[Kim+ ICML2012] Dirichlet Process with Mixed Random Measures : A Nonparametric Topic Model for Labeled Data
1. [Kim+ ICML2012] Dirichlet Process
with Mixed Random Measures : A
Nonparametric Topic Model for
Labeled Data
2012/07/28
Nakatani Shuyo @ Cybozu Labs, Inc
twitter : @shuyo
2. LDA(Latent Dirichlet Allocation)
[Blei+ 03]
• Unsupervised Topic Model
– Each word has an unobserved topic
• Parametric
– The topic size K is given in advance
via Wikipedia
3. Labeled LDA [Ramage+ 09]
• Supervised Topic Model
– Each document has an observed label
• Parametric
via [Ramage+ 09]
5. Pros/Cons of L-LDA
• Pros
– Easy to implement
• Cons via [Ramage+ 09]
– It is necessary to specify label-topic
correspondence manually
• Its performance depends on the corresponds
※) My implementation is here : https://github.com/shuyo/iir/blob/master/lda/llda.py
6. DP-MRM [Kim+ 12]
– Dirichlet Process with Mixed Random Measures
• Supervised Topic Model
• Nonparametric
– K is not the topic size, but the label size
𝛼
𝑁𝑗
𝐻 𝐺0𝑘 𝐺𝑗 𝜃 𝑗𝑖 𝑥 𝑗𝑖
𝜆j 𝑟𝑗 𝐷
𝛽 𝛾𝑘 𝜂
𝐾
7. Generative Process for DP-MRM
𝛼
Each label has a random
measure as topic space 𝑁𝑗
𝐻 𝐺0𝑘 𝐺𝑗 𝜃 𝑗𝑖 𝑥 𝑗𝑖
• 𝐻 = Dir 𝛽
𝜆j 𝑟𝑗 𝐷
• 𝐺0𝑘 ~DP 𝛾 𝑘 , 𝐻 𝛽
𝐾
𝛾𝑘 𝜂
• 𝜆 𝑗 ~Dir 𝒓 𝑗 𝜂 where 𝒓 𝑗 = 𝐼 𝑘∈label 𝑗
• 𝐺 𝑗 ~DP 𝛼, 𝑘∈label 𝑗 𝜆 𝑗𝑘 𝐺0𝑘 mixed random measures
• 𝜃 𝑗𝑖 ~𝐺 𝑗 , 𝑥 𝑗𝑖 ~𝐹 𝜃 𝑗𝑖 = Multi 𝜃 𝑗𝑖
9. Chinese Restaurant Franchise
• 𝑡 𝑗𝑖 : table index of 𝑖-th term in 𝑗-th document
• 𝑘 𝑗𝑡 , 𝑙 𝑗𝑡 : dish indexes on 𝑡-th table of 𝑗-th
document This layer consists on
only a single DP G0
on normal HDP
13. via [Kim+ 12]
• L-LDA can also predict single labeled document to
assign a common second label to any documents.
14. References
• [Kim+ ICML2012] Dirichlet Process with Mixed
Random Measures : A Nonparametric Topic
Model for Labeled Data
• [Ramage+ EMNLP2009] Labeled LDA : A
supervised topic model for credit attribution in
multi-labeled corpora
• [Blei+ 2003] Latent Dirichlet Allocation