Part IV - Department of Computer Science and Engineering

Report
AAAI 2014 Tutorial
Latent Tree Models
Part IV: Applications
Nevin L. Zhang
Dept. of Computer Science & Engineering
The Hong Kong Univ. of Sci. & Tech.
http://www.cse.ust.hk/~lzhang
Applications of Latent Tree Analysis (LTA)

What can LTA be used for:





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Discovery of co-occurrence patterns in binary data
Discovery of correlation patterns in general discrete data
Discovery of latent variable/structures
Multidimensional clustering
Topic detection in text data
Probabilistic modelling
Applications

Analysis of survey data


Analysis of text data


Market survey data, social survey, medical survey data
Topic detection
Approximate probabilistic inference
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Part IV: Applications

Approximate Inference in Bayesian Networks

Analysis of social survey data

Topic detection in text data

Analysis of medical symptom survey data

Software
AAAI 2014 Tutorial Nevin L. Zhang HKUST
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LTMs for Probabilistic Modelling

Attractive Representation of Joint Distributions

Computationally very simple to work with.

Represent complex relationships among observed variables.

What does the structure look like without the latent variables?
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Approximate Inference in Bayesian Networks

In a Bayesian network over observed variables,
exact inference can be computationally prohibitive.

Two-phase approximate inference:
 Offline



(Wang et al. AAAI 2008)
Sample data set from the original network
Learn a latent tree model (secondary representation)
Online

Make inference using the latent tree model. (Fast)
Sample
Learn LTM
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Empirical Evaluations

Alternatives

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Original networks

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LTM (1k), LTM (10k), LTM (100k): with different sample size for Phase 1.
CL (100k): Phase 1 learns Chow-Liu tree
LCM (100k): Phase 1 learns latent class model
Loopy Belief Propagation (LBP)
ALARM, INSURANCE, MILDEW, BARLEY, etc.
Evaluation:


500 random queries
Quality of approximation measured using KL from exact answer.
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Empirical Results
sparse

C: cardinality of latent
variables

When C is large enough,
LTM achieves good
approximation in all cases.

Better than LBP on g, d,h

Better than CL on d, h.

Key Advantage: Online
phase is 2 to 3 orders of
magnitude faster than
exact inference
AAAI 2014 Tutorial Nevin L. Zhang HKUST
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7
Part III: Applications

Approximate Inference in Bayesian networks

Analysis of social survey data

Topic detection

Analysis of medical symptom survey data

Software
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Social Survey Data
// Survey on corruption in Hong Kong and performance of the anti-corruption
agency -- ICAC
//31 questions, 1200 samples
C_City:
s0 s1 s2 s3
// very common, quite common, uncommon, very uncommon
C_Gov:
s0 s1 s2 s3
C_Bus:
s0 s1 s2 s3
Tolerance_C_Gov:
s0 s1 s2 s3
Tolerance_C_Bus:
s0 s1 s2 s3
WillingReport_C:
s0 s1 s2
// yes, no, depends
LeaveContactInfo:
s0 s1
// yes, no
//totally intolerable, intolerable, tolerable, totally tolerable
I_EncourageReport:
s0 s1 s2 s3 s4
// very sufficient, sufficient, average, ...
I_Effectiveness:
s0 s1 s2 s3 s4
//very e, e, a, in-e, very in-e
I_Deterrence:
s0 s1 s2 s3 s4
// very sufficient, sufficient, average, ...
…..
-1 -1 -1 0 0 -1 -1 -1 -1 -1 -1 0 -1 -1 -1 0 1 1 -1 -1 2 0 2 2 1 3 1 1 4 1 0 1.0
-1 -1 -1 0 0 -1 -1 1 1 -1 -1 0 0 -1 1 -1 1 3 2 2 0 0 0 2 1 2 0 0 2 1 0 1.0
-1 -1 -1 0 0 -1 -1 2 1 2 0 0 0 2 -1 -1 1 1 1 0 2 0 1 2 -1 2 0 1 2 1 0 1.0
….
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Latent Structure Discovery
Y2: Demographic info;
Y3: Tolerance toward corruption;
Y4: ICAC performance;
Y5: Change in level of corruption;
Y6: Level of corruption;
Y7: ICAC accountability
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Multidimensional Clustering
Y2=s0: Low income youngsters;
Y2=s1: Women with no/low income;
Y2=s2: people with good education and good income;
Y2=s3: people with poor education and average income.
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Multidimensional Clustering
Y3=s0: people who find corruption totally intolerable; 57%
Y3=s1: people who find corruption intolerable; 27%
Y3=s2: people who find corruption tolerable; 15%
Interesting finding:
Y3=s2: 29+19=48% find C-Gov totally intolerable or intolerable; 5% for C-Bus
Y3=s1: 54% find C-Gov totally intolerable; 2% for C-Bus
Y3=s0: Same attitude toward C-Gov and C-Bus
People who are tough on corruption are equally tough toward C-Gov and C-Bus.
People who are lenient about corruption are more lenient C-Bus than C-GOv
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Multidimensional Clustering
 Who are the toughest toward corruption among the 4 groups?
Y2=s2: ( good education and good income) the least tolerant. 4% tolerable
Y2=s3: (poor education and average income) the most tolerant. 32% tolerable
The other two classes are in between.
 Summary: Latent tree analysis of social survey data can reveal
• Interesting latent structures
• Interesting clusters
• Interesting relationships among the clusters.
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Part III: Applications

