939:
725:
743:
551:
1847:-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. However, we know empirically that if two strings of real text have a similar vector representation (as measured by
1745:
934:{\displaystyle P({\text{I, saw, the, red, house}})\approx P({\text{I}}\mid \langle s\rangle ,\langle s\rangle )P({\text{saw}}\mid \langle s\rangle ,I)P({\text{the}}\mid {\text{I, saw}})P({\text{red}}\mid {\text{saw, the}})P({\text{house}}\mid {\text{the, red}})P(\langle /s\rangle \mid {\text{red, house}})}
1772:
when the input includes words which were not present in a system's dictionary or database during its preparation. By default, when a language model is estimated, the entire observed vocabulary is used. In some cases, it may be necessary to estimate the language model with a specific fixed vocabulary.
1304:
448:
Unigram models of different documents have different probabilities of words in it. The probability distributions from different documents are used to generate hit probabilities for each query. Documents can be ranked for a query according to the probabilities. Example of unigram models of two
1912:-gram model, 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.
720:{\displaystyle P({\text{I, saw, the, red, house}})\approx P({\text{I}}\mid \langle s\rangle )P({\text{saw}}\mid {\text{I}})P({\text{the}}\mid {\text{saw}})P({\text{red}}\mid {\text{the}})P({\text{house}}\mid {\text{red}})P(\langle /s\rangle \mid {\text{house}})}
1482:
103:
To prevent a zero probability being assigned to unseen words, each word's probability is slightly lower than its frequency count in a corpus. To calculate it, various methods were used, from simple "add-one" smoothing (assign a count of 1 to unseen
138: = 1, is called a unigram model. Probability of each word in a sequence is independent from probabilities of other word in the sequence. Each word's probability in the sequence is equal to the word's probability in an entire document.
35:. It is based on an assumption that the probability of the next word in a sequence depends only on a fixed size window of previous words. If only one previous word was considered, it was called a bigram model; if two words, a trigram model; if
2267:
1074:
2295:-grams defined by paths in syntactic dependency or constituent trees rather than the linear structure of the text. For example, the sentence "economic news has little effect on financial markets" can be transformed to syntactic
444:
1468:
2895:
264:
2423:
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
382:
2720:
2145:
1022:
2976:
1068:
98:
67:
2018:
2844:
1845:
1740:{\displaystyle P(w_{i}\mid w_{i-(n-1)},\ldots ,w_{i-1})={\frac {\mathrm {count} (w_{i-(n-1)},\ldots ,w_{i-1},w_{i})}{\mathrm {count} (w_{i-(n-1)},\ldots ,w_{i-1})}}}
391:
1998:-gram probabilities. However, the more sophisticated smoothing models were typically not derived in this fashion, but instead through independent considerations.
143:
1299:{\displaystyle P(w_{1},\ldots ,w_{m})=\prod _{i=1}^{m}P(w_{i}\mid w_{1},\ldots ,w_{i-1})\approx \prod _{i=2}^{m}P(w_{i}\mid w_{i-(n-1)},\ldots ,w_{i-1})}
2716:
3024:
2707:
1820:-grams were also used for approximate matching. If we convert strings (with only letters in the English alphabet) into character 3-grams, we get a
340:
2745:
1346:
1788:
Nonetheless, it is essential in some cases to explicitly model the probability of out-of-vocabulary words by introducing a special token (e.g.
2049:-gram language model) faced. Words represented in an embedding vector were not necessarily consecutive anymore, but could leave gaps that are
2337:-grams, defined as fixed-length contiguous overlapping subsequences that are extracted from part-of-speech sequences of text. Part-of-speech
2653:
1323: − 1 words) can be approximated by the probability of observing it in the shortened context window consisting of the preceding
2957:
1868:
2792:
2917:
Sidorov, Grigori; Velasquez, Francisco; Stamatatos, Efstathios; Gelbukh, Alexander; Chanona-Hernández, Liliana (2014). "Syntactic
1792:) into the vocabulary. Out-of-vocabulary words in the corpus are effectively replaced with this special <unk> token before
2685:
Mikolov, Tomas; Chen, Kai; Corrado, Greg; Dean, Jeffrey (2013). "Efficient estimation of word representations in vector space".
