4514:
3966:
3970:
5069:
2579:
1996:
3541:
6115:
4509:{\displaystyle p_{a}(j|i,l_{e},l_{f})\leftarrow {\frac {1}{\lambda _{i,l_{e},l_{f}}}}\sum _{k}{\frac {t(e_{i}^{(k)}|f_{j}^{(k)})p_{a}(j|i,l_{e},l_{f})\delta (e_{x},e_{i}^{(k)})\delta (f_{y},f_{j}^{(k)})\delta (l_{e},l_{e}^{(k)})\delta (l_{f},l_{f}^{(k)})}{\sum _{j'}t(e_{i}^{(k)}|f_{j'}^{(k)})p_{a}(j'|i,l_{e},l_{f})}}}
6464:
5852:
The alignment models that use first-order dependencies like the HMM or IBM Models 4 and 5 produce better results than the other alignment methods. The main idea of HMM is to predict the distance between subsequent source language positions. On the other hand, IBM Model 4 tries to predict the distance
5219:
In IBM Model 4, each word is dependent on the previously aligned word and on the word classes of the surrounding words. Some words tend to get reordered during translation more than others (e.g. adjective–noun inversion when translating Polish to
English). Adjectives often get moved before the noun
5590:
IBM Model 5 reformulates IBM Model 4 by enhancing the alignment model with more training parameters in order to overcome the model deficiency. During the translation in Model 3 and Model 4 there are no heuristics that would prohibit the placement of an output word in a position already taken. In
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Both Model 3 and Model 4 ignore if an input position was chosen and if the probability mass was reserved for the input positions outside the sentence boundaries. It is the reason for the probabilities of all correct alignments not sum up to unity in these two models (deficient models).
4749:
26:
to train a translation model and an alignment model, starting with lexical translation probabilities and moving to reordering and word duplication. They underpinned the majority of statistical machine translation systems for almost twenty years starting in the early 1990s, until
1696:
2288:
3961:{\displaystyle t(e_{x}|f_{y})\leftarrow {\frac {1}{\lambda _{y}}}\sum _{k,i,j}{\frac {t(e_{i}^{(k)}|f_{j}^{(k)})p_{a}(j|i,l_{e},l_{f})\delta (e_{x},e_{i}^{(k)})\delta (f_{y},f_{j}^{(k)})}{\sum _{j'}t(e_{i}^{(k)}|f_{j'}^{(k)})p_{a}(j'|i,l_{e},l_{f})}}}
5591:
Model 5 it is important to place words only in free positions. It is done by tracking the number of free positions and allowing placement only in such positions. The distortion model is similar to IBM Model 4, but it is based on free positions. If
5220:
that precedes them. The word classes introduced in Model 4 solve this problem by conditioning the probability distributions of these classes. The result of such distribution is a lexicalized model. Such a distribution can be defined as follows:
1402:
4720:
The last step is called distortion instead of alignment because it is possible to produce the same translation with the same alignment in different ways. For example, in the above example, we have another way to get the same alignment:
3536:
5853:
between subsequent target language positions. Since it was expected to achieve better alignment quality when using both types of such dependencies, HMM and Model 4 were combined in a log-linear manner in Model 6 as follows:
6242:
5859:
5848:
4709:
The number of inserted words depends on sentence length. This is why the NULL token insertion is modeled as an additional step: the fertility step. It increases the IBM Model 3 translation process to four steps:
5064:{\displaystyle P(S\mid E,A)=\prod _{i=1}^{I}\Phi _{i}!n(\Phi \mid e_{j})*\prod _{j=1}^{J}t(f_{j}\mid e_{a_{j}})*\prod _{j:a(j)\neq 0}^{J}d(j|a_{j},I,J){\binom {J-\Phi _{0}}{\Phi _{0}}}p_{0}^{\Phi _{0}}p_{1}^{J}}
3097:
5725:
1067:
590:
385:
5338:
5423:
2574:{\displaystyle t(e_{x}|f_{y})\leftarrow {\frac {t(e_{x}|f_{y})}{\lambda _{y}}}\sum _{k,i,j}{\frac {\delta (e_{x},e_{i}^{(k)})\delta (f_{y},f_{j}^{(k)})}{\sum _{j'}t(e_{i}^{(k)}|f_{j'}^{(k)})}}}
1991:{\displaystyle {\begin{cases}\max _{t'}\sum _{k}\sum _{i}\sum _{a^{(k)}}t(a^{(k)}|e^{(k)},f^{(k)})\ln t(e_{i}^{(k)}|f_{a^{(k)}(i)}^{(k)})\\\sum _{x}t'(e_{x}|f_{y})=1\quad \forall y\end{cases}}}
464:
This in general happens due to the different grammar and conventions of speech in different languages. English sentences require a subject, and when there is no subject available, it uses a
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2225:
2078:
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931:
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405:
231:
211:
191:
128:
108:
88:
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Does not explicitly model fertility: some foreign words tend to produce a fixed number of
English words. For example, for German-to-English translation,
236:
The meaning of an alignment grows increasingly complicated as the model version number grew. See Model 1 for the most simple and understandable version.
6459:{\displaystyle p_{6}(f,a\lor e)={\frac {\prod _{k=1}^{K}p_{k}(f,a\lor e)^{\alpha _{k}}}{\sum _{a',f'}\prod _{k=1}^{K}p_{k}(f',a'\mid e)^{\alpha _{k}}}}}
6110:{\displaystyle p_{6}(f,a\lor e)={\frac {p_{4}(f,a\lor e)^{\alpha }*p_{HMM}(f,a\lor e)}{\sum _{a',f'}p_{4}(f',a'\lor e)^{\alpha }*p_{HMM}(f',a'\lor e)}}}
1693:. Due to the simplistic assumptions, the algorithm has a closed-form, efficiently computable solution, which is the solution to the following equations:
471:. Japanese verbs do not have different forms for future and present tense, and the future tense is implied by the noun 明日 (tomorrow). Conversely, the
6749:
Wołk, K. (2015). "Noisy-Parallel and
Comparable Corpora Filtering Methodology for the Extraction of Bi-Lingual Equivalent Data at Sentence Level".
6688:. Proceedings of the Fourteenth Conference on Computational Natural Language Learning. Association for Computational Linguistics. pp. 98–106.
1690:
1404:
IBM Model 1 uses very simplistic assumptions on the statistical model, in order to allow the following algorithm to have closed-form solution.
6607:
3034:
6671:
FERNÁNDEZ, Pablo Malvar. Improving Word-to-word
Alignments Using Morphological Information. 2008. PhD Thesis. San Diego State University.
6557:
5732:
4714:
5624:
475:は and the grammar word だ (roughly "to be") do not correspond to any word in the English sentence. So, we can write the alignment as
23:
966:
489:
284:
5226:
6808:
6623:
5345:
4544:
The fertility problem is addressed in IBM Model 3. The fertility is modeled using probability distribution defined as:
70:
The IBM alignment models translation as a conditional probability model. For each source-language ("foreign") sentence
28:
5618:
denotes the number of free positions in the output, the IBM Model 5 distortion probabilities would be defined as:
2614:
2163:
2012:
1415:
6698:
KNIGHT, Kevin. A statistical MT tutorial workbook. Manuscript prepared for the 1999 JHU Summer
Workshop, 1999.
4665:
1075:
38:
proposed five models, and a model 6 was proposed later. The sequence of the six models can be summarized as:
31:
began to dominate. These models offer principled probabilistic formulation and (mostly) tractable inference.
3182:
3179:
Model 2 allows alignment to be conditional on sentence lengths. That is, we have a probability distribution
6813:
3102:
2140:
This could either be uniform or random. It is only required that every entry is positive, and for each
1171:
6472:
6147:
5551:
are distortion probability distributions of the words. The cept is formed by aligning each input word
6768:
6195:
2759:
1642:
1593:
1490:
1412:
If a dictionary is not provided at the start, but we have a corpus of
English-foreign language pairs
6708:
Brown, Peter F. (1993). "The mathematics of statistical machine translation: Parameter estimation".
4550:
2921:
2686:
2234:
2088:
1705:
1539:
715:
610:
6141:
1999:
58:
6651:. Proceedings of the 11th International Workshop on Spoken Language Translation, Lake Tahoe, USA.
2587:
6784:
6758:
6652:
5077:
2762:-- it equals 1 if the two entries are equal, and 0 otherwise. The index notation is as follows:
6603:
6564:
6517:
values are typically different in terms of their orders of magnitude for HMM and IBM Model 4.
