models (and algorithms that use them) are relative simplicity and the ability to scale up – by simply increasing ''n'' a model can be used to store more context with a well-understood [[space–time tradeoff]], enabling small experiments to scale up very efficiently.
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| ==Examples==
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| {| class="wikitable" style="font-size:85%;"
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| |+ Figure 1 ''n''-gram examples from various disciplines
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| ! Field !! Unit !!Sample sequence !! 1-gram sequence !! 2-gram sequence !! 3-gram sequence
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| |-
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| ! Vernacular name !! !! !! unigram !! bigram !! trigram
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| |-
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| ! Order of resulting [[Markov model]] !! !! !! 0 !! 1 !! 2
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| |-
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| | [[Protein sequencing]] || [[amino acid]] || … Cys-Gly-Leu-Ser-Trp … || …, Cys, Gly, Leu, Ser, Trp, … || …, Cys-Gly, Gly-Leu, Leu-Ser, Ser-Trp, … || …, Cys-Gly-Leu, Gly-Leu-Ser, Leu-Ser-Trp, …
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| | [[DNA sequencing]]|| [[base pair]] || …AGCTTCGA… || …, A, G, C, T, T, C, G, A, … || …, AG, GC, CT, TT, TC, CG, GA, … || …, AGC, GCT, CTT, TTC, TCG, CGA, …
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| | [[Computational linguistics]] || [[Character (computing)|character]] || …to_be_or_not_to_be… || …, t, o, _, b, e, _, o, r, _, n, o, t, _, t, o, _, b, e, … || …, to, o_, _b, be, e_, _o, or, r_, _n, no, ot, t_, _t, to, o_, _b, be, … || …, to_, o_b, _be, be_, e_o, _or, or_, r_n, _no, not, ot_, t_t, _to, to_, o_b, _be, …
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| | [[Computational linguistics]] ||[[word]] || … to be or not to be … || …, to, be, or, not, to, be, … || …, to be, be or, or not, not to, to be, … || …, to be or, be or not, or not to, not to be, …
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| |}
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| Figure 1 shows several example sequences and the corresponding 1-gram, 2-gram and 3-gram sequences.
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| Here are further examples; these are word-level 3-grams and 4-grams (and counts of the number of times they appeared) from the Google ''n''-gram corpus.<ref>
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| {{cite web
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| |author= Alex Franz and Thorsten Brants
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| |title=All Our N-gram are Belong to You
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| |year=2006
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| |work=Google Research Blog
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| |url=http://googleresearch.blogspot.com/2006/08/all-our-n-gram-are-belong-to-you.html
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| |accessdate=2011-12-16
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| }}</ref>
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| *ceramics collectables collectibles (55)
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| *ceramics collectables fine (130)
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| *ceramics collected by (52)
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| *ceramics collectible pottery (50)
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| *ceramics collectibles cooking (45)
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| 4-grams
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| *serve as the incoming (92)
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| *serve as the incubator (99)
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| *serve as the independent (794)
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| *serve as the index (223)
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| *serve as the indication (72)
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| *serve as the indicator (120)
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| ==''n''-gram models==
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| An '''''n''-gram model''' models sequences, notably natural languages, using the statistical properties of ''n''-grams.
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| This idea can be traced to an experiment by [[Claude Shannon]]'s work in [[information theory]]. Shannon posed the question: given a sequence of letters (for example, the sequence "for ex"), what is the [[likelihood]] of the next letter? From training data, one can derive a [[probability distribution]] for the next letter given a history of size <math>n</math>: ''a'' = 0.4, ''b'' = 0.00001, ''c'' = 0, ....; where the probabilities of all possible "next-letters" sum to 1.0.
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| More concisely, an ''n''-gram model predicts <math>x_{i}</math> based on <math>x_{i-(n-1)}, \dots, x_{i-1}</math>. In probability terms, this is <math>P(x_{i} | x_{i-(n-1)}, \dots, x_{i-1})</math>. When used for [[language model]]ing, independence assumptions are made so that each word depends only on the last ''n-1'' words. This [[Markov model]] is used as an approximation of the true underlying language. This assumption is important because it massively simplifies the problem of learning the language model from data. In addition, because of the open nature of language, it is common to group words unknown to the language model together.