2818:
2786:
2396:
assess the probability of a given word sequence appearing in text of a language of interest in pattern recognition systems,
2012:
1882:-grams, modeling similarity as the likelihood that two strings came from the same source directly in terms of a problem in
2762:
Sidorov, Grigori; Velasquez, Francisco; Stamatatos, Efstathios; Gelbukh, Alexander; Chanona-Hernández, Liliana (2013).
2409:
2405:
3001:
1963:. Various smoothing methods were used, from simple "add-one" (Laplace) smoothing (assign a count of 1 to unseen
1755:
2401:
972:
1796:-grams counts are cumulated. With this option, it is possible to estimate the transition probabilities of
2045:
Skip-gram language model is an attempt at overcoming the data sparsity problem that preceding (i.e. word
1972:
1812:
1769:
1027:
113:
72:
3019:
2570:
Wołk, K.; Marasek, K.; Glinkowski, W. (2015). "Telemedicine as a special case of
Machine Translation".
46:
1785:-gram probabilities are smoothed over all the words in the vocabulary even if they were not observed.
2353:
2262:{\displaystyle v(\mathrm {king} )-v(\mathrm {male} )+v(\mathrm {female} )\approx v(\mathrm {queen} )}
1960:
1765:
2839:
2739:
2471:
2034:
2028:
1976:
117:
28:
2631:. Proceedings of the 11th International Workshop on Spoken Language Translation. Tahoe Lake, USA.
2272:
2660:
3029:
2834:
2530:
2372:
2085:
the set of 1-skip-2-grams includes all the bigrams (2-grams), and in addition the subsequences
1992:
954:
Additionally, without an end-of-sentence marker, the probability of an ungrammatical sequence
2428:
2420:
1823:
2585:
2002:
1893:
269:
32:
1947:
the probability distributions by also assigning non-zero probabilities to unseen words or
8:
2868:"Contextual Language Models For Ranking Answers To Natural Language Definition Questions"
2466:
2461:
2413:
1851:) then they are likely to be similar. Other metrics have also been applied to vectors of
109:
2763:
2589:
2434:
identify the language a text is in or the species a small sequence of DNA was taken from
1867:, of documents (which form the "background" vector). In the event of small counts, the
2938:
2887:
2686:
2632:
2609:
2575:
2397:
2315:
2300:
2121:
2023:
1988:
1980:
1968:
1883:
129:
2706:
Mikolov, Tomas; Sutskever, Ilya; Chen, Kai; Corrado irst4=Greg S.; Dean, Jeff (2013).
2597:
2506:
Bengio, Yoshua; Ducharme, Réjean; Vincent, Pascal; Janvin, Christian (March 1, 2003).
335:
Total mass of word probabilities distributed across the document's vocabulary, is 1.
43:-gram model. Special tokens were introduced to denote the start and end of a sentence
2942:
2883:
2867:
2782:
2601:
2438:
1848:
2891:
2613:
2930:
2879:
2774:
2593:
2386:
2368:
2125:
1859:
have been used to compare documents by examining how many standard deviations each
1764:-gram language models are out-of-vocabulary (OOV) words. They are encountered in
1332:
2778:
2629:
Polish-English Speech
Statistical Machine Translation Systems for the IWSLT 2014
272:. Words with their probabilities in a document can be illustrated as follows.
2934:
2507:
2310:-grams are intended to reflect syntactic structure more faithfully than linear
439:{\displaystyle P({\text{query}})=\prod _{\text{word in query}}P({\text{word}})}
951:-grams is filled with start-of-sentence markers, typically denoted <s>.
3013:
2823:-grams in Rule Based Automatic English as Second Language Grammar Correction"
2486:
2444:
2006:
2529:
Jurafsky, Dan; Martin, James H. (7 January 2023). "N-gram
Language Models".
2314:-grams, and have many of the same applications, especially as features in a
2271:
where ≈ is made precise by stipulating that its right-hand side must be the
1878:
It is also possible to take a more principled approach to the statistics of
2709:
Distributed
Representations of Words and Phrases and their Compositionality
2605:
2364:
1463:{\displaystyle P(w_{i}\mid w_{i-(n-1)},\ldots ,w_{i-1})=P(w_{2}\mid w_{1})}
2341:-grams have several applications, most commonly in information retrieval.
