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Technical Foundationsand Inference
Topic Model Tutorial - Part 2 Hannover, 2016
Arnim [email protected]
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● Probabilistic Graphical Models are a general framework to represent assumptions about the (in-) dependence between random variables.
● Knowing the inner workings of Topic Models helps us to better interpret their results.
Why should we care?
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Outline
● Generative storylines & Plates
● Gibbs sampling
● Simple Topic Model
● Latent Dirichlet Allocation
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Recap: Conference dinner
?
k 1 k 2k 1 k 3510
210
310
for k 1
for k 2
Probabilities:
for k 3
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Recap: Conference dinner
k 1 k 2k 1 k 3
?
=normalizing constant
number of observations in k
General case:
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Generative Storyline
=
N+1
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Generative Storyline
N+1
prior
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Plate Notation
i ;
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Gibbs sampling
X
Iteratively sample each variable conditioned on all other variables.
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Gibbs sampling
X
prior
iterations
stationarydistribution
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Simple Topic Model
Generative Storyline:
d
Draw a global distribution over topics.
For each document ddraw a topic.
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Simple Topic Model
Generative Storyline:
d
For each topic k, draw a distribution over the vocabulary.
dw
For each document ddraw the words w from the topic
indexed by z .
d
d
d
* Mixture of Unigrams
*
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Likelihood of document d being generated from topic k.
Simple Topic Model
*
* Approximation not considering the dependence of words within documents.
d
di=1
d
d
di
d
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Simple Topic Model
*
d
di=1
d
d
di
d= ?
We need to know from which topic k document d was generated.
Global distribution over topics.
topics
document
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Simple Topic Model
document
*
d
di=1
d
d
di
d=
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Simple Topic Model
document
*
d
di=1
d
d
di
d=
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Simple Topic Model
document
*
d
di=1
d
d
di
d=
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Simple Topic Model
document
*
d
di=1
d
d
di
d=
We can now sample the membership for document d and update the model.
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Latent Dirichlet Allocation
Generative Storyline:
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Latent Dirichlet Allocation
Generative Storyline:
Document specific distribution over topics.
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Latent Dirichlet Allocation
Likelihood of word i in document d being generated from topic k.
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(Simple Topic Model)Associated Press Topics
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Associated Press Topics(LDA)
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Conclusions
● Topic Models can be formulated within the wider framework of Probabilistic Graphical Models.
● Different versions of Topic Models can be formulated.
● More complex models are not necessarily better.
● However, more complex models can help to express assumptions about the dataset.
Thank you!
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References
● M. Steyvers, T. Griffiths. Latent Semantic Analysis: A Road to Meaning, chap. Probabilistic topic models, 2007
● Heinrich, Gregor. Parameter estimation for text analysis, 2008.
● P. Resnik, E. Hardisty. Gibbs sampling for the uninitiated, 2010.
● M. D. Lee, E. J. Wagenmakers. Bayesian cognitive modeling: A practical course, 2014.
● S. Jackman. Bayesian analysis for the social sciences , 2009.