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| Note that in a simple n-gram language model, the probability of a word, conditioned on some number of previous words (one word in a bigram model, two words in a trigram model, etc.) can be described as following a [[categorical distribution]] (often imprecisely called a "[[multinomial distribution]]").
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| In practice, the probability distributions are smoothed by assigning non-zero probabilities to unseen words or n-grams; see [[N-gram#Smoothing techniques|smoothing techniques]].
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| ==Applications and considerations==
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| ''n''-gram models are widely used in statistical [[natural language processing]]. In [[speech recognition]], [[phonemes]] and sequences of phonemes are modeled using a ''n''-gram distribution. For parsing, words are modeled such that each ''n''-gram is composed of ''n'' words. For [[language identification]], sequences of [[Character (symbol)|characters]]/[[grapheme]]s (''e.g.'', [[Letter (alphabet)|letters of the alphabet]]) are modeled for different languages.<ref>{{cite journal
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| |author=Ted Dunning
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| |year=1994
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| |title=Statistical Identification of Language
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| |url=http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.1958
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| |publisher= New Mexico State University
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| }} Technical Report MCCS 94-273</ref> For sequences of characters, the 3-grams (sometimes referred to as "trigrams") that can be generated from "good morning" are "goo", "ood", "od ", "d m", " mo", "mor" and so forth (sometimes the beginning and end of a text are modeled explicitly, adding "__g", "_go", "ng_", and "g__"). For sequences of words, the trigrams that can be generated from "the dog smelled like a skunk" are "# the dog", "the dog smelled", "dog smelled like", "smelled like a", "like a skunk" and "a skunk #". Some practitioners preprocess strings to remove spaces, most simply collapse [[Whitespace character|whitespace]] to a single space while preserving paragraph marks. Punctuation is also commonly reduced or removed by preprocessing. ''n''-grams can also be used for sequences of words or almost any type of data. For example, they have been used for extracting features for clustering large sets of satellite earth images and for determining what part of the Earth a particular image came from.<ref>Soffer, A., "Image categorization using texture features," Document Analysis and Recognition, 1997., Proceedings of the Fourth International Conference on , vol.1, no., pp.233,237 vol.1, 18-20 Aug 1997 doi: 10.1109/ICDAR.1997.619847</ref> They have also been very successful as the first pass in genetic sequence search and in the identification of the species from which short sequences of DNA originated.<ref>Andrija Tomović, Predrag Janičić, Vlado Kešelj, n-Gram-based classification and unsupervised hierarchical clustering of genome sequences, Computer Methods and Programs in Biomedicine, Volume 81, Issue 2, February 2006, Pages 137-153, ISSN 0169-2607, http://dx.doi.org/10.1016/j.cmpb.2005.11.007.</ref>
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| ''n''-gram models are often criticized because they lack any explicit representation of long range dependency. (In fact, it was [[Noam Chomsky|Chomsky]]'s critique of [[Markov model]]s in the late 1950s that caused their virtual disappearance from [[natural language processing]], along with statistical methods in general, until well into the 1980s.) This is because the only explicit dependency range is (''n''-1) tokens for an ''n''-gram model, and since natural languages incorporate many cases of unbounded dependencies (such as [[wh-movement]]), this means that an ''n''-gram model cannot in principle distinguish unbounded dependencies from noise (since long range correlations drop exponentially with distance for any Markov model). For this reason, ''n''-gram models have not made much impact on linguistic theory, where part of the explicit goal is to model such dependencies.
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| Another criticism that has been made is that Markov models of language, including n-gram models, do not explicitly capture the performance/competence distinction discussed by Chomsky. This is because n-gram models are not designed to model linguistic knowledge as such, and make no claims to being (even potentially) complete models of linguistic knowledge; instead, they are used in practical applications.
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| In practice, n-gram models have been shown to be extremely effective in modeling language data, which is a core component in modern statistical [[natural language processing|language]] applications.