2705:
2456:
2379:
1937:
1929:
1864:
1778:
259:{\displaystyle P_{\text{uni}}(t_{1}t_{2}t_{3})=P(t_{1})P(t_{2})P(t_{3}).}
2120:
In skip-gram model, semantic relations between words are represented by
2322:-grams for certain tasks gives better results than the use of standard
2921:-Grams as Machine Learning Features for Natural Language Processing".
2437:
predict letters or words at random in order to create text, as in the
2427:
improve retrieval performance in genetic sequence analysis as in the
1955:-gram frequency counts have severe problems when confronted with any
1933:
27:
is a purely statistical model of language. It has been superseded by
2773:. Lecture Notes in Computer Science. Vol. 7630. pp. 1–11.
2556:
Christopher D. Manning, Prabhakar
Raghavan, Hinrich Schütze (2009).
2827:
International
Journal of Computational Linguistics and Applications
2637:
2580:
2691:
1924:(for example, if a proper name appeared in the training data) and
2916:
2761:
2481:
2476:
1936:. For unseen but plausible data from a sample, one can introduce
1863:-gram differs from its mean occurrence in a large collection, or
1856:
542: = 2) language model, the probability of the sentence
386:
The probability generated for a specific query is calculated as
3002:
Method for rule-based correction of spelling and grammar errors
2764:"Syntactic Dependency-Based N-grams as Classification Features"
1872:
1928:. Also, items not seen in the training data will be given a
2303:: news-economic, effect-little, effect-on-markets-financial.
1951:-grams. The reason is that models derived directly from the
1940:. Pseudocounts are generally motivated on Bayesian grounds.
1855:-grams with varying, sometimes better, results. For example,
377:{\displaystyle \sum _{\text{word in doc}}P({\text{word}})=1}
2505:
2068:
subsequence where the components occur at distance at most
1781:
that contain an out-of-vocabulary word are ignored. The
958:
would always be higher than that of the longer sentence
1979:. Some of these methods are equivalent to assigning a
268:
The model consists of units, each treated as one-state
2684:
2352:-grams find use in several areas of computer science,
2569:
2148:
1826:
1485:
1349:
1077:
1030:
975:
746:
738: = 3) language model, the approximation is
554:
394:
343:
146:
75:
49:
1308:
It is assumed that the probability of observing the
969:
The approximation method calculates the probability
2955:
2626:
1959:-grams that have not explicitly been seen before –
1803:
1473:The conditional probability can be calculated from
1319:(in the context window consisting of the preceding
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1839:
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1462:
1298:
1062:
1016:
933:
719:
438:
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92:
61:
2717:Advances in Neural Information Processing Systems
2326:-grams, for example, for authorship attribution.
1899:
3011:
2865:
2699:
2528:
2651:
1920:There are problems of balance weight between
31:–based models, which have been superseded by
2956:Lioma, C.; van Rijsbergen, C. J. K. (2008).
2866:Figueroa, Alejandro; Atkinson, John (2012).
2518:: 1137–1155 – via ACM Digital Library.
917:
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2769:. In Batyrshin, I.; Mendoza, M. G. (eds.).
2744:: CS1 maint: numeric names: authors list (
2299:-grams following the tree structure of its
2080:the rain in Spain falls mainly on the plain
2040:
2560:. pp. 237–240. Cambridge University Press.
1800:-grams involving out-of-vocabulary words.
1749:
2838:
2690:
2636:
2579:
2572:Computerized Medical Imaging and Graphics
2558:An Introduction to Information Retrieval
2512:The Journal of Machine Learning Research
1971:) to more sophisticated models, such as
1892:-gram-based searching was also used for
112:) to more sophisticated models, such as
3025:Statistical natural language processing
2816:
2508:"A neural probabilistic language model"
2128:. For example, in some such models, if
1915:
964:
3012:
2771:Advances in Computational Intelligence
2678:
2654:"A Closer Look at Skip-gram Modelling"
1017:{\displaystyle P(w_{1},\ldots ,w_{m})}
2757:
2755:
2344:
2275:of the value of the left-hand side.
2969:French Review of Applied Linguistics
2898:from the original on 27 October 2021
2726:from the original on 29 October 2020
2389:where a small area of data requires
2278:
2009:of the unigram, bigram, and trigram)
16:Purely statistical model of language
2847:from the original on 7 October 2021
2652:David Guthrie; et al. (2006).