Approximate Inference

Analysis of social survey data

Topic detection (Analysis of text data)

Analysis of medical symptom survey data

Software
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Latent Tree Models for Topic Detection

Basics
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Aggregation of miniature topics
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Topic extraction and characterization

Empirical results
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What is a topic in LTA?
LTM for
toy text data

Topic: State of latent variable, soft collection of documents
Characterized by: Conditional probability of word given latent state, or, document
frequency of word in collection:

# docs containing the word / total # of docs in the topic



Probabilities all words for a topic (in a column) do not sum to 1.
Y1=2: oop; Y1=1: Programming; Y1=0: background
Background topics for other latent variables not shown.
How are topics and documents are related?


Topic: A collection of documents
A document is a member of a topic


Can belong to multiple topics with different probabilities
Probabilities for each document (in each row) do not sum to 1.
D97, D115, D205, D528 are documents from the toy text data
Table shows:

D97 is a web page on OOP from U of Wisconsin Madison

D528 is a web page on AI from U of Texas Austin
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LTA Differs from Latent Dirichlet Allocation (LDA)

LDA Topic: Distribution over vocabulary



Frequencies a writer would use each word when writing about the topic
Probabilities for a topic (in a column) sum to 1
In LDA a document is a mixture of topics (LTA: Topic is a collection of
documents)

Probabilities in each row sum to 1
Latent Tree Models for Topic Detection

Basics

Aggregation of miniature topics

Topic extraction and characterization

Empirical results
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Latent Tree Model for a Subset of Newsgroup Data

Latent variable give miniature topics.

Intuitively, more interesting topics can be detected if we combine

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Z11, Z12, Z13
Z14, Z15, Z16
Z17, Z18, Z19
BI algorithm produces flat models: Each latent variable directly
connected to at least one observed variables.
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Hierarchical Latent Tree Analysis (HLTA)

Convert the latent variables into observed one via hard assignment.


Afterwards, Z11-Z19 become observed.
Run BI on Z11-Z19
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Hierarchical Latent Tree Analysis (HLTA)

Stack model for Z11-Z19 on top of model for the words

Repeat until no more than 2 latent variables or predetermined level
reached.

The result is called a hierarchical latent tree model (HLTM)
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Hierarchical Latent Tree Analysis (HLTA)

Part II: Cannot determine edge orientations based solely on data.

Here hierarchical structure introduced to improve model
interpretability.
Data + interpretability  hierarchical structure.

It does not necessarily improve model fit.
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Latent Tree Models for Topic Detection

Basics

Aggregation of miniature topics

Topic extraction and characterization

Empirical results
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Semantic Base

Interpreting states of Z21

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Z11, Z12, and Z13 introduced because of co-occurrence of

“computer”, “Science”;

“card”, “display”, …., “video”; and

“dos” , “windows”
Z21 introduced because of correlations among Z11, Z12, Z13
So, interpretation of the states of Z21 is to be based on the words in
the sub-tree rooted at Z21. They form the semantic base of Z21.
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Effective Semantic Base

Semantic base might be too large to handle.

Effective base: Subset of semantic base that matters.

Sort variables Xi from semantic base in descending of I(Z; Xi).

I(Z; X1, …, Xi): Mutual information between Z and first i-th variables

Chen et al. AIJ 2012
Estimated via sampling, increases with i.

I(Z; X1, …, Xm): Mutual information between Z and all m variables in

Information coverage of the first i-th variable
semantic base
I(Z; X1, …, Xi)/ I(Z; X1, …, Xm):

Effective semantic base:

Set of leading variables with information coverage higher than a certain level,
i.e., 95%.
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Z22:
Upper: Information coverage
Lower: Mutual Information

Effective semantic bases are typically smaller than Semantic bases.