4519:
1397:{\displaystyle p(e,a|f)={\frac {1/N}{(1+l_{f})^{l_{e}}}}\prod _{i=1}^{l_{e}}t(e_{i}|f_{a(i)})}
603:
Given the above definition of alignment, we can define the statistical model used by Model 1:
133:
6123:
4628:
2741:
845:
6776:
4659:
token that can also have its fertility modeled using a conditional distribution defined as:
3531:{\displaystyle p(e,a|f)={1/N}\prod _{i=1}^{l_{e}}t(e_{i}|f_{a(i)})p_{a}(a(i)|i,l_{e},l_{f})}
6724:
5594:
5554:
5488:
5104:
4608:
3319:
3292:
2889:
1144:
936:
818:
791:
688:
661:
252:
5515:
5459:
5430:
410:
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are still normalization factors. See section 4.4.1 of for a derivation and an algorithm.
6772:
3006:
963:
Then, we generate an alignment uniformly in the set of all possible alignment functions
5191:
5171:
5151:
5131:
4588:
3272:
3252:
2986:
2856:
2834:
2812:
2790:
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2143:
916:
771:
390:
216:
196:
176:
113:
93:
73:
595:
Future models will allow one
English world to be aligned with multiple foreign words.
6802:
1483:(without alignment information), then the model can be cast into the following form:
465:
6788:
4625:
it usually translates. This model deals with dropping input words because it allows
3538:
The EM algorithm can still be solved in closed-form, giving the following algorithm:
2002:, then simplified. For a detailed derivation of the algorithm, see chapter 4 and.
472:
444:
We can align some
English words to corresponding Japanese words, but not everyone:
6597:
5208:
refer to the absolute lengths of the target and source sentences, respectively.
6649:
Polish-English Speech
Statistical Machine Translation Systems for the IWSLT 2014
6780:
6534:
4651:. But there is still an issue when adding words. For example, the English word
3031:
No length preference: The probability of each length of translation is equal:
6469:
The log-linear combination is used instead of linear combination because the
1141:, generate each one independently of every other English word. For the word
4713:
486:
Thus, we see that the alignment function is in general a function of type
3092:{\displaystyle \sum _{e{\text{ has length }}l}p(e|f)={\frac {1}{N}}}
6763:
6657:
5843:{\displaystyle d_{1}(v_{j}-v_{\pi _{i,k-1}}\lor B(e_{j}),v_{max'})}
173:, the probability that we would generate English language sentence
6140:
is used in order to count the weight of Model 4 relatively to the
2851:
ranges over the entire vocabulary of
English words in the corpus;
2873:
ranges over the entire vocabulary of foreign words in the corpus.
6624:"CS288, Spring 2020, Lectur 05: Statistical Machine Translation"
4655:
is often inserted when negating. This issue generates a special
6144:. A log-linear combination of several models can be defined as
5720:{\displaystyle d_{1}(v_{j}\lor B(e_{j}),v_{\odot i-1},v_{max})}
35:
6558:"A Systematic Bayesian Treatment of the IBM Alignment Models"
2918:, any permutation of the English sentence is equally likely:
6686:
Computing optimal alignments for the IBM-3 translation model
4712:
1689:
In this form, this is exactly the kind of problem solved by
1984:
281:, an alignment for the sentence pair is a function of type
130:. The problem then is to find a good statistical model for
90:, we generate both a target-language ("English") sentence
5211:
See section 4.4.2 of for a derivation and an algorithm.
1062:{\displaystyle \{1,.,...,l_{e}\}\to \{0,1,.,...,l_{f}\}}
585:{\displaystyle \{1,.,...,l_{e}\}\to \{0,1,.,...,l_{f}\}}
483:
where 0 means that there is no corresponding alignment.
436:. For example, consider the following pair of sentences
380:{\displaystyle \{1,.,...,l_{e}\}\to \{0,1,.,...,l_{f}\}}
34:
The original work on statistical machine translation at
5333:{\displaystyle d_{1}(j-\odot _{}\lor A(f_{}),B(e_{j}))}
4605:, such distribution indicates to how many output words
658:, which can be interpreted as saying "the foreign word
387:. That is, we assume that the English word at location
2785:
ranges over English-foreign sentence pairs in corpus;
22:
are a sequence of increasingly complex models used in
6475:
6245:
6198:
6150:
6126:
5862:
5735:
5627:
5597:
5557:
5518:
5491:
5462:
5433:
5348:
5229:
5194:
5174:
5154:
5134:
5107:
5080:
4752:
4668:
4631:
4611:
4591:
4553:
4522:
3973:
3544:
3352:
3346:
The rest of Model 1 is unchanged. With that, we have
3322:
3295:
3275:
3255:
3185:
3105:
3037:
3009:
2989:
2924:
2892:
2859:
2837:
2815:
2793:
2771:
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2590:
2291:
2237:
2166:
2146:
2091:
2015:
1699:
1645:
1596:
1542:
1493:
1418:
1238:
1174:
1147:
1078:
969:
939:
919:
848:
821:
794:
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718:
691:
664:
613:
492:
413:
393:
287:
255:
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199:
179:
136:
116:
96:
76:
16:
Sequence of models in statistical machine translation
1536:
learnable parameters: the entries of the dictionary
479:
1-> 0; 2 -> 0; 3 -> 3; 4 -> 4; 5 -> 1
607:Start with a "dictionary". Its entries are of form
6509:
6458:
6228:
6184:
6132:
6109:
5842:
5719:
5610:
5570:
5543:
5504:
5477:
5448:
5418:{\displaystyle d_{1}(j-\pi _{i,k-1}\lor B(e_{j}))}
5417:
5332:
5200:
5180:
5160:
5140:
5120:
5093:
5063:
4698:
4643:
4617:
4597:
4574:
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3530:
3335:
3308:
3281:
3261:
3241:
3147:
3091:
3020:
2995:
2975:
2910:
2882:There are several limitations to the IBM model 1.
2865:
2843:
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2750:
2726:
2670:
2603:
2573:
2274:
2219:
2152:
2128:
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2009:INPUT. a corpus of English-foreign sentence pairs
1990:
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1396:
1220:
1160:
1133:
1061:
952:
925:
905:
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704:
677:
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428:
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379:
273:
225:
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185:
165:
122:
102:
82:
5018:
4983:
2829:ranges over words in foreign language sentences;
2611:is a normalization constant that makes sure each
2085:INITIALIZE. matrix of translations probabilities
4743:IBM Model 3 can be mathematically expressed as:
1709:
6596:Koehn, Philipp (2010). "4. Word-Based Models".
5485:functions map words to their word classes, and
815:, we first generate an English sentence length
407:is "explained" by the foreign word at location
6679:
6677:
6537:. SMT Research Survey Wiki. 11 September 2015
3249:, meaning "the probability that English word
8:
3142:
3112:
2983:for any permutation of the English sentence
2061:
2016:
1666:
1646:
1617:
1597:
1590:observable variables: the English sentences
1514:
1494:
1464:
1419:
1056:
1013:
1007:
970:
579:
536:
530:
493:
440:It will surely rain tomorrow -- 明日 は きっと 雨 だ
374:
331:
325:
288:
45:Model 2: additional absolute alignment model
6725:"Term Alignment. State of the Art Overview"
2005:In short, the EM algorithm goes as follows:
6762:
6656:
6563:. University of Cambridge. Archived from
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6392:
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3289:, when the English sentence is of length
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2743:
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2706:
2700:
2688:
2671:{\displaystyle \sum _{x}t(e_{x}|f_{y})=1}
2653:
2644:
2638:
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2220:{\displaystyle \sum _{x}t(e_{x}|f_{y})=1}
2202:
2193:
2187:
2171:
2165:
2145:
2117:
2108:
2102:
2090:
2073:{\displaystyle \{(e^{(k)},f^{(k)})\}_{k}}
2064:
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2014:
1959:
1950:
1944:
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1501:
1492:
1476:{\displaystyle \{(e^{(k)},f^{(k)})\}_{k}}
1467:
1448:
1429:
1417:
1376:
1367:
1361:
1343:
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1327:
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75:
6556:Yarin Gal; Phil Blunsom (12 June 2013).
4699:{\displaystyle n(\varnothing \lor NULL)}
3316:, and the foreign sentence is of length
2807:ranges over words in English sentences;
1487:fixed parameters: the foreign sentences
1134:{\displaystyle e_{1},e_{2},...e_{l_{e}}}
249:Given any foreign-English sentence pair
6526:
4675:
913:. In particular, it does not depend on
51:Model 4: added relative alignment model
3242:{\displaystyle p_{a}(j|i,l_{e},l_{f})}
5148:is assigned a fertility distribution
768:After being given a foreign sentence
7:
6591:
6589:
6587:
6585:
2886:No fluency: Given any sentence pair
5621:For the initial word in the cept:
61:alignment model in a log linear way
6120:where the interpolation parameter
5223:For the initial word in the cept:
5082:
5035:
5007:
4996:
4987:
4820:
4802:
3148:{\displaystyle l\in \{1,2,...,N\}}
1975:
1691:expectation–maximization algorithm
685:is translated to the English word
54:Model 5: fixed deficiency problem.