1063:{\displaystyle w_{1},\ldots ,w_{m}}
943:Note that the context of the first
13:
2982:from the original on 13 March 2018
2798:from the original on 8 August 2017
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93:{\displaystyle \langle /s\rangle }
14:
3041:
2962:-Grams and Information Retrieval"
2598:10.1016/j.compmedimag.2015.09.005
2522:
2406:Intelligent Character Recognition
2132:is the function that maps a word
62:{\displaystyle \langle s\rangle }
2923:Expert Systems with Applications
2884:10.1111/j.1467-8640.2012.00426.x
2075:For example, in the input text:
1943:In practice it was necessary to
729:
123:
2994:
2949:
2910:
2859:
2810:
2378:find likely candidates for the
2140:-d vector representation, then
1807:-grams for approximate matching
1756:Statistical machine translation
533:
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2620:
2563:
2550:
2532:Speech and Language Processing
2499:
2256:
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1900:Bias-versus-variance trade-off
1731:
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1489:
1477:-gram model frequency counts:
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1:
2492:
2402:optical character recognition
2819:"Syntactic Dependency-Based
2627:Wołk K., Marasek K. (2014).
2538:(3rd edition draft ed.)
1983:to the probabilities of the
7:
2779:10.1007/978-3-642-37798-3_1
2450:
2356:, and applied mathematics.
1813:Approximate string matching
1770:natural language processing
10:
3046:
2935:10.1016/j.eswa.2013.08.015
2872:Computational Intelligence
2333:-grams are part-of-speech
2329:Another type of syntactic
1961:the zero-frequency problem
1810:
1753:
1024:of observing the sentence
127:
2817:Sidorov, Grigori (2013).
2375:to learn from string data
2354:computational linguistics
1991:to compute the resulting
1766:computational linguistics
39: − 1 words, an
2472:Longest common substring
2416:and similar applications
2393:-grams of greater length
2359:They have been used to:
2041:Skip-gram language model
1773:In such a scenario, the
461:Its probability in Doc2
29:recurrent neural network
2385:improve compression in
2373:support vector machines
2019:Witten–Bell discounting
1973:Good–Turing discounting
1875:) gave better results.
1750:Out-of-vocabulary words
1343: = 2 we have
755:I, saw, the, red, house
563:I, saw, the, red, house
458:Its probability in Doc1
281:Its probability in doc
114:Good–Turing discounting
2719:. pp. 3111–3119.
2387:compression algorithms
2263:
2124:, capturing a form of
1904:To choose a value for
1841:
1840:{\displaystyle 26^{3}}
1741:
1464:
1327: − 1 words (
1300:
1220:
1139:
1064:
1018:
935:
721:
440:
378:
260:
134:A special case, where
94:
63:
3000:U.S. Patent 6618697,
2421:information retrieval
2419:improve retrieval in
2264:
2029:Katz's back-off model
1842:
1742:
1465:
1301:
1200:
1119:
1065:
1019:
936:
722:
441:
379:
261:
95:
64:
33:large language models
2382:of a misspelled word
2301:dependency relations
2146:
2035:Kneser–Ney smoothing
2024:Lidstone's smoothing
2003:Linear interpolation
1916:Smoothing techniques
1894:plagiarism detection
1824:
1760:An issue when using
1483:
1347:
1075:
1028:
973:
965:Approximation method
960:I saw the red house.
744:
552:
392:
341:
144:
73:
47:
25:-gram language model
2590:2015arXiv151004600W
2574:. 46 Pt 2: 249–56.
2467:Hidden Markov model
2462:Feature engineering
2414:machine translation
2371:algorithms such as
2122:linear combinations
1339: = 3 and
1335:). To clarify, for
546:is approximated as
544:I saw the red house
110:uninformative prior
2990:– via Cairn.
2431:family of programs
2398:speech recognition
2345:Other applications
2316:vector space model
2259:
2064:-gram is a length-
2005:(e.g., taking the
1989:Bayesian inference
1981:prior distribution
1969:Rule of succession
1884:Bayesian inference
1837:
1737:
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931:
717:
538:In a bigram word (
436:
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374:
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256:
130:Bag-of-words model
90:
59:
3020:Language modeling
2788:978-3-642-37797-6
2439:dissociated press
2072:from each other.