Z22: Semantic base --10 variables, Effective semantic base – 8 variable
Differences are much larger in models with hundreds of variables.
Words are the front are more informative in distinguishing between
the states of the latent variable.
Topic Characterizations

HLTA characterizes Latent state (topics) using
probabilities of words from effective semantic base

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Topic Z22=s1 characterized using words


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NOT sorted according to probability, but mutual information
Occur with high probabilities in documents on to the topic,
and
Occur with low probability in documents NOT on the topic.
LDA, HLDA, …


Topic characterized using words that occur with highest
probability in the topic.
Not necessarily the best words to distinguish the topic from
other topics.
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Latent Tree Models for Topic Detection

Basics

Aggregation of miniature topics

Topic extraction and characterization

Empirical results
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Empirical Results

Show the results of HLTA on real-world data

Compare HLTA with HLDA and LDA
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NIPS Data
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1,740 papers published at NIPS between 1988 – 1999.
Vocabulary:


HLTA produced a model with 382 latent variables, arranged on 5
levels.


Level 1 – 279; Level 2 – 72; Level 3 - 21; Level 4 - 8; Level 5 - 2
Example topics on next few slides


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1,000 words selected using average TF-IDF.
Topic characterizations, topic sizes,
Topic groups, topic group labels.
For details: http://www.cse.ust.hk/~lzhang/ltm/index.htm
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HLTA Topics: Level-3

likelihood bayesian statistical gaussian
conditional

0.34 likelihood bayesian statistical conditional
0.16 gaussian covariance variance matrix
0.21 eigenvalues matrix gaussian covariance


0.20 markov speech speaker hmms hmm
0.14 speech hmm speaker hmms markov
0.13 reinforcement sutton barto policy actions
0.10 reinforcement sutton barto actions policy
trained classification classifier
regression classifiers
0.25 validation regression svm machines
0.07 svm machines vapnik regression
0.38 trained test table train testing
0.30 classification classifier classifiers class cl

0.27 cells cortex cortical activity visual
0.33 neurons neuron synaptic synapses
images image pixel pixels object
0.18 membrane potentials spike spikes firing
0.15 firing spike membrane spikes potentials
0.18 circuit voltage circuits vlsi chip
0.26 dynamics dynamical attractor stable
attractors
hidden propagation layer backpropagation
units
0.40 hidden backpropagation multilayer
architecture architectures
0.40 propagation layer units back net
cells neurons cortex firing visual
0.17 visual cells cortical cortex activity
0.25 images image pixel pixels texture
0.16 receptive orientation objects object
0.21 object objects perception receptive

reinforcement markov speech hmm
transition

…..
HLTA Topics: Level-2

markov speech hmm speaker hmms

reinforcement sutton barto actions policy
0.14 markov stochastic hmms sequence hmm
0.12 transition states reinforcement reward
0.10 hmm hmms sequence markov stochastic
0.10 reinforcement policy reward states
0.15 speech language word speaker acoustic
0.14 trajectory trajectories path adaptive
0.06 speech speaker acoustic word language
0.12 actions action control controller agent
0.16 delay cycle oscillator frame sound
0.09 sutton barto td critic moore
0.10 frame sound delay oscillator cycle
0.14 strings string length symbol
HLTA Topics: Level-2

likelihood bayesian statistical conditional
posterior
0.34 likelihood statistical conditional density
0.35 entropy variables divergence mutual
0.19 probabilistic bayesian prior posterior
0.11 bayesian posterior prior bayes
0.15 mixture mixtures experts latent
0.14 mixture mixtures experts hierarchical
0.34 estimate estimation estimating estimated
0.21 estimate estimation estimates estimated


regression validation vapnik svm
machines
0.24 regression svm vapnik margin kernel
0.05 svm vapnik margin kernel regression
0.19 validation cross stopping pruning
0.07 machines boosting machine boltzmann

classification classifier classifiers class
classes
gaussian covariance matrix variance
eigenvalues
0.28 classification classifier classifiers class
0.09 matrix pca gaussian covariance variance
0.23 gaussian covariance variance matrix pca
0.09 pca gaussian matrix covariance variance
0.18 eigenvalues eigenvalue eigenvectors ij
0.15 blind mixing ica coefficients inverse
0.13 handwritten digit character digits
0.24 discriminant label labels discrimination

trained test table train testing
0.38 trained test table train testing
0.44 experiments correct improved
improvement correctly

…
HLTA Topics: Level-1

likelihood statistical conditional density log

mixture mixtures experts hierarchical latent
0.30 likelihood conditional log em maximum
0.19 mixture mixtures
0.42 statistical statistics
0.34 multiple individual missing hierarchical
0.19 density densities
0.15 hierarchical sparse missing multiple
0.07 experts expert

0.32 weighted sum
entropy variables variable divergence
mutual
0.16 entropy divergence mutual
0.31 variables variable

estimate estimation estimated estimates
estimating
0.38 estimate estimation estimated estimating

bayesian posterior probabilistic prior bayes
0.19 bayesian prior bayes posterior priors
0.09 bayesian posterior prior priors bayes
0.29 probabilistic distributions probabilities
0.16 inference gibbs sampling generative
0.19 estimate estimates estimation estimated
0.29 estimator true unknown
0.33 sample samples
0.40 assumption assume assumptions assumed
0.27 observations observation observed
0.19 mackay independent averaging ensemble
0.08 belief graphical variational
0.09 monte carlo
0.09 uk ac