14:
6636:from the original on 24 Oct 2020.
1639:latent variables: the alignments
1232:Together, we have the probability
1221:{\displaystyle t(e_{i}|f_{a(i)})}
57:Model 6: Model 4 combined with a
6730:. Katholieke Universiteit Leuven
6510:{\displaystyle P_{r}(f,a\mid e)}
6185:{\displaystyle p_{k}(f,a\mid e)}
3166:is usually translated to one of
6599:Statistical Machine Translation
6229:{\displaystyle k=1,2,\dotsc ,K}
2160:, the probability sums to one:
1974:
1678:{\displaystyle \{a^{(k)}\}_{k}}
1629:{\displaystyle \{e^{(k)}\}_{k}}
1526:{\displaystyle \{f^{(k)}\}_{k}}
1072:Finally, for each English word
24:statistical machine translation
6602:. Cambridge University Press.
6504:
6486:
6437:
6408:
6333:
6314:
6274:
6256:
6179:
6161:
6101:
6073:
6045:
6016:
5975:
5957:
5929:
5910:
5891:
5873:
5837:
5810:
5797:
5746:
5714:
5670:
5657:
5638:
5536:
5524:
5472:
5466:
5443:
5437:
5412:
5409:
5396:
5359:
5327:
5324:
5311:
5302:
5297:
5285:
5277:
5266:
5254:
5240:
4977:
4951:
4944:
4925:
4919:
4899:
4866:
4836:
4817:
4774:
4756:
4693:
4672:
4575:{\displaystyle n(\phi \lor f)}
4569:
4557:
4500:
4467:
4455:
4442:
4437:
4431:
4412:
4406:
4400:
4387:
4364:
4359:
4353:
4327:
4321:
4316:
4310:
4284:
4278:
4273:
4267:
4241:
4235:
4230:
4224:
4198:
4192:
4159:
4152:
4139:
4134:
4128:
4114:
4108:
4102:
4089:
4027:
4024:
3991:
3984:
3952:
3919:
3907:
3894:
3889:
3883:
3864:
3858:
3852:
3839:
3816:
3811:
3805:
3779:
3773:
3768:
3762:
3736:
3730:
3697:
3690:
3677:
3672:
3666:
3652:
3646:
3640:
3627:
3579:
3576:
3562:
3548:
3525:
3492:
3488:
3482:
3476:
3463:
3458:
3452:
3440:
3426:
3376:
3369:
3356:
3236:
3203:
3196:
3073:
3066:
3059:
2976:{\displaystyle p(e|f)=p(e'|f)}
2970:
2963:
2951:
2942:
2935:
2928:
2905:
2893:
2727:{\displaystyle t(e_{x}|f_{y})}
2721:
2707:
2693:
2659:
2645:
2631:
2565:
2560:
2554:
2535:
2529:
2523:
2510:
2487:
2482:
2476:
2450:
2444:
2439:
2433:
2407:
2363:
2349:
2335:
2326:
2323:
2309:
2295:
2275:{\displaystyle t(e_{x}|f_{y})}
2269:
2255:
2241:
2208:
2194:
2180:
2129:{\displaystyle t(e_{x}|f_{y})}
2123:
2109:
2095:
2057:
2052:
2046:
2033:
2027:
2019:
1965:
1951:
1937:
1912:
1907:
1901:
1896:
1890:
1885:
1879:
1865:
1859:
1853:
1840:
1828:
1823:
1817:
1804:
1798:
1789:
1783:
1777:
1769:
1759:
1753:
1660:
1654:
1611:
1605:
1580:{\displaystyle t(e_{i}|f_{j})}
1574:
1560:
1546:
1508:
1502:
1460:
1455:
1449:
1436:
1430:
1422:
1391:
1386:
1380:
1368:
1354:
1304:
1284:
1262:
1255:
1242:
1215:
1210:
1204:
1192:
1178:
1010:
900:
870:
756:{\displaystyle t(e_{i}|f_{j})}
750:
736:
722:
651:{\displaystyle t(e_{i}|f_{j})}
645:
631:
617:
533:
423:
417:
328:
268:
256:
160:
153:
140:
48:Model 3: extra fertility model
1:
5578:to at least one output word.
6684:Schoenemann, Thomas (2010).
6647:Wołk K., Marasek K. (2014).
5101:represents the fertility of
3168:to the, for the, to a, for a
2604:{\displaystyle \lambda _{y}}
42:Model 1: lexical translation
3269:is aligned to foreign word
1168:, generate it according to
6830:
6781:10.7494/csci.2015.16.2.169
29:neural machine translation
6710:Computational Linguistics
5094:{\displaystyle \Phi _{i}}
213:given a foreign sentence
4739:I do not go to the house
4529:{\displaystyle \lambda }
3162:is usually omitted, and
166:{\displaystyle p(e,a|f)}
6133:{\displaystyle \alpha }
5729:For additional words:
4644:{\displaystyle \phi =0}
2751:{\displaystyle \delta }
906:{\displaystyle Uniform}
6511:
6460:
6397:
6303:
6230:
6186:
6134:
6111:
5844:
5721:
5612:
5572:
5545:
5506:
5479:
5450:
5419:
5342:For additional words:
5334:
5202:
5182:
5162:
5142:
5122:
5095:
5065:
4940:
4862:
4800:
4725:ja NULL nie pôjde tak
4717:
4700:
4645:
4619:
4599:
4585:For each foreign word
4576:
4530:
4510:
3962:
3532:
3422:
3337:
3310:
3283:
3263:
3243:
3149:
3093:
3048: has length
3022:
2997:
2977:
2912:
2875:
2867:
2845:
2823:
2801:
2779:
2752:
2738:In the above formula,
2736:
2728:
2681:
2680:
2672:
2605:
2575:
2276:
2229:
2221:
2154:
2130:
2074:
2000:Lagrangian multipliers
1998:This can be solved by
1992:
1679:
1630:
1581:
1527:
1477:
1408:Learning from a corpus
1398:
1350:
1222:
1162:
1135:
1063:
954:
927:
907:
836:
809:
782:
757:
706:
679:
652:
586:
481:
462:
442:
430:
401:
381:
275:
227:
207:
187:
167:
124:
104:
84:
6512:
6461:
6377:
6283:
6231:
6187:
6135:
6112:
5845:
5722:
5613:
5611:{\displaystyle v_{j}}
5573:
5571:{\displaystyle f_{i}}
5546:
5507:
5505:{\displaystyle e_{j}}
5480:
5451:
5420:
5335:
5203:
5183:
5163:
5143:
5123:
5121:{\displaystyle e_{i}}
5096:
5066:
4905:
4842:
4780:
4716:
4701:
4646:
4620:
4618:{\displaystyle \phi }
4600:
4577:
4531:
4511:
3963:
3533:
3395:
3338:
3336:{\displaystyle l_{f}}
3311:
3309:{\displaystyle l_{e}}
3284:
3264:
3244:
3150:
3094:
3023:
2998:
2978:
2913:
2911:{\displaystyle (e,f)}
2868:
2846:
2824:
2802:
2780:
2764:
2753:
2729:
2673:
2606:
2582:
2576:
2284:
2277:
2222:
2155:
2138:
2131:
2075:
2007:
1993:
1680:
1631:
1582:
1528:
1478:
1399:
1323:
1223:
1163:
1161:{\displaystyle e_{i}}
1136:
1064:
955:
953:{\displaystyle l_{f}}
928:
908:
842:uniformly in a range
837:
835:{\displaystyle l_{e}}
810:
808:{\displaystyle l_{f}}
783:
758:
707:
705:{\displaystyle e_{i}}
680:
678:{\displaystyle f_{j}}
653:
587:
477:
446:
438:
431:
402:
382:
276:
274:{\displaystyle (e,f)}
228:
208:
188:
168:
125:
105:
85:
6473:
6243:
6196:
6148:
6124:
5860:
5733:
5625:
5595:
5555:
5544:{\displaystyle f_{}}
5516:
5489:
5478:{\displaystyle B(e)}
5460:
5449:{\displaystyle A(f)}
5431:
5346:
5227:
5192:
5172:
5152:
5132:
5105:
5078:
4750:
4666:
4629:
4609:
4589:
4551:
4520:
3971:
3542:
3350:
3320:
3293:
3273:
3253:
3183:
3103:
3035:
3007:
2987:
2922:
2890:
2857:
2835:
2813:
2791:
2769:
2760:Dirac delta function
2742:
2687:
2615:
2588:
2289:
2235:
2164:
2144:
2089:
2013:
1697:
1643:
1594:
1540:
1491:
1416:
1236:
1172:
1145:
1076:
967:
937:
917:
846:
819:
792:
772:
716:
689:
662:
611:
490:
429:{\displaystyle a(i)}
411:
391:
285:
253:
217:
197:
177:
134:
114:
94:
74:
20:IBM alignment models
6809:Machine translation
6773:2015arXiv151004500W
6142:hidden Markov model
5128:, each source word
5060:
5045:
4441:
4410:
4363:
4320:
4277:
4234:
4138:
4112:
3893:
3862:
3815:
3772:
3676:
3650:
2564:
2533:
2486:
2443:
1911:
1863:
6507:
6456:
6376:
6226:
6182:
6130:
6107:
6005:
5840:
5717:
5608:
5568:
5541:
5502:
5475:
5446:
5415:
5330:
5198:
5178:
5158:
5138:
5118:
5091:
5061:
5046:
5024:
4718:
4696:
4641:
4615:
4595:
4572:
4526:
4506:
4416:
4390:
4383:
4343:
4300:
4257:
4214:
4118:
4092:
4082:
3958:
3868:
3842:
3835:
3795:
3752:
3656:
3630:
3620:
3528:
3333:
3306:
3279:
3259:
3239:
3145:
3089:
3055:
3021:{\displaystyle e'}
3018:
2993:
2973:
2908:
2863:
2841:
2819:
2797:
2775:
2748:
2724:
2668:
2627:
2601:
2571:
2539:
2513:
2506:
2466:
2423:
2400:
2272:
2217:
2176:
2150:
2126:
2070:
1988:
1983:
1928:
1869:
1843:
1765:
1742:
1732:
1722:
1675:
1626:
1577:
1523:
1473:
1394:
1218:
1158:
1131:
1059:
950:
923:
903:
832:
805:
778:
753:
702:
675:
648:
582:
451:will -> ?
