LDA Beginner's Tutorial

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Introduction to Latent Dirichlet Allocation (LDA). We cover the basic ideas necessary to understand LDA then construct the model from its generative process. Intuitions are emphasized but little guidance is given for fitting the model which is not very insightful.

Bildung Technologie

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Latent Dirichlet Allocation (LDA)
- for ML-IR Discussion Group
1
Prepared by Wayne Tai Lee, Satpreet Singh

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Latent Dirichlet Allocation:
A Bayesian Unsupervised Learning Model
Roadmap
2
• Unsupervised learning
• Bayesian Statistics
• Mixture Models
• LDA – theory and intuition
• LDA – practice and applications

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Unsupervised Learning
Learning patterns with no labels
3
• Clustering is a form of “Unsupervised learning”
• Classification is known as supervised learning
• Validation is difficult

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How would you cluster?

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Documents of wikipedia
Now try these ones!

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Bayesian Statistics
A framework to update your beliefs
6
• Probabilities as beliefs
• Updates your belief as data is observed
• Requires a model that describes the data generation

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Candidate potential
Example: Evaluating Candidates

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Candidate potential
Example: Evaluating Candidates
Schooling
Experience
Interview
Internship

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Candidate potential
Example: Evaluating Candidates
Schooling
Experience
Interview
Internship
How to update?!

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Model for candidates Model for data generation

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Mixture Models
A popular statistical model
12
• An easy way to build hierarchical relationships

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Mixture models visualized
13
Candidate Quality
High
Low

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Marginal Distribution of Candidate Performance: ignore quality

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Distribution of Candidate Performance:

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Distribution of Candidate Performance:
Mixture Weights

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Mixture Weights
Distribution of Candidate Performance:

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Distribution of Candidate Performance:
?
? ?
?

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How are words in a document generated?
19

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One possibility:
20
Each word comes from different topics (bag of words: ignore order)

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How are words in a document generated?
21
Each word comes from different topics
Mixture Weight
for Topic k
Multinomial Distribution
over ALL words based
on topic k

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Just a mixture model
22
Word
Topic 1
Topic K
Leadership
Big Data
Machine Learning

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Just a mixture model
23
Word
Topic 1
Topic K
Leadership
Big Data
Machine Learning
1) Pick a topic
2) Pick a word

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Just a mixture model
24
Word
Topic 1
Topic K
Leadership
Big Data
Machine Learning
The chosen
Topic: Z

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Just a mixture model
25
Word
Topic 1
Topic K
Leadership
Big Data
Machine Learning
So we really want to know
1) Z
2) _
3) _
The chosen
Topic: Z

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Just a mixture model
26
Word
Topic 1
Topic K
Leadership
Big Data
Machine Learning
So we really want to know
1) Z (cluster for the word)
2) (document composition)
3) (key words)
The chosen
Topic: Z

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Review!
27
Z W

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Zd,n
k=1…K
Wd,n
n=1,…,Nd
d=1,…,D
K: number of topics
Nd: number of words
D: number of documents

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Zd,n
k=1…K
Wd,n
n=1,…,Nd
d=1,…,D
K: number of topics
Nd: number of words
D: number of documents
Bayesian: But what about the distribution for and ??

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Zd,n
k=1…K
Wd,n
n=1,…,Nd
d=1,…,D
K: number of topics
Nd: number of words
D: number of documents
Bayesian: But what about the distribution for and ??

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and control the “sparsity” of the weights for the multinomial.
Implications: a priori we assume
- Topics have few key words
- Documents only have a small subset of topics

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Dirichlet Distribution with Different Sparsity Parameters
32

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Latent Dirichlet Allocation!!!
Zd,n
k=1…K
Wd,n
n=1,…,Nd

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How do we fit this model?
Want the posterior:
Worst part of Bayesian Analysis…..personally speaking~

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Two main ways to get posterior:
- Sampling methods
- Asymtotically correct
- Time consuming
- Lots of black magic in sampling tricks
- Variational methods (practical solution!)
- An approximation with no guarantees
- Faster
- Need math skills

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Variational Bayes (specifically mean field variational bayes):
What’s crazy?
- Assumes all the latent variables are independent
What’s not crazy?
- Finds the “best” model within this crazy class.
- Best under KL divergence
Empirically have shown promising results!
For “sufficient” details:
“Explaining Variational Approximations ” by Ormerod and Wand

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LDA Take Home
37
- An intuitively appealing Bayesian unsupervised learning model
- Training is difficult
- Lots of packages exist, main issue is scalability
- Validation is difficult
- Usually cast into a supervised learning framework
- Presentation is difficult
- Visualization for the Bayesian model is hard.