1987:-grams and using
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2958:"Part of Speech
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2659:. Archived from
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2380:correct spelling
2369:machine learning
2273:nearest neighbor
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2126:compositionality
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2740:cite conference
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2535:
2527:
2523:
2504:
2500:
2495:
2453:
2347:
2285:
2239:
2207:
2181:
2155:
2147:
2144:
2143:
2137:
2133:
2129:
2069:
2065:
2061:
2057:
2043:
1977:back-off models
1932:of 0.0 without
1918:
1902:
1871:(also known as
1849:cosine distance
1831:
1827:
1825:
1822:
1821:
1815:
1809:
1758:
1752:
1719:
1715:
1682:
1678:
1658:
1657:
1647:
1643:
1628:
1624:
1591:
1587:
1567:
1566:
1564:
1546:
1542:
1509:
1505:
1496:
1492:
1484:
1481:
1480:
1451:
1447:
1438:
1434:
1410:
1406:
1373:
1369:
1360:
1356:
1348:
1345:
1344:
1333:Markov property
1317:
1281:
1277:
1244:
1240:
1231:
1227:
1215:
1204:
1182:
1178:
1163:
1159:
1150:
1146:
1134:
1123:
1107:
1103:
1088:
1084:
1076:
1073:
1072:
1054:
1050:
1035:
1031:
1029:
1026:
1025:
1005:
1001:
986:
982:
974:
971:
970:
967:
947: – 1
923:
909:
892:
884:
870:
862:
848:
840:
808:
770:
753:
745:
742:
741:
732:
709:
695:
678:
670:
656:
648:
634:
626:
612:
604:
578:
561:
553:
550:
549:
536:
428:
416:
401:
393:
390:
389:
360:
348:
342:
339:
338:
270:finite automata
244:
240:
225:
221:
206:
202:
184:
180:
174:
170:
164:
160:
151:
147:
145:
142:
141:
132:
126:
118:back-off models
79:
74:
71:
70:
48:
45:
44:
17:
12:
11:
5:
3043:
3033:
3032:
3027:
3022:
3006:
3005:
2993:
2948:
2929:(3): 853–860.
2909:
2878:(4): 528–548.
2858:
2840:10.1.1.644.907
2833:(2): 169–188.
2809:
2787:
2751:
2698:
2677:
2666:on 17 May 2017
2644:
2619:
2562:
2549:
2521:
2497:
2496:
2494:
2491:
2490:
2489:
2484:
2479:
2474:
2469:
2464:
2459:
2452:
2449:
2448:
2447:
2442:
2435:
2432:
2425:
2417:
2394:
2383:
2376:
2346:
2343:
2284:
2277:
2258:
2254:
2251:
2248:
2245:
2242:
2238:
2235:
2232:
2229:
2225:
2222:
2219:
2216:
2213:
2210:
2206:
2203:
2200:
2197:
2193:
2190:
2187:
2184:
2180:
2177:
2174:
2171:
2167:
2164:
2161:
2158:
2154:
2151:
2118:
2117:
2083:
2082:
2042:
2039:
2038:
2037:
2032:
2026:
2021:
2016:
2010:
1926:frequent grams
1917:
1914:
1901:
1898:
1834:
1830:
1811:Main article:
1808:
1802:
1777:-grams in the
1754:Main article:
1751:
1748:
1733:
1728:
1725:
1722:
1718:
1714:
1711:
1708:
1703:
1700:
1697:
1694:
1691:
1688:
1685:
1681:
1677:
1673:
1670:
1667:
1664:
1661:
1655:
1650:
1646:
1642:
1637:
1634:
1631:
1627:
1623:
1620:
1617:
1612:
1609:
1606:
1603:
1600:
1597:
1594:
1590:
1586:
1582:
1579:
1576:
1573:
1570:
1563:
1560:
1555:
1552:
1549:
1545:
1541:
1538:
1535:
1530:
1527:
1524:
1521:
1518:
1515:
1512:
1508:
1504:
1499:
1495:
1491:
1488:
1459:
1454:
1450:
1446:
1441:
1437:
1433:
1430:
1427:
1424:
1419:
1416:
1413:
1409:
1405:
1402:
1399:
1394:
1391:
1388:
1385:
1382:
1379:
1376:
1372:
1368:
1363:
1359:
1355:
1352:
1315:
1295:
1290:
1287:
1284:
1280:
1276:
1273:
1270:
1265:
1262:
1259:
1256:
1253:
1250:
1247:
1243:
1239:
1234:
1230:
1226:
1223:
1218:
1213:
1210:
1207:
1203:
1199:
1196:
1191:
1188:
1185:
1181:
1177:
1174:
1171:
1166:
1162:
1158:
1153:
1149:
1145:
1142:
1137:
1132:
1129:
1126:
1122:
1118:
1115:
1110:
1106:
1102:
1099:
1096:
1091:
1087:
1083:
1080:
1057:
1053:
1049:
1046:
1043:
1038:
1034:
1013:
1008:
1004:
1000:
997:
994:
989:
985:
981:
978:
966:
963:
930:
922:
919:
916:
912:
908:
905:
902:
899:
891:
883:
880:
877:
869:
861:
858:
855:
847:
839:
836:
833:
830:
827:
824:
821:
818:
815:
807:
804:
801:
798:
795:
792:
789:
786:
783:
780:
777:
769:
766:
763:
760:
752:
749:
734:In a trigram (
731:
728:
716:
708:
705:
702:
698:
694:
691:
688:
685:
677:
669:
666:
663:
655:
647:
644:
641:
633:
625:
622:
619:
611:
603:
600:
597:
594:
591:
588:
585:
577:
574:
571:
568:
560:
557:
535:
532:
529:
528:
525:
522:
518:
517:
514:
511:
507:
506:
503:
500:
496:
495:
492:
489:
485:
484:
481:
478:
474:
473:
470:
467:
463:
462:
459:
456:
435:
427:
424:
415:
411:
408:
400:
397:
373:
370:
367:
359:
356:
347:
331:
330:
327:
323:
322:
319:
315:
314:
311:
307:
306:
303:
299:
298:
295:
291:
290:
287:
283:
282:
279:
255:
252:
247:
243:
239:
236:
233:
228:
224:
220:
217:
214:
209:
205:
201:
198:
195:
192:
187:
183:
177:
173:
167:
163:
159:
150:
125:
122:
108:-grams, as an
89:
86:
82:
78:
58:
55:
52:
15:
9:
6:
4:
3:
2:
3042:
3031:
3030:Markov models
3028:
3026:
3023:
3021:
3018:
3017:
3015:
3003:
2997:
2978:
2974:
2970:
2963:
2961:
2952:
2944:
2940:
2936:
2932:
2928:
2924:
2920:
2913:
2897:
2893:
2889:
2885:
2881:
2877:
2873:
2869:
2862:
2846:
2841:
2836:
2832:
2828:
2824:
2822:
2813:
2794:
2790:
2784:
2780:
2776:
2772:
2765:
2758:
2756:
2747:
2741:
2722:
2718:
2711:
2710:
2702:
2693:
2688:
2681:
2662:
2655:
2648:
2639:
2634:
2630:
2623:
2615:
2611:
2607:
2603:
2599:
2595:
2591:
2587:
2582:
2577:
2573:
2566:
2559:
2553:
2534:
2533:
2525:
2517:
2513:
2509:
2502:
2498:
2488:
2487:String kernel
2485:
2483:
2480:
2478:
2475:
2473:
2470:
2468:
2465:
2463:
2460:
2458:
2455:
2454:
2446:
2445:cryptanalysis
2443:
2440:
2436:
2433:
2430:
2426:
2422:
2418:
2415:
2411:
2407:
2403:
2399:
2395:
2392:
2388:
2384:
2381:
2377:
2374:
2370:
2366:
2362:
2361:
2360:
2357:
2355:
2351:
2342:
2340:
2336:
2332:
2327:
2325:
2321:
2317:
2313:
2309:
2304:
2302:
2298:
2294:
2290:
2282:
2276:
2274:
2269:
2233:
2230:
2201:
2198:
2175:
2172:
2149:
2141:
2127:
2123:
2115:
2111:
2107:
2103:
2099:
2095:
2091:
2088:
2087:
2086:
2081:
2078:
2077:
2076:
2073:
2054:
2052:
2048:
2036:
2033:
2030:
2027:
2025:
2022:
2020:
2017:
2014:
2011:
2008:
2007:weighted mean
2004:
2001:
2000:
1999:
1997:
1994:
1990:
1986:
1982:
1978:
1974:
1970:
1966:
1962:
1958:
1954:
1950:
1946:
1941:
1939:
1935:
1931:
1927:
1923:
1913:
1911:
1907:
1897:
1895:
1891:
1887:
1885:
1881:
1876:
1874:
1870:
1866:
1862:
1858:
1854:
1850:
1832:
1828:
1819:
1814:
1806:
1801:
1799:
1795:
1791:
1786:
1784:
1780:
1776:
1771:
1767:
1763:
1757:
1747:
1726:
1723:
1720:
1716:
1712:
1709:
1706:
1698:
1695:
1692:
1686:
1683:
1679:
1648:
1644:
1640:
1635:
1632:
1629:
1625:
1621:
1618:
1615:
1607:
1604:
1601:
1595:
1592:
1588:
1561:
1553:
1550:
1547:
1543:
1539:
1536:
1533:
1525:
1522:
1519:
1513:
1510:
1506:
1502:
1497:
1493:
1486:
1478:
1476:
1471:
1452:
1448:
1444:
1439:
1435:
1428:
1425:
1417:
1414:
1411:
1407:
1403:
1400:
1397:
1389:
1386:
1383:
1377:
1374:
1370:
1366:
1361:
1357:
1350:
1342:
1338:
1334:
1330:
1326:
1322:
1318:
1311:
1306:
1288:
1285:
1282:
1278:
1274:
1271:
1268:
1260:
1257:
1254:
1248:
1245:
1241:
1237:
1232:
1228:
1221:
1216:
1211:
1208:
1205:
1201:
1197:
1189:
1186:
1183:
1179:
1175:
1172:
1169:
1164:
1160:
1156:
1151:
1147:
1140:
1135:
1130:
1127:
1124:
1120:
1116:
1108:
1104:
1100:
1097:
1094:
1089:
1085:
1078:
1070:
1055:
1051:
1047:
1044:
1041:
1036:
1032:
1006:
1002:
998:
995:
992:
987:
983:
976:
962:
961:
957:
952:
950:
946:
941:
920:
914:
910:
900:
889:
878:
867:
856:
845:
834:
828:
825:
819:
813:
802:
793:
787:
781:
775:
764:
761:
747:
739:
737:
730:Trigram model
727:
706:
700:
696:
686:
675:
664:
653:
642:
631:
620:
609:
598:
589:
583:
572:
569:
555:
547:
545:
541:
526:
523:
520:
519:
515:
512:
509:
508:
504:
501:
498:
497:
493:
490:
487:
486:
482:
479:
476:
475:
471:
468:
465:
464:
460:
457:
454:
453:
450:
446:
422:
418:word in query
413:
409:
395:
387:
384:
371:
368:
354:
345:
336:
328:
325:
324:
320:
317:
316:
312:
309:
308:
304:
301:
300:
296:
293:
292:
288:
285:
284:
280:
277:
276:
273:
271:
266:
253:
245:
241:
234:
226:
222:
215:
207:
203:
196:
193:
185:
181:
175:
171:
165:
161:
148:
139:
137:
131:
124:Unigram model
121:
119:
115:
111:
107:
101:
84:
80:
53:
42:
38:
34:
30:
26:
24:
2996:
2984:. Retrieved
2972:
2968:
2959:
2951:
2926:
2922:
2918:
2912:
2900:. Retrieved
2875:
2871:
2861:
2849:. Retrieved
2830:
2826:
2820:
2812:
2800:. Retrieved
2770:
2728:. Retrieved
2708:
2701:
2680:
2668:. Retrieved
2661:the original
2647:
2628:
2622:
2571:
2565:
2557:
2552:
2540:. Retrieved
2531:
2524:
2515:
2511:
2501:
2390:
2358:
2349:
2348:
2338:
2334:
2330:
2328:
2323:
2319:
2318:. Syntactic
2311:
2307:
2305:
2296:
2292:
2288:
2286:
2280:
2270:
2142:
2119:
2113:
2109:
2105:
2102:Spain mainly
2101:
2097:
2093:
2089:
2084:
2079:
2074:
2056:Formally, a
2055:
2050:
2046:
2044:
1995:
1984:
1967:-grams; see
1964:
1956:
1952:
1948:
1944:
1942:
1938:pseudocounts
1925:
1921:
1919:
1909:
1905:
1903:
1889:
1888:
1879:
1877:
1860:
1852:
1817:
1816:
1804:
1797:
1793:
1789:
1787:
1782:
1774:
1761:
1759:
1479:
1474:
1472:
1340:
1336:
1328:
1324:
1320:
1313:
1309:
1307:
1071:
968:
959:
955:
953:
948:
944:
942:
740:
735:
733:
548:
543:
539:
537:
534:Bigram model
447:
388:
385:
337:
334:
267:
140:
135:
133:
105:
102:
40:
36:
22:
20:
18:
2975:(1): 9–22.