426:
397:
377:
271:
223:
203:
183:
163:
120:
100:
80:
66:Mathematical setup
6723:Vulić I. (2010).
6609:978-0-521-87415-1
6454:
6351:
6105:
5980:
5201:{\displaystyle J}
5181:{\displaystyle I}
5161:{\displaystyle n}
5141:{\displaystyle s}
5016:
4598:{\displaystyle j}
4504:
4369:
4073:
4071:
3956:
3821:
3599:
3597:
3282:{\displaystyle j}
3262:{\displaystyle i}
3087:
3049:
3038:
2996:{\displaystyle e}
2866:{\displaystyle y}
2844:{\displaystyle x}
2822:{\displaystyle j}
2800:{\displaystyle i}
2778:{\displaystyle k}
2618:
2569:
2492:
2379:
2377:
2167:
2153:{\displaystyle y}
1919:
1743:
1733:
1723:
1708:
1321:
926:{\displaystyle f}
781:{\displaystyle f}
712:with probability
599:Statistical model
460:tomorrow -> 明日
454:surely -> きっと
400:{\displaystyle i}
226:{\displaystyle f}
206:{\displaystyle a}
193:and an alignment
186:{\displaystyle e}
123:{\displaystyle a}
110:and an alignment
103:{\displaystyle e}
83:{\displaystyle f}
6821:
6793:
6792:
6766:
6751:Computer Science
6746:
6740:
6739:
6737:
6735:
6729:
6720:
6714:
6713:
6705:
6699:
6696:
6690:
6689:
6681:
6672:
6669:
6663:
6662:
6660:
6644:
6638:
6637:
6635:
6628:
6620:
6614:
6613:
6593:
6580:
6579:
6577:
6575:
6569:
6562:
6553:
6547:
6546:
6544:
6542:
6531:
6516:
6514:
6513:
6508:
6485:
6484:
6465:
6463:
6462:
6457:
6455:
6453:
6452:
6451:
6450:
6449:
6429:
6418:
6407:
6406:
6396:
6391:
6375:
6374:
6363:
6349:
6348:
6347:
6346:
6345:
6313:
6312:
6302:
6297:
6281:
6255:
6254:
6235:
6233:
6232:
6227:
6191:
6189:
6188:
6183:
6160:
6159:
6139:
6137:
6136:
6131:
6116:
6114:
6113:
6108:
6106:
6104:
6094:
6083:
6072:
6071:
6053:
6052:
6037:
6026:
6015:
6014:
6004:
6003:
5992:
5978:
5956:
5955:
5937:
5936:
5909:
5908:
5898:
5872:
5871:
5849:
5847:
5846:
5841:
5836:
5835:
5834:
5809:
5808:
5790:
5789:
5788:
5787:
5758:
5757:
5745:
5744:
5726:
5724:
5723:
5718:
5713:
5712:
5694:
5693:
5669:
5668:
5650:
5649:
5637:
5636:
5617:
5615:
5614:
5609:
5607:
5606:
5577:
5575:
5574:
5569:
5567:
5566:
5550:
5548:
5547:
5542:
5540:
5539:
5511:
5509:
5508:
5503:
5501:
5500:
5484:
5482:
5481:
5476:
5455:
5453:
5452:
5447:
5424:
5422:
5421:
5416:
5408:
5407:
5389:
5388:
5358:
5357:
5339:
5337:
5336:
5331:
5323:
5322:
5301:
5300:
5270:
5269:
5239:
5238:
5207:
5205:
5204:
5199:
5187:
5185:
5184:
5179:
5167:
5165:
5164:
5159:
5147:
5145:
5144:
5139:
5127:
5125:
5124:
5119:
5117:
5116:
5100:
5098:
5097:
5092:
5090:
5089:
5070:
5068:
5067:
5062:
5059:
5054:
5044:
5043:
5042:
5032:
5023:
5022:
5021:
5015:
5014:
5005:
5004:
5003:
4986:
4964:
4963:
4954:
4939:
4934:
4898:
4897:
4896:
4895:
4878:
4877:
4861:
4856:
4835:
4834:
4810:
4809:
4799:
4794:
4705:
4703:
4702:
4697:
4650:
4648:
4647:
4642:
4624:
4622:
4621:
4616:
4604:
4602:
4601:
4596:
4581:
4579:
4578:
4573:
4535:
4533:
4532:
4527:
4515:
4513:
4512:
4507:
4505:
4503:
4499:
4498:
4486:
4485:
4470:
4465:
4454:
4453:
4440:
4429:
4428:
4415:
4409:
4398:
4382:
4381:
4367:
4362:
4351:
4339:
4338:
4319:
4308:
4296:
4295:
4276:
4265:
4253:
4252:
4233:
4222:
4210:
4209:
4191:
4190:
4178:
4177:
4162:
4151:
4150:
4137:
4126:
4117:
4111:
4100:
4084:
4081:
4072:
4070:
4069:
4068:
4067:
4055:
4054:
4031:
4023:
4022:
4010:
4009:
3994:
3983:
3982:
3967:
3965:
3964:
3959:
3957:
3955:
3951:
3950:
3938:
3937:
3922:
3917:
3906:
3905:
3892:
3881:
3880:
3867:
3861:
3850:
3834:
3833:
3819:
3814:
3803:
3791:
3790:
3771:
3760:
3748:
3747:
3729:
3728:
3716:
3715:
3700:
3689:
3688:
3675:
3664:
3655:
3649:
3638:
3622:
3619:
3598:
3596:
3595:
3583:
3575:
3574:
3565:
3560:
3559:
3537:
3535:
3534:
3529:
3524:
3523:
3511:
3510:
3495:
3475:
3474:
3462:
3461:
3443:
3438:
3437:
3421:
3420:
3419:
3409:
3394:
3390:
3372:
3342:
3340:
3339:
3334:
3332:
3331:
3315:
3313:
3312:
3307:
3305:
3304:
3288:
3286:
3285:
3280:
3268:
3266:
3265:
3260:
3248:
3246:
3245:
3240:
3235:
3234:
3222:
3221:
3206:
3195:
3194:
3154:
3152:
3151:
3146:
3098:
3096:
3095:
3090:
3088:
3080:
3069:
3054:
3050:
3047:
3027:
3025:
3024:
3019:
3017:
3002:
3000:
2999:
2994:
2982:
2980:
2979:
2974:
2966:
2961:
2938:
2917:
2915:
2914:
2909:
2872:
2870:
2869:
2864:
2850:
2848:
2847:
2842:
2828:
2826:
2825:
2820:
2806:
2804:
2803:
2798:
2784:
2782:
2781:
2776:
2757:
2755:
2754:
2749:
2733:
2731:
2730:
2725:
2720:
2719:
2710:
2705:
2704:
2677:
2675:
2674:
2669:
2658:
2657:
2648:
2643:
2642:
2626:
2610:
2608:
2607:
2602:
2600:
2599:
2580:
2578:
2577:
2572:
2570:
2568:
2563:
2552:
2551:
2538:
2532:
2521:
2505:
2504:
2490:
2485:
2474:
2462:
2461:
2442:
2431:
2419:
2418:
2402:
2399:
2378:
2376:
2375:
2366:
2362:
2361:
2352:
2347:
2346:
2330:
2322:
2321:
2312:
2307:
2306:
2281:
2279:
2278:
2273:
2268:
2267:
2258:
2253:
2252:
2226:
2224:
2223:
2218:
2207:
2206:
2197:
2192:
2191:
2175:
2159:
2157:
2156:
2151:
2135:
2133:
2132:
2127:
2122:
2121:
2112:
2107:
2106:
2079:
2077:
2076:
2071:
2069:
2068:
2056:
2055:
2037:
2036:
1997:
1995:
1994:
1989:
1987:
1986:
1964:
1963:
1954:
1949:
1948:
1936:
1927:
1910:
1899:
1889:
1888:
1868:
1862:
1851:
1827:
1826:
1808:
1807:
1792:
1787:
1786:
1764:
1763:
1762:
1741:
1731:
1721:
1720:
1684:
1682:
1681:
1676:
1674:
1673:
1664:
1663:
1635:
1633:
1632:
1627:
1625:
1624:
1615:
1614:
1586:
1584:
1583:
1578:
1573:
1572:
1563:
1558:
1557:
1532:
1530:
1529:
1524:
1522:
1521:
1512:
1511:
1482:
1480:
1479:
1474:
1472:
1471:
1459:
1458:
1440:
1439:
1403:
1401:
1400:
1395:
1390:
1389:
1371:
1366:
1365:
1349:
1348:
1347:
1337:
1322:
1320:
1319:
1318:
1317:
1316:
1302:
1301:
1282:
1278:
1269:
1258:
1227:
1225:
1224:
1219:
1214:
1213:
1195:
1190:
1189:
1167:
1165:
1164:
1159:
1157:
1156:
1140:
1138:
1137:
1132:
1130:
1129:
1128:
1127:
1101:
1100:
1088:
1087:
1068:
1066:
1065:
1060:
1055:
1054:
1006:
1005:
959:
957:
956:
951:
949:
948:
932:
930:
929:
924:
912:
910:
909:
904:
841:
839:
838:
833:
831:
830:
814:
812:
811:
806:
804:
803:
787:
785:
784:
779:
762:
760:
759:
754:
749:
748:
739:
734:
733:
711:
709:
708:
703:
701:
700:
684:
682:
681:
676:
674:
673:
657:
655:
654:
649:
644:
643:
634:
629:
628:
591:
589:
588:
583:
578:
577:
529:
528:
448:it -> ?
435:
433:
432:
427:
406:
404:
403:
398:
386:
384:
383:
378:
373:
372:
324:
323:
280:
278:
277:
272:
232:
230:
229:
224:
212:
210:
209:
204:
192:
190:
189:
184:
172:
170:
169:
164:
156:
129:
127:
126:
121:
109:
107:
106:
101:
89:
87:
86:
81:
6829:
6828:
6824:
6823:
6822:
6820:
6819:
6818:
6799:
6798:
6797:
6796:
6748:
6747:
6743:
6733:
6731:
6727:
6722:
6721:
6717:
6707:
6706:
6702:
6697:
6693:
6683:
6682:
6675:
6670:
6666:
6646:
6645:
6641:
6633:
6626:
6622:
6621:
6617:
6610:
6595:
6594:
6583:
6573:
6571:
6567:
6560:
6555:
6554:
6550:
6540:
6538:
6533:
6532:
6528:
6523:
6476:
6471:
6470:
6441:
6436:
6422:
6411:
6398:
6367:
6356:
6350:
6337:
6332:
6304:
6282:
6246:
6241:
6240:
6194:
6193:
6151:
6146:
6145:
6122:
6121:
6087:
6076:
6057:
6044:
6030:
6019:
6006:
5996:
5985:
5979:
5941:
5928:
5900:
5899:
5863:
5858:
5857:
5827:
5816:
5800:
5767:
5762:
5749:
5736:
5731:
5730:
5698:
5676:
5660:
5641:
5628:
5623:
5622:
5598:
5593:
5592:
5588:
5558:
5553:
5552:
5519:
5514:
5513:
5492:
5487:
5486:
5458:
5457:
5429:
5428:
5399:
5368:
5349:
5344:
5343:
5314:
5280:
5249:
5230:
5225:
5224:
5217:
5190:
5189:
5170:
5169:
5150:
5149:
5130:
5129:
5108:
5103:
5102:
5081:
5076:
5075:
5034:
5006:
4995:
4988:
4981:
4955:
4887:
4882:
4869:
4826:
4801:
4748:
4747:
4664:
4663:
4627:
4626:
4607:
4606:
4587:
4586:
4549:
4548:
4542:
4518:
4517:
4490:
4477:
4458:
4445:
4421:
4374:
4368:
4330:
4287:
4244:
4201:
4182:
4169:
4142:
4085:
4059:
4046:
4035:
4014:
4001:
3974:
3969:
3968:
3942:
3929:
3910:
3897:
3873:
3826:
3820:
3782:
3739:
3720:
3707:
3680:
3623:
3587:
3566:
3551:
3540:
3539:
3515:
3502:
3466:
3444:
3429:
3411:
3348:
3347:
3323:
3318:
3317:
3296:
3291:
3290:
3271:
3270:
3251:
3250:
3226:
3213:
3186:
3181:
3180:
3177:
3101:
3100:
3033:
3032:
3010:
3005:
3004:
2985:
2984:
2954:
2920:
2919:
2888:
2887:
2880:
2855:
2854:
2833:
2832:
2811:
2810:
2789:
2788:
2767:
2766:
2740:
2739:
2711:
2696:
2685:
2684:
2649:
2634:
2613:
2612:
2591:
2586:
2585:
2544:
2497:
2491:
2453:
2410:
2403:
2367:
2353:
2338:
2331:
2313:
2298:
2287:
2286:
2259:
2244:
2233:
2232:
2198:
2183:
2162:
2161:
2142:
2141:
2113:
2098:
2087:
2086:
2082:
2060:
2041:
2022:
2011:
2010:
1982:
1981:
1955:
1940:
1929:
1916:
1915:
1874:
1812:
1793:
1772:
1748:
1713:
1701:
1695:
1694:
1688:
1665:
1649:
1641:
1640:
1616:
1600:
1592:
1591:
1564:
1549:
1538:
1537:
1513:
1497:
1489:
1488:
1463:
1444:
1425:
1414:
1413:
1410:
1372:
1357:
1339:
1308:
1303:
1293:
1283:
1270:
1234:
1233:
1196:
1181:
1170:
1169:
1148:
1143:
1142:
1119:
1114:
1092:
1079:
1074:
1073:
1046:
997:
965:
964:
940:
935:
934:
915:
914:
844:
843:
822:
817:
816:
795:
790:
789:
770:
769:
740:
725:
714:
713:
692:
687:
686:
665:
660:
659:
635:
620:
609:
608:
601:
569:
520:
488:
487:
409:
408:
389:
388:
364:
315:
283:
282:
251:
250:
247:
242:
215:
214:
195:
194:
175:
174:
132:
131:
112:
111:
92:
91:
72:
71:
68:
17:
12:
11:
5:
6827:
6825:
6817:
6816:
6811:
6801:
6800:
6795:
6794:
6757:(2): 169–184.
6741:
6715:
6712:(19): 263–311.