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| Most modern applications that rely on n-gram based models, such as [[machine translation]] applications, do not rely exclusively on such models; instead, they typically also incorporate [[Bayesian inference]]. Modern statistical models are typically made up of two parts, a [[prior distribution]] describing the inherent likelihood of a possible result and a [[likelihood function]] used to assess the compatibility of a possible result with observed data. When a language model is used, it is used as part of the prior distribution (e.g. to gauge the inherent "goodness" of a possible translation), and even then it is often not the only component in this distribution. Handcrafted features of various sorts are also used, for example variables that represent the position of a word in a sentence or the general topic of discourse. In addition, features based on the structure of the potential result, such as syntactic considerations, are often used. Such features are also used as part of the likelihood function, which makes use of the observed data. Conventional linguistic theory can be incorporated in these features (although in practice, it is rare that features specific to generative or other particular theories of grammar are incorporated, as [[computational linguistics|computational linguists]] tend to be "agnostic" towards individual theories of grammar{{Citation needed|date=November 2011}}).
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| ==''n''-grams for approximate matching==
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| {{main|Approximate string matching}}
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| ''n''-grams can also be used for efficient approximate matching. By converting a sequence of items to a set of ''n''-grams, it can be embedded in a [[vector space]], thus allowing the sequence to be compared to other sequences in an efficient manner. For example, if we convert strings with only letters in the English alphabet into 3-grams, we get a <math>26^3</math>-dimensional space (the first dimension measures the number of occurrences of "aaa", the second "aab", and so forth for all possible combinations of three letters). Using this representation, we lose information about the string. For example, both the strings "abc" and "bca" give rise to exactly the same 2-gram "bc" (although {"ab", "bc"} is clearly not the same as {"bc", "ca"}). However, we know empirically that if two strings of real text have a similar vector representation (as measured by [[cosine similarity|cosine distance]]) then they are likely to be similar. Other metrics have also been applied to vectors of ''n''-grams with varying, sometimes better, results. For example [[z-score]]s have been used to compare documents by examining how many standard deviations each ''n''-gram differs from its mean occurrence in a large collection, or [[text corpus]], of documents (which form the "background" vector). In the event of small counts, the [[g-score]] may give better results for comparing alternative models.
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| It is also possible to take a more principled approach to the statistics of ''n''-grams, modeling similarity as the likelihood that two strings came from the same source directly in terms of a problem in [[Bayesian inference]].
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| ''n''-gram-based searching can also be used for [[plagiarism detection]].
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| ==Other applications==
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| ''n''-grams find use in several areas of computer science, [[computational linguistics]], and applied mathematics.
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| They have been used to:
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| * design [[kernel trick|kernels]] that allow [[machine learning]] algorithms such as [[support vector machine]]s to learn from string data
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| * find likely candidates for the correct spelling of a misspelled word
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| * improve compression in [[data compression|compression algorithms]] where a small area of data requires ''n''-grams of greater length
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| * assess the probability of a given word sequence appearing in text of a language of interest in pattern recognition systems, [[speech recognition]], OCR ([[optical character recognition]]), [[Intelligent Character Recognition]] ([[Intelligent character recognition|ICR]]), [[machine translation]] and similar applications
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| * improve retrieval in [[information retrieval]] systems when it is hoped to find similar "documents" (a term for which the conventional meaning is sometimes stretched, depending on the data set) given a single query document and a database of reference documents
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| * improve retrieval performance in genetic sequence analysis as in the [[BLAST]] family of programs
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| * identify the language a text is in or the species a small sequence of DNA was taken from
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| * predict letters or words at random in order to create text, as in the [[dissociated press]] algorithm.
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| == Bias-versus-variance trade-off ==
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| What goes into picking the ''n'' for the ''n''-gram?
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| With ''n''-gram models it is necessary to find the right trade off between the stability of the estimate against its appropriateness. This means that trigram (i.e. triplets of words) is a common choice with large training corpora (millions of words), whereas a bigram is often used with smaller ones.