2457:Collocation
2367:that allow
2291:-grams are
2015:discounting
2013:Good–Turing
1930:probability
1865:text corpus
1790:<unk>
449:documents:
350:word in doc
3014:Categories
2638:1509.09097
2581:1510.04600
2493:References
2441:algorithm.
2306:Syntactic
2287:Syntactic
2279:Syntactic
2110:mainly the
2094:rain Spain
956:*I saw the
925:red, house
128:See also:
2943:207738654
2851:7 October
2835:CiteSeerX
2692:1301.3781
2424:documents
2231:≈
2173:−
2031:(trigram)
1993:posterior
1934:smoothing
1724:−
1710:…
1696:−
1687:−
1633:−
1619:…
1605:−
1596:−
1551:−
1537:…
1523:−
1514:−
1503:∣
1445:∣
1415:−
1401:…
1387:−
1378:−
1367:∣
1286:−
1272:…
1258:−
1249:−
1238:∣
1202:∏
1198:≈
1187:−
1173:…
1157:∣
1121:∏
1098:…
1045:…
996:…
921:∣
918:⟩
907:⟨
890:∣
868:∣
846:∣
823:⟩
817:⟨
814:∣
797:⟩
791:⟨
785:⟩
779:⟨
776:∣
762:≈
707:∣
704:⟩
693:⟨
676:∣
654:∣
632:∣
610:∣
593:⟩
587:⟨
584:∣
570:≈
414:∏
346:∑
88:⟩
77:⟨
57:⟩
51:⟨
2986:12 March
2977:Archived
2896:Archived
2892:27378409
2845:Archived
2793:Archived
2721:Archived
2670:27 April
2614:12361426
2606:26617328
2451:See also
2114:on plain
2106:falls on
2098:in falls
1857:z-scores
894:the, red
872:saw, the
2730:22 June
2586:Bibcode
2482:n-tuple
2477:MinHash
2400:, OCR (
2365:kernels
2363:design
2136:to its
2051:skipped
1869:g-score
1331:-order
2941:
2902:27 May
2890:
2837:
2802:18 May
2785:
2612:
2604:
2542:24 May
2283:-grams
2112:, and
2090:the in
2060:-skip-
2053:over.
1945:smooth
1908:in an
1873:g-test
1779:corpus
850:I, saw
2980:(PDF)
2965:(PDF)
2939:S2CID
2888:S2CID
2796:(PDF)
2767:(PDF)
2724:(PDF)
2713:(PDF)
2687:arXiv
2664:(PDF)
2657:(PDF)
2633:arXiv
2610:S2CID
2576:arXiv
2536:(PDF)
2429:BLAST
1312:word
886:house
711:house
672:house
510:share
505:0.02
494:0.03
488:likes
477:world
403:query
318:share
313:0.05
305:0.05
302:likes
294:world
21:word
2988:2018
2973:XIII
2904:2015
2853:2021
2804:2019
2783:ISBN
2746:link
2732:2015
2672:2014
2602:PMID
2544:2022
1768:and
527:...
516:0.2
502:0.05
491:0.05
483:0.1
472:0.3
455:Word
430:word
362:word
329:...
321:0.3
297:0.2
289:0.1
278:Word
69:and
2931:doi
2880:doi
2775:doi
2594:doi
2412:),
2410:ICR
2404:),
1975:or
864:red
842:the
810:saw
680:red
658:the
650:red
636:saw
628:the
606:saw
524:...
521:...
513:0.3
480:0.2
469:0.1
326:...
153:uni
116:or
3016::
2971:.
2967:.
2937:.
2927:41
2925:.
2894:.
2886:.
2876:28
2874:.
2870:.
2843:.
2829:.
2825:.
2791:.
2781:.
2754:^
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