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2. ©2013 LinkedIn Corporation. All Rights Reserved. Latent Dirichlet Allocation: A Bayesian Unsupervised Learning Model Roadmap 2 • Unsupervised learning • Bayesian Statistics • Mixture Models • LDA – theory and intuition • LDA – practice and applications

3. ©2013 LinkedIn Corporation. All Rights Reserved. Unsupervised Learning Learning patterns with no labels 3 • Clustering is a form of “Unsupervised learning” • Classification is known as supervised learning • Validation is difficult

6. ©2013 LinkedIn Corporation. All Rights Reserved. Bayesian Statistics A framework to update your beliefs 6 • Probabilities as beliefs • Updates your belief as data is observed • Requires a model that describes the data generation

21. ©2013 LinkedIn Corporation. All Rights Reserved. How are words in a document generated? 21 Each word comes from different topics Mixture Weight for Topic k Multinomial Distribution over ALL words based on topic k

26. ©2013 LinkedIn Corporation. All Rights Reserved. Just a mixture model 26 Word Topic 1 Topic K Leadership Big Data Machine Learning So we really want to know 1) Z (cluster for the word) 2) (document composition) 3) (key words) The chosen Topic: Z

29. ©2013 LinkedIn Corporation. All Rights Reserved. 29 Zd,n k=1…K Wd,n n=1,…,Nd d=1,…,D K: number of topics Nd: number of words D: number of documents Bayesian: But what about the distribution for and ??

30. ©2013 LinkedIn Corporation. All Rights Reserved. 30 Zd,n k=1…K Wd,n n=1,…,Nd d=1,…,D K: number of topics Nd: number of words D: number of documents Bayesian: But what about the distribution for and ??

31. ©2013 LinkedIn Corporation. All Rights Reserved. 31 and control the “sparsity” of the weights for the multinomial. Implications: a priori we assume - Topics have few key words - Documents only have a small subset of topics

35. ©2013 LinkedIn Corporation. All Rights Reserved. 35 Two main ways to get posterior: - Sampling methods - Asymtotically correct - Time consuming - Lots of black magic in sampling tricks - Variational methods (practical solution!) - An approximation with no guarantees - Faster - Need math skills

36. ©2013 LinkedIn Corporation. All Rights Reserved. 36 Variational Bayes (specifically mean field variational bayes): What’s crazy? - Assumes all the latent variables are independent What’s not crazy? - Finds the “best” model within this crazy class. - Best under KL divergence Empirically have shown promising results! For “sufficient” details: “Explaining Variational Approximations ” by Ormerod and Wand

37. ©2013 LinkedIn Corporation. All Rights Reserved. LDA Take Home 37 - An intuitively appealing Bayesian unsupervised learning model - Training is difficult - Lots of packages exist, main issue is scalability - Validation is difficult - Usually cast into a supervised learning framework - Presentation is difficult - Visualization for the Bayesian model is hard.

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Take home: validation is difficult….no true answer here.
Clustering documents is difficult because many repeated words are used. Some documents may be similar to one another on different topics. So we might want to cluster allowing membership.
2 stage process
Example: the word usage of “professional” is probably higher in the topic of professional network than a social network.
2 stage process
2 stage process
2 stage process
2 stage process
2 stage process
Example: the word usage of “professional” is probably higher in the topic of professional network than a social network.
Example: the word usage of “professional” is probably higher in the topic of professional network than a social network.
Example: the word usage of “professional” is probably higher in the topic of professional network than a social network.
Example: the word usage of “professional” is probably higher in the topic of professional network than a social network.
Example: the word usage of “professional” is probably higher in the topic of professional network than a social network.
Example: the word usage of “professional” is probably higher in the topic of professional network than a social network.
Example: the word usage of “professional” is probably higher in the topic of professional network than a social network.
Example: the word usage of “professional” is probably higher in the topic of professional network than a social network.
Example: the word usage of “professional” is probably higher in the topic of professional network than a social network.

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