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| === Smoothing techniques ===
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| There are problems of balance weight between ''infrequent grams'' (for example, if a proper name appeared in the training data) and ''frequent grams''. Also, items not seen in the training data will be given a [[probability]] of 0.0 without [[smoothing]]. For unseen but plausible data from a sample, one can introduce [[pseudocount]]s. Pseudocounts are generally motivated on Bayesian grounds.
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| In practice it is necessary to ''smooth'' the probability distributions by also assigning non-zero probabilities to unseen words or n-grams. The reason is that models derived directly from the n-gram frequency counts have severe problems when confronted with any n-grams that have not explicitly been seen before -- [[PPM compression algorithm|the zero-frequency problem]]. Various smoothing methods are used, from simple "add-one" (Laplace) smoothing (assign a count of 1 to unseen n-grams; see [[Rule of succession]]) to more sophisticated models, such as [[Good-Turing discounting]] or [[Katz's back-off model|back-off model]]s. Some of these methods are equivalent to assigning a [[prior distribution]] to the probabilities of the N-grams and using [[Bayesian inference]] to compute the resulting [[posterior distribution|posterior]] N-gram probabilities. However, the more sophisticated smoothing models were typically not derived in this fashion, but instead through independent considerations.
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| * [[Linear interpolation]] (e.g., taking the [[weighted mean]] of the unigram, bigram, and trigram)
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| * [[Good-Turing]] discounting
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| * [[Witten-Bell discounting]]
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| * [[Additive smoothing|Lidstone's smoothing]]
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| * [[Katz's back-off model]] (trigram)
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| * [[Kneser-Ney smoothing]]
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| == See also ==
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| * [[Collocation]]
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| * [[Hidden Markov model]]
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| * [[n-tuple]]
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| * [[k-mer]]
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| * [[String Kernel]]
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| * [[MinHash]]
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| * [[Feature extraction]]
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| == References ==
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| {{reflist}}
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| * Christopher D. Manning, Hinrich Schütze, ''Foundations of Statistical Natural Language Processing'', MIT Press: 1999. ISBN 0-262-13360-1.
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| * Owen White, Ted Dunning, Granger Sutton, Mark Adams, J.Craig Venter, and Chris Fields. A quality control algorithm for dna sequencing projects. Nucleic Acids Research, 21(16):3829—3838, 1993.
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| * Frederick J. Damerau, ''Markov Models and Linguistic Theory''. Mouton. The Hague, 1971.
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| *{{cite conference |last=Brocardo|first=Marcelo Luiz |coauthors=Issa Traore, Sherif Saad, Isaac Woungang |url=http://www.uvic.ca/engineering/ece/isot/assets/docs/Authorship_Verification_for_Short_Messages_using_Stylometry.pdf |title=Authorship Verification for Short Messages Using Stylometry |conference= IEEE Intl. Conference on Computer, Information and Telecommunication Systems (CITS) |year=2013}}
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| == External links ==
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| * [http://ngrams.googlelabs.com/ Google's Google Book n-gram viewer] and [http://googleresearch.blogspot.com/2006/08/all-our-n-gram-are-belong-to-you.html Web n-grams database] (September 2006)
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| * [http://research.microsoft.com/web-ngram Microsoft's web n-grams service]
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| * [http://www.ngrams.info/ 1,000,000 most frequent 2,3,4,5-grams from the 425 million word [[Corpus of Contemporary American English]]]
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| * [http://www.peachnote.com/ Peachnote's music ngram viewer]
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| * [http://www.w3.org/TR/ngram-spec/ Stochastic Language Models (N-Gram) Specification] (W3C)
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| * [http://www.cs.columbia.edu/~mcollins/courses/nlp2011/notes/lm.pdf Michael Collin's notes on N-Gram Language Models]
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| {{DEFAULTSORT:N-Gram}}
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| [[Category:Natural language processing]]
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| [[Category:Computational linguistics]]
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| [[Category:Speech recognition]]
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| [[Category:Corpus linguistics]]
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| [[Category:Probabilistic models]]
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