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In the original paper, a dynamic topic model is applied to the corpus of
Science articles published between 1881 and 1999 aiming to show that this method can be used to analyze the trends of word usage inside topics. The authors also show that the model trained with past documents is able to fit
435:
The former representation has some disadvantages due to the fact that the parameters are constrained to be non-negative and sum to one. When defining the evolution of these distributions, one would need to assure that such constraints were satisfied. Since both distributions are in the
43:, in a dynamic topic model the order of the documents plays a fundamental role. More precisely, the documents are grouped by time slice (e.g.: years) and it is assumed that the documents of each group come from a set of topics that evolved from the set of the previous slice.
776:
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432:, respectively. Even though multinomial distributions are usually written in terms of the mean parameters, representing them in terms of the natural parameters is better in the context of dynamic topic models.
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63:
over a set of terms. Thus, for each word of each document, a topic is drawn from the mixture and a term is subsequently drawn from the multinomial distribution corresponding to that topic.
370:
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In LDA, both the order the words appear in a document and the order the documents appear in the corpus are oblivious to the model. Whereas words are still assumed to be
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to do inference in this model is more difficult than in static models, due to the nonconjugacy of the
Gaussian and multinomial distributions. They propose the use of
1168:
665:
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Going beyond text documents, dynamic topic models were used to study musical influence, by learning musical topics and how they evolve in recent history.
440:, one solution to this problem is to represent them in terms of the natural parameters, that can assume any real value and can be individually changed.
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28:
that can be used to analyze the evolution of (unobserved) topics of a collection of documents over time. This family of models was proposed by
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59:, in a dynamic topic model, each document is viewed as a mixture of unobserved topics. Furthermore, each topic defines a
52:
33:
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is observable. Learning the other parameters constitutes an inference problem. Blei and
Lafferty argue that applying
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A continuous dynamic topic model was developed by Wang et al. and applied to predict the timestamp of documents.
60:
40:
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The topics, however, evolve over time. For instance, the two most likely terms of a topic at time
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25:
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Wang, Chong; Blei, David; Heckerman, David (2008). "Continuous Time
Dynamic Topic Models".
1334:, in particular, the Variational Kalman Filtering and the Variational Wavelet Regression.
1327:
771:{\displaystyle \beta _{t,k}|\beta _{t-1,k}\sim N(\beta _{t-1,k},\sigma ^{2}I)\forall k}
70:
could be "network" and "Zipf" (in descending order) while the most likely ones at time
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1396:
443:
Using the natural parameterization, the dynamics of the topic model are given by
1451:
1371:
Proceedings of the 23rd international conference on
Machine learning - ICML '06
549:{\displaystyle \beta _{t,k}|\beta _{t-1,k}\sim N(\beta _{t-1,k},\sigma ^{2}I)}
29:
17:
1378:
865:{\displaystyle \alpha _{t}|\alpha _{t-1}\sim N(\alpha _{t-1},\delta ^{2}I)}
647:{\displaystyle \alpha _{t}|\alpha _{t-1}\sim N(\alpha _{t-1},\delta ^{2}I)}
1127:{\displaystyle W_{t,d,n}\sim {\textrm {Mult}}(\pi (\beta _{t,Z_{t,d,n}}))}
1271:{\displaystyle \pi (x_{i})={\frac {\exp(x_{i})}{\sum _{i}\exp(x_{i})}}}
1026:{\displaystyle Z_{t,d,n}\sim {\textrm {Mult}}(\pi (\eta _{t,d}))}
1369:
Blei, David M; Lafferty, John D (2006). "Dynamic topic models".
56:
74:
could be "Zipf" and "percolation" (in descending order).
658:
The generative process at time slice 't' is therefore:
1450:
Shalit, Uri; Weinshall, Daphna; Chechik, Gal (2013).
1293:
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959:
941:{\displaystyle \eta _{t,d}\sim N(\alpha _{t},a^{2}I)}
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1343:documents of an incoming year better than LDA.
1170:is a mapping from the natural parameterization
112:as the per-document topic distribution at time
1452:"Modeling musical influence with topic models"
300:In this model, the multinomial distributions
8:
36:(LDA) that can handle sequential documents.
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32:and John Lafferty and is an extension to
1494:Statistical natural language processing
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194:as the topic distribution for document
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1174:to the mean parameterization, namely
7:
1459:Journal of Machine Learning Research
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151:as the word distribution of topic
14:
1287:In the dynamic topic model, only
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365:{\displaystyle \beta _{t+1,k}}
1:
1373:. ICML'06. pp. 113–120.
326:{\displaystyle \alpha _{t+1}}
425:{\displaystyle \beta _{t,k}}
144:{\displaystyle \beta _{t,k}}
392:{\displaystyle \alpha _{t}}
187:{\displaystyle \eta _{t,d}}
105:{\displaystyle \alpha _{t}}
34:Latent Dirichlet Allocation
1510:
1412:"Mixtures of Multinomials"
1319:{\displaystyle W_{t,d,n}}
289:{\displaystyle w_{t,d,n}}
236:{\displaystyle z_{t,d,n}}
61:multinomial distribution
1379:10.1145/1143844.1143859
1163:{\displaystyle \pi (x)}
1489:Latent variable models
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296:as the specific word.
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243:as the topic for the
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22:Dynamic topic models'
1410:Rennie, Jason D. M.
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247:th word in document
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1437:Proceedings of ICML
1332:variational methods
874:For each document:
780:Draw mixture model
372:are generated from
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1328:Gibbs sampling
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51:Similarly to
46:
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1418:. Retrieved
1405:
1370:
1348:
1345:
1341:
1338:Applications
1286:
1171:
1140:
662:Draw topics
657:
558:
442:
434:
299:
252:
248:
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199:
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156:
152:
113:
81:
65:
50:
41:exchangeable
38:
21:
15:
1439:. ICML '08.
953:Draw topic
1483:Categories
1420:5 December
1353:References
1035:Draw word
30:David Blei
18:statistics
1283:Inference
1247:
1235:∑
1213:
1185:π
1149:π
1085:β
1078:π
1065:∼
1003:η
996:π
983:∼
911:α
901:∼
886:η
848:δ
836:−
829:α
819:∼
811:−
804:α
789:α
763:∀
748:σ
730:−
723:β
713:∼
699:−
692:β
671:β
630:δ
618:−
611:α
601:∼
593:−
586:α
571:α
532:σ
514:−
507:β
497:∼
483:−
476:β
455:β
408:β
381:α
342:β
309:α
170:η
127:β
94:α
251:in time
198:in time
155:at time
1397:5405229
82:Define
16:Within
1395:
1385:
1141:where
47:Topics
1455:(PDF)
1415:(PDF)
1393:S2CID
877:Draw
255:, and
78:Model
1422:2011
1383:ISBN
1070:Mult
988:Mult
559:and
399:and
333:and
57:pLSA
55:and
24:are
1375:doi
1244:exp
1210:exp
72:t+1
53:LDA
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