6700:
6691:
6673:
6664:
6639:
6615:
6608:
6581:
6548:
6525:
6524:
6522:
6519:
6506:
6503:
6500:
6497:
6494:
6491:
6488:
6483:
6479:
6467:
6466:
6448:
6444:
6439:
6435:
6432:
6428:
6425:
6421:
6417:
6414:
6410:
6405:
6401:
6395:
6390:
6387:
6384:
6380:
6373:
6370:
6366:
6362:
6359:
6354:
6344:
6340:
6335:
6331:
6328:
6325:
6322:
6319:
6316:
6311:
6307:
6301:
6296:
6293:
6290:
6286:
6279:
6276:
6273:
6270:
6267:
6264:
6261:
6258:
6253:
6249:
6225:
6222:
6219:
6216:
6213:
6210:
6207:
6204:
6201:
6181:
6178:
6175:
6172:
6169:
6166:
6163:
6158:
6154:
6129:
6118:
6117:
6103:
6100:
6097:
6093:
6090:
6086:
6082:
6079:
6075:
6070:
6067:
6064:
6060:
6056:
6051:
6047:
6043:
6040:
6036:
6033:
6029:
6025:
6022:
6018:
6013:
6009:
6002:
5999:
5995:
5991:
5988:
5983:
5977:
5974:
5971:
5968:
5965:
5962:
5959:
5954:
5951:
5948:
5944:
5940:
5935:
5931:
5927:
5924:
5921:
5918:
5915:
5912:
5907:
5903:
5896:
5893:
5890:
5887:
5884:
5881:
5878:
5875:
5870:
5866:
5839:
5833:
5830:
5826:
5823:
5819:
5815:
5812:
5807:
5803:
5799:
5796:
5793:
5786:
5783:
5780:
5777:
5774:
5770:
5765:
5761:
5756:
5752:
5748:
5743:
5739:
5716:
5711:
5708:
5705:
5701:
5697:
5692:
5689:
5686:
5683:
5679:
5675:
5672:
5667:
5663:
5659:
5656:
5653:
5648:
5644:
5640:
5635:
5631:
5605:
5601:
5587:
5584:
5565:
5561:
5538:
5535:
5532:
5529:
5526:
5522:
5499:
5495:
5474:
5471:
5468:
5465:
5445:
5442:
5439:
5436:
5414:
5411:
5406:
5402:
5398:
5395:
5392:
5387:
5384:
5381:
5378:
5375:
5371:
5367:
5364:
5361:
5356:
5352:
5329:
5326:
5321:
5317:
5313:
5310:
5307:
5304:
5299:
5296:
5293:
5290:
5287:
5283:
5279:
5276:
5273:
5268:
5265:
5262:
5259:
5256:
5252:
5248:
5245:
5242:
5237:
5233:
5216:
5213:
5197:
5177:
5157:
5137:
5115:
5111:
5088:
5084:
5072:
5071:
5058:
5053:
5049:
5041:
5037:
5031:
5027:
5020:
5013:
5009:
5002:
4998:
4994:
4991:
4985:
4979:
4976:
4973:
4970:
4967:
4962:
4958:
4953:
4949:
4946:
4943:
4938:
4933:
4930:
4927:
4924:
4921:
4918:
4915:
4912:
4908:
4904:
4901:
4894:
4890:
4885:
4881:
4876:
4872:
4868:
4865:
4860:
4855:
4852:
4849:
4845:
4841:
4838:
4833:
4829:
4825:
4822:
4819:
4816:
4813:
4808:
4804:
4798:
4793:
4790:
4787:
4783:
4779:
4776:
4773:
4770:
4767:
4764:
4761:
4758:
4755:
4741:
4740:
4737:
4730:
4707:
4706:
4695:
4692:
4689:
4686:
4683:
4680:
4677:
4674:
4671:
4640:
4637:
4634:
4614:
4594:
4583:
4582:
4571:
4568:
4565:
4562:
4559:
4556:
4541:
4538:
4525:
4502:
4497:
4493:
4489:
4484:
4480:
4476:
4473:
4469:
4464:
4461:
4457:
4452:
4448:
4444:
4439:
4436:
4433:
4427:
4424:
4419:
4414:
4408:
4405:
4402:
4397:
4393:
4389:
4386:
4380:
4377:
4372:
4366:
4361:
4358:
4355:
4350:
4346:
4342:
4337:
4333:
4329:
4326:
4323:
4318:
4315:
4312:
4307:
4303:
4299:
4294:
4290:
4286:
4283:
4280:
4275:
4272:
4269:
4264:
4260:
4256:
4251:
4247:
4243:
4240:
4237:
4232:
4229:
4226:
4221:
4217:
4213:
4208:
4204:
4200:
4197:
4194:
4189:
4185:
4181:
4176:
4172:
4168:
4165:
4161:
4157:
4154:
4149:
4145:
4141:
4136:
4133:
4130:
4125:
4121:
4116:
4110:
4107:
4104:
4099:
4095:
4091:
4088:
4080:
4076:
4066:
4062:
4058:
4053:
4049:
4045:
4042:
4038:
4034:
4029:
4026:
4021:
4017:
4013:
4008:
4004:
4000:
3997:
3993:
3989:
3986:
3981:
3977:
3954:
3949:
3945:
3941:
3936:
3932:
3928:
3925:
3921:
3916:
3913:
3909:
3904:
3900:
3896:
3891:
3888:
3885:
3879:
3876:
3871:
3866:
3860:
3857:
3854:
3849:
3845:
3841:
3838:
3832:
3829:
3824:
3818:
3813:
3810:
3807:
3802:
3798:
3794:
3789:
3785:
3781:
3778:
3775:
3770:
3767:
3764:
3759:
3755:
3751:
3746:
3742:
3738:
3735:
3732:
3727:
3723:
3719:
3714:
3710:
3706:
3703:
3699:
3695:
3692:
3687:
3683:
3679:
3674:
3671:
3668:
3663:
3659:
3654:
3648:
3645:
3642:
3637:
3633:
3629:
3626:
3618:
3615:
3612:
3609:
3606:
3602:
3594:
3590:
3586:
3581:
3578:
3573:
3569:
3564:
3558:
3554:
3550:
3547:
3527:
3522:
3518:
3514:
3509:
3505:
3501:
3498:
3494:
3490:
3487:
3484:
3481:
3478:
3473:
3469:
3465:
3460:
3457:
3454:
3451:
3447:
3442:
3436:
3432:
3428:
3425:
3418:
3414:
3408:
3405:
3402:
3398:
3393:
3389:
3385:
3381:
3378:
3375:
3371:
3367:
3364:
3361:
3358:
3355:
3330:
3326:
3303:
3299:
3278:
3258:
3238:
3233:
3229:
3225:
3220:
3216:
3212:
3209:
3205:
3201:
3198:
3193:
3189:
3176:
3173:
3172:
3171:
3156:
3144:
3141:
3138:
3135:
3132:
3129:
3126:
3123:
3120:
3117:
3114:
3111:
3108:
3086:
3083:
3078:
3075:
3072:
3068:
3064:
3061:
3058:
3053:
3045:
3041:
3029:
3016:
3013:
2992:
2972:
2969:
2965:
2960:
2957:
2953:
2950:
2947:
2944:
2941:
2937:
2933:
2930:
2927:
2907:
2904:
2901:
2898:
2895:
2879:
2876:
2862:
2840:
2818:
2796:
2774:
2747:
2723:
2718:
2714:
2709:
2703:
2699:
2695:
2692:
2667:
2664:
2661:
2656:
2652:
2647:
2641:
2637:
2633:
2630:
2625:
2621:
2598:
2594:
2567:
2562:
2559:
2556:
2550:
2547:
2542:
2537:
2531:
2528:
2525:
2520:
2516:
2512:
2509:
2503:
2500:
2495:
2489:
2484:
2481:
2478:
2473:
2469:
2465:
2460:
2456:
2452:
2449:
2446:
2441:
2438:
2435:
2430:
2426:
2422:
2417:
2413:
2409:
2406:
2398:
2395:
2392:
2389:
2386:
2382:
2374:
2370:
2365:
2360:
2356:
2351:
2345:
2341:
2337:
2334:
2328:
2325:
2320:
2316:
2311:
2305:
2301:
2297:
2294:
2271:
2266:
2262:
2257:
2251:
2247:
2243:
2240:
2216:
2213:
2210:
2205:
2201:
2196:
2190:
2186:
2182:
2179:
2174:
2170:
2149:
2125:
2120:
2116:
2111:
2105:
2101:
2097:
2094:
2067:
2063:
2059:
2054:
2051:
2048:
2044:
2040:
2035:
2032:
2029:
2025:
2021:
2018:
1985:
1980:
1977:
1973:
1970:
1967:
1962:
1958:
1953:
1947:
1943:
1939:
1935:
1932:
1926:
1922:
1918:
1917:
1914:
1909:
1906:
1903:
1898:
1895:
1892:
1887:
1884:
1881:
1877:
1872:
1867:
1861:
1858:
1855:
1850:
1846:
1842:
1839:
1836:
1833:
1830:
1825:
1822:
1819:
1815:
1811:
1806:
1803:
1800:
1796:
1791:
1785:
1782:
1779:
1775:
1771:
1768:
1761:
1758:
1755:
1751:
1746:
1740:
1736:
1730:
1726:
1719:
1716:
1711:
1707:
1706:
1704:
1686:
1685:
1672:
1668:
1662:
1659:
1656:
1652:
1648:
1637:
1623:
1619:
1613:
1610:
1607:
1603:
1599:
1588:
1576:
1571:
1567:
1562:
1556:
1552:
1548:
1545:
1534:
1520:
1516:
1510:
1507:
1504:
1500:
1496:
1470:
1466:
1462:
1457:
1454:
1451:
1447:
1443:
1438:
1435:
1432:
1428:
1424:
1421:
1409:
1406:
1393:
1388:
1385:
1382:
1379:
1375:
1370:
1364:
1360:
1356:
1353:
1346:
1342:
1336:
1333:
1330:
1326:
1315:
1311:
1306:
1300:
1296:
1292:
1289:
1286:
1281:
1277:
1273:
1267:
1264:
1261:
1257:
1253:
1250:
1247:
1244:
1241:
1230:
1229:
1217:
1212:
1209:
1206:
1203:
1199:
1194:
1188:
1184:
1180:
1177:
1155:
1151:
1126:
1122:
1117:
1113:
1110:
1107:
1104:
1099:
1095:
1091:
1086:
1082:
1070:
1058:
1053:
1049:
1045:
1042:
1039:
1036:
1033:
1030:
1027:
1024:
1021:
1018:
1015:
1012:
1009:
1004:
1000:
996:
993:
990:
987:
984:
981:
978:
975:
972:
961:
947:
943:
922:
902:
899:
896:
893:
890:
887:
884:
881:
878:
875:
872:
869:
866:
863:
860:
857:
854:
851:
829:
825:
802:
798:
777:
765:
764:
752:
747:
743:
738:
732:
728:
724:
721:
699:
695:
672:
668:
647:
642:
638:
633:
627:
623:
619:
616:
600:
597:
581:
576:
572:
568:
565:
562:
559:
556:
553:
550:
547:
544:
541:
538:
535:
532:
527:
523:
519:
516:
513:
510:
507:
504:
501:
498:
495:
425:
422:
419:
416:
396:
376:
371:
367:
363:
360:
357:
354:
351:
348:
345:
342:
339:
336:
333:
330:
327:
322:
318:
314:
311:
308:
305:
302:
299:
296:
293:
290:
270:
267:
264:
261:
258:
246:
245:Word alignment
243:
241:
238:
222:
202:
182:
162:
159:
155:
151:
148:
145:
142:
139:
119:
99:
79:
67:
64:
63:
62:
55:
52:
49:
46:
43:
15:
13:
10:
9:
6:
4:
3:
2:
6826:
6815:
6812:
6810:
6807:
6806:
6804:
6790:
6786:
6782:
6778:
6774:
6770:
6765:
6760:
6756:
6752:
6745:
6742:
6726:
6719:
6716:
6711:
6704:
6701:
6695:
6692:
6687:
6680:
6678:
6674:
6668:
6665:
6659:
6654:
6650:
6643:
6640:
6632:
6625:
6619:
6616:
6611:
6605:
6601:
6600:
6592:
6590:
6588:
6586:
6582:
6570:on 4 Mar 2016
6566:
6559:
6552:
6549:
6536:
6530:
6527:
6520:
6518:
6501:
6498:
6495:
6492:
6489:
6481:
6477:
6446:
6442:
6433:
6430:
6426:
6423:
6419:
6415:
6412:
6403:
6399:
6393:
6388:
6385:
6382:
6378:
6371:
6368:
6364:
6360:
6357:
6352:
6342:
6338:
6329:
6326:
6323:
6320:
6317:
6309:
6305:
6299:
6294:
6291:
6288:
6284:
6277:
6271:
6268:
6265:
6262:
6259:
6251:
6247:
6239:
6238:
6237:
6223:
6220:
6217:
6214:
6211:
6208:
6205:
6202:
6199:
6176:
6173:
6170:
6167:
6164:
6156:
6152:
6143:
6127:
6098:
6095:
6091:
6088:
6084:
6080:
6077:
6068:
6065:
6062:
6058:
6054:
6049:
6041:
6038:
6034:
6031:
6027:
6023:
6020:
6011:
6007:
6000:
5997:
5993:
5989:
5986:
5981:
5972:
5969:
5966:
5963:
5960:
5952:
5949:
5946:
5942:
5938:
5933:
5925:
5922:
5919:
5916:
5913:
5905:
5901:
5894:
5888:
5885:
5882:
5879:
5876:
5868:
5864:
5856:
5855:
5854:
5850:
5831:
5828:
5824:
5821:
5817:
5813:
5805:
5801:
5794:
5791:
5784:
5781:
5778:
5775:
5772:
5768:
5763:
5759:
5754:
5750:
5741:
5737:
5727:
5709:
5706:
5703:
5699:
5695:
5690:
5687:
5684:
5681:
5677:
5673:
5665:
5661:
5654:
5651:
5646:
5642:
5633:
5629:
5619:
5603:
5599:
5585:
5583:
5579:
5563:
5559:
5533:
5530:
5527:
5520:
5497:
5493:
5469:
5463:
5440:
5434:
5425:
5404:
5400:
5393:
5390:
5385:
5382:
5379:
5376:
5373:
5369:
5365:
5362:
5354:
5350:
5340:
5319:
5315:
5308:
5305:
5294:
5291:
5288:
5281:
5274:
5271:
5263:
5260:
5257:
5250:
5246:
5243:
5235:
5231:
5221:
5214:
5212:
5209:
5195:
5175:
5155:
5135:
5113:
5109:
5086:
5056:
5051:
5047:
5039:
5029:
5025:
5011:
5000:
4992:
4989:
4974:
4971:
4968:
4965:
4960:
4956:
4947:
4941:
4936:
4931:
4928:
4922:
4916:
4913:
4910:
4906:
4902:
4892:
4888:
4883:
4879:
4874:
4870:
4863:
4858:
4853:
4850:
4847:
4843:
4839:
4831:
4827:
4823:
4814:
4811:
4806:
4796:
4791:
4788:
4785:
4781:
4777:
4771:
4768:
4765:
4762:
4759:
4753:
4746:
4745:
4744:
4738:
4735:
4731:
4728:
4724:
4723:
4722:
4715:
4711:
4690:
4687:
4684:
4681:
4678:
4669:
4662:
4661:
4660:
4658:
4654:
4638:
4635:
4632:
4612:
4592:
4566:
4563:
4560:
4554:
4547:
4546:
4545:
4539:
4537:
4523:
4495:
4491:
4487:
4482:
4478:
4474:
4471:
4462:
4459:
4450:
4446:
4434:
4425:
4422:
4417:
4403:
4395:
4391:
4384:
4378:
4375:
4370:
4356:
4348:
4344:
4340:
4335:
4331:
4324:
4313:
4305:
4301:
4297:
4292:
4288:
4281:
4270:
4262:
4258:
4254:
4249:
4245:
4238:
4227:
4219:
4215:
4211:
4206:
4202:
4195:
4187:
4183:
4179:
4174:
4170:
4166:
4163:
4155:
4147:
4143:
4131:
4123:
4119:
4105:
4097:
4093:
4086:
4078:
4074:
4064:
4060:
4056:
4051:
4047:
4043:
4040:
4036:
4032:
4019:
4015:
4011:
4006:
4002:
3998:
3995:
3987:
3979:
3975:
3947:
3943:
3939:
3934:
3930:
3926:
3923:
3914:
3911:
3902:
3898:
3886:
3877:
3874:
3869:
3855:
3847:
3843:
3836:
3830:
3827:
3822:
3808:
3800:
3796:
3792:
3787:
3783:
3776:
3765:
3757:
3753:
3749:
3744:
3740:
3733:
3725:
3721:
3717:
3712:
3708:
3704:
3701:
3693:
3685:
3681:
3669:
3661:
3657:
3643:
3635:
3631:
3624:
3616:
3613:
3610:
3607:
3604:
3600:
3592:
3588:
3584:
3571:
3567:
3556:
3552:
3545:
3520:
3516:
3512:
3507:
3503:
3499:
3496:
3485:
3479:
3471:
3467:
3455:
3449:
3445:
3434:
3430:
3423:
3416:
3412:
3406:
3403:
3400:
3396:
3391:
3387:
3383:
3379:
3373:
3365:
3362:
3359:
3353:
3344:
3328:
3324:
3301:
3297:
3276:
3256:
3231:
3227:
