Date post: | 13-Apr-2017 |
Category: |
Engineering |
Upload: | tomonari-masada |
View: | 444 times |
Download: | 2 times |
A Simple SGVB(Stochastic Gradient Variational Bayes)
for the CTM(Correlated Topic Model)
Tomonari MASADA ( 正田备也 )Nagasaki University (长崎大学 )
APWeb 2016 @ Suzhou
Aim•Make an informative summary of
large document sets by
•extracting word lists, each relating to
a different and particular topic.
Topic modeling2
Contribution•We propose a new posterior estimation for the correlated topic model (CTM) [Blei+ 07],•an extension of LDA [Blei+ 03] for modeling topic correlations,
•with stochastic gradient variational Bayes (SGVB) [Kingma+ 14].
4
LDA [Blei+ 03]
•Clustering word tokens by assigning each word token to
one among the topics.• : To which topic is the -th word token in document is assigned?
• : How often is the topic talked about in document ?
•Multinomial distribution for each
• : How often is the word used to talk about the topic ?
•Multinomial distribution for each
discrete variables
continuous variables
5
CTM [Blei+ 05]
•Clustering word tokens by assigning each word token to
one among the topics.• : To which topic is the -th word token in document is assigned?
• : How often is the topic talked about in document ?
• where (logistic normal distribution)
• : How often is the word used to talk about the topic ?
•Multinomial distribution for each
discrete variables
continuous variables
6
Variational BayesMaximization of ELBO (evidence lower bound)
•VB (variational Bayes) approximates the true posterior.•An approximate posterior is introduced when ELBO is
obtained by Jensen's inequality:
• : discrete hidden variables (topic assignments)• : continuous hidden variables (multinomial parameters)
7
log evidence approximate posterior
Factorization assumption
•We assume the approximate posterior factorizes
as .
•Then ELBO can be written as
8
×discrete continuous
SGVB[Kingma+ 14]
•SGVB (stochastic gradient variational Bayes) is a general framework for estimating ELBO in VB.
•SGVB is only applicable to continuous distributions .•Monte Carlo integration for expectation
9
Reparameterization
•We use the diagonal logistic normal for approximating the true posterior of .•We can efficiently sample from the logistic normal with reparameterization.
10
Monte Carlo integration
•ELBO is estimated with a sample from the approximate posterior.
• The discrete part is estimated as in the original VB. 11
"Stochastic" gradient•The expectation integrations are estimated by Monte Carlo method.•The derivatives of ELBO depend on samples.•Randomness is incorporated into the maximization of ELBO.•Does this make it easier to avoid local minima?
13
Data sets# docs # word types
NYT 149,890 46,650MOVIE 27,859 62,408
NSF 128,818 21,471
MED 125,490 42,83014
Conclusion•We incorporate randomness into the posterior inference for the CTM by using SGVB.
•The proposed method gives perplexities comparable to those achieved by LDA.
19
Pro/Con•No explicit inversion of covariance matrix is required.
•Careful tuning of gradient descent seems required.
•Only Adam was tested.20