3223:
3218:
3214:
3210:
3207:
3199:
3191:
3187:
3174:
3169:
3165:
3161:
3157:
3139:
3136:
3133:
3130:
3127:
3124:
3121:
3118:
3115:
3109:
3106:
3084:
3081:
3076:
3070:
3062:
3056:
3051:
3043:
3039:
3030:
3014:
3011:
2990:
2967:
2958:
2955:
2948:
2945:
2939:
2931:
2925:
2902:
2899:
2896:
2885:
2884:
2883:
2877:
2874:
2860:
2852:
2838:
2830:
2816:
2808:
2794:
2786:
2772:
2763:
2761:
2745:
2735:
2716:
2712:
2701:
2697:
2690:
2679:
2665:
2662:
2654:
2650:
2639:
2635:
2628:
2623:
2619:
2596:
2592:
2581:
2557:
2548:
2545:
2540:
2526:
2518:
2514:
2507:
2501:
2498:
2493:
2479:
2471:
2467:
2463:
2458:
2454:
2447:
2436:
2428:
2424:
2420:
2415:
2411:
2404:
2396:
2393:
2390:
2387:
2384:
2380:
2372:
2368:
2358:
2354:
2343:
2339:
2332:
2318:
2314:
2303:
2299:
2292:
2283:
2264:
2260:
2249:
2245:
2238:
2228:
2214:
2211:
2203:
2199:
2188:
2184:
2177:
2172:
2168:
2147:
2137:
2118:
2114:
2103:
2099:
2092:
2083:
2080:
2065:
2049:
2042:
2038:
2030:
2023:
2006:
2003:
2001:
1978:
1971:
1968:
1960:
1956:
1945:
1941:
1933:
1930:
1924:
1920:
1904:
1893:
1882:
1875:
1870:
1856:
1848:
1844:
1837:
1834:
1831:
1820:
1813:
1809:
1801:
1794:
1780:
1773:
1766:
1756:
1749:
1744:
1738:
1734:
1728:
1724:
1717:
1714:
1702:
1692:
1670:
1657:
1650:
1638:
1621:
1608:
1601:
1589:
1569:
1565:
1554:
1550:
1543:
1535:
1518:
1505:
1498:
1486:
1485:
1484:
1468:
1452:
1445:
1441:
1433:
1426:
1407:
1405:
1383:
1377:
1373:
1362:
1358:
1351:
1344:
1340:
1334:
1331:
1328:
1324:
1313:
1309:
1298:
1294:
1290:
1287:
1279:
1275:
1271:
1265:
1259:
1251:
1248:
1245:
1239:
1207:
1201:
1197:
1186:
1182:
1175:
1153:
1149:
1124:
1120:
1115:
1111:
1108:
1105:
1102:
1097:
1093:
1089:
1084:
1080:
1071:
1051:
1047:
1043:
1040:
1037:
1034:
1031:
1028:
1025:
1022:
1019:
1016:
1002:
998:
994:
991:
988:
985:
982:
979:
976:
973:
962:
945:
941:
920:
897:
894:
891:
888:
885:
882:
879:
876:
873:
867:
864:
861:
858:
855:
852:
849:
827:
823:
800:
796:
775:
767:
766:
745:
741:
730:
726:
719:
697:
693:
670:
666:
640:
636:
625:
621:
614:
606:
605:
604:
598:
596:
593:
574:
570:
566:
563:
560:
557:
554:
551:
548:
545:
542:
539:
525:
521:
517:
514:
511:
508:
505:
502:
499:
496:
484:
480:
476:
474:
470:
467:
466:dummy pronoun
461:
458:
457:rain -> 雨
455:
452:
449:
445:
441:
437:
420:
414:
394:
369:
365:
361:
358:
355:
352:
349:
346:
343:
340:
337:
334:
320:
316:
312:
309:
306:
303:
300:
297:
294:
291:
265:
262:
259:
244:
239:
237:
234:
220:
200:
180:
157:
149:
146:
143:
137:
117:
97:
77:
65:
60:
56:
53:
50:
47:
44:
41:
40:
39:
37:
32:
30:
25:
21:
6814:IBM software
6754:
6750:
6744:
6732:. Retrieved
6718:
6709:
6703:
6694:
6685:
6667:
6648:
6642:
6618:
6598:
6572:. Retrieved
6565:the original
6551:
6539:. Retrieved
6535:"IBM Models"
6529:
6468:
6119:
5851:
5728:
5620:
5589:
5580:
5426:
5341:
5222:
5218:
5210:
5073:
4742:
4733:
4732:I do not go
4726:
4719:
4708:
4656:
4652:
4584:
4543:
3345:
3178:
3167:
3163:
3159:
2881:
2853:
2831:
2809:
2787:
2765:
2737:
2682:
2583:
2285:
2231:LOOP. until
2230:
2139:
2084:
2081:
2008:
2004:
1687:
1411:
1231:
788:with length
602:
594:
485:
482:
478:
473:topic-marker
468:
463:
459:
456:
453:
450:
447:
443:
439:
248:
235:
69:
33:
19:
18:
2878:Limitations
2584:where each
6803:Categories
6764:1510.04500
6734:26 October
6658:1509.08874
6574:26 October
6541:26 October
6521:References
2282:converges:
6499:∣
6443:α
6431:∣
6379:∏
6353:∑
6339:α
6327:∨
6285:∏
6269:∨
6218:…
6174:∣
6128:α
6096:∨
6055:∗
6050:α
6039:∨
5982:∑
5970:∨
5939:∗
5934:α
5923:∨
5886:∨
5792:∨
5782:−
5769:π
5760:−
5688:−
5682:⊙
5652:∨
5531:−
5391:∨
5383:−
5370:π
5366:−
5292:−
5272:∨
5261:−
5251:⊙
5247:−
5083:Φ
5036:Φ
5008:Φ
4997:Φ
4993:−
4929:≠
4907:∏
4903:∗
4880:∣
4844:∏
4840:∗
4824:∣
4821:Φ
4803:Φ
4782:∏
4763:∣
4679:∨
4676:∅
4633:ϕ
4613:ϕ
4564:∨
4561:ϕ
4524:λ
4371:∑
4325:δ
4282:δ
4239:δ
4196:δ
4075:∑
4037:λ
4028:←
3823:∑
3777:δ
3734:δ
3601:∑
3589:λ
3580:←
3397:∏
3110:∈
3040:∑
2746:δ
2620:∑
2593:λ
2494:∑
2448:δ
2405:δ
2381:∑
2369:λ
2327:←
2169:∑
1976:∀
1921:∑
1835:
1745:∑
1735:∑
1725:∑
1325:∏
1011:→
534:→
329:→
6789:12860633
6631:Archived
6427:′
6416:′
6372:′
6361:′
6092:′
6081:′
6035:′
6024:′
6001:′
5990:′
5832:′
4463:′
4426:′
4379:′
3915:′
3878:′
3831:′
3099:for any
3015:′
2959:′
2683:RETURN.
2549:′
2502:′
1934:′
1718:′
6769:Bibcode
5586:Model 5
5215:Model 4
4540:Model 3
3175:Model 2
2758:is the
240:Model 1
6787:
6606:
5427:where
5168:, and
5074:where
4734:the to
4516:where
6785:S2CID
6759:arXiv
6728:(PDF)
6653:arXiv
6634:(PDF)
6627:(PDF)
6568:(PDF)
6561:(PDF)
6192:with
4736:house
4727:do do
3003:into
6736:2015
6604:ISBN
6576:2015
6543:2015
6236:as:
5512:and
5456:and
5188:and
4729:domu
4657:NULL
6777:doi
3343:".
3164:zum
1710:max
933:or
59:HMM
36:IBM
6805::
6783:.
6775:.
6767:.
6755:16
6753:.
6676:^
6629:.
6584:^
4653:do
3160:ja
1832:ln
763:".
592:.
469:it
233:.
6791:.
6779::
6771::
6761::
6738:.
6661:.
6655::
6612:.
6578:.
6545:.
6505:)
6502:e
6496:a
6493:,
6490:f
6487:(
6482:r
6478:P
6447:k
6438:)
6434:e
6424:a
6420:,
6413:f
6409:(
6404:k
6400:p
6394:K
6389:1
6386:=
6383:k
6369:f
6365:,
6358:a
6343:k
6334:)
6330:e
6324:a
6321:,
6318:f
6315:(
6310:k
6306:p
6300:K
6295:1
6292:=
6289:k
6278:=
6275:)
6272:e
6266:a
6263:,
6260:f
6257:(
6252:6
6248:p
6224:K
6221:,
6215:,
6212:2
6209:,
6206:1
6203:=
6200:k
6180:)
6177:e
6171:a
6168:,
6165:f
6162:(
6157:k
6153:p
6102:)
6099:e
6089:a
6085:,
6078:f
6074:(
6069:M
6066:M
6063:H
6059:p
6046:)
6042:e
6032:a
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