… for aggregate miniature topics:
Reason
Many Level 1 topics correspond to
trivial word co-occurrences , not
meaningful
HLTA Topics: Level-4 & 5
Level 4

visual cortex cells neurons firing
0.34 cells cortex firing neurons visual
0.28 cells neurons cortex firing visual
0.41 approximation gradient optimization
0.29 algorithms optimal approximation
0.39 likelihood bayesian statistical gaussian

images image trained hidden pixel
0.22 regression classification classifier
0.29 trained classification classifier classifiers
0.02 classification classifier regression
0.28 learn learned structure feature features
0.23 feature features structure learn learned
0.24 images image pixel pixels object
0.13 reinforcement transition markov speech
0.14 speech hmm markov transition
0.40 hidden propagation layer
backpropagation units
Level 5

visual cortex cells neurons firing
0.37 visual cortex firing neurons cells
0.39 visual cells firing cortex neurons
0.25 images image pixel hidden trained
0.09 hidden trained images image pixel
0.20 trained hidden images image pixel
0.15 image images pixel trained hidden
Summary of HLTA Results on NIPS Data

Level 1: 279 latent variables


Level 2: 72 latent variables



Meaningful topics, very general
Level 5: 2 latent variables


Meaningful topics, and meaningful topic groups
More general than Level 2 topics
Level 4: 8 latent variables


Meaningful topics, and meaningful topic groups
Level 3 : 21 latent variables


Many capture trivial word co-occurrence patterns
Too few
In application, one can choose to output the topics at a certain level
according the desired number of topics.

For NIPS data, either level-2 topics or level-3 topics.
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HLDA Topics
units hidden layer unit weight
 gaussian log density likelihood estimate
margin kernel support xi bound
generalization student weight teacher optimal
gaussian bayesian kernel evidence posterior
chip analog circuit neuron voltage
classifier rbf class classifiers classification
speech recognition hmm context word
ica independent separation source sources
image images matching level object
tree trees node nodes boosting
variables variable bayesian conditional
family face strategy differential functional
weighting source grammar sequences
polynomial regression derivative
em machine annealing max min

regression prediction selection criterion query
validation obs generalization cross pruning
mlp risk classifier classification confidence
loss song transfer bounds wt
principal curve eq curves rules

control optimal algorithms approximation step
policy action reinforcement states actions
experts mixture em expert gaussian
convergence gradient batch descent means
control controller nonlinear series forward
distance tangent vectors euclidean distances
robot reinforcement position control path
bias variance regression learner exploration
blocks block length basic experiment
td evaluation features temporal expert
path reward light stimuli paths
Long hmms recurrent matrix term
channel call cell channels rl


image images recognition pixel feature
video motion visual speech recognition
face images faces recognition facial
ocular dominance orientation cortical cortex
character characters pca coding field
resolution false true detection context
….
LDA Topics
inputs outputs trained produce actual
dynamics dynamical stable attractor
synaptic synapses inhibitory excitatory
correlation power correlations cross
states stochastic transition dynamic
basis rbf radial gaussian centers
solution constraints solutions constraint
type elements group groups element
edge light intensity edges contour
recurrent language string symbol strings
propagation back rumelhart bp hinton
ii region regions iii chain
graph matching annealing match
context mlp letter nn letters
fig eq proposed fast proc
variables variable belief conditional i
pp vol ca eds ieee
units unit hidden connections connected
hmm markov probabilities hidden hybrid
object objects recognition view shape
robot environment goal grid world
entropy natural statistical log statistics
experts expert gating architecture jordan
trajectory arm inverse trajectories hand
sequence step sequences length s
gaussian density covariance densities
positive negative instance instances np
target detection targets FALSE normal
activity active module modules brain
mixture likelihood em log maximum
channel stage channels call routing
term long scale factor range
…
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Comparisons between HLTA and HLDA
HLTA Topics

HLDA Topics
likelihood bayesian statistical conditional
posterior

gaussian log density likelihood estimate
margin kernel support xi bound
generalization student weight teacher optimal
gaussian bayesian kernel evidence posterior
chip analog circuit neuron voltage
classifier rbf class classifiers classification
speech recognition hmm context word

control optimal algorithms approximation step
policy action reinforcement states actions
experts mixture em expert gaussian
convergence gradient batch descent means
control controller nonlinear series forward
distance tangent vectors euclidean distances
robot reinforcement position control path
bias variance regression learner exploration
blocks block length basic experiment
0.34 likelihood statistical conditional density
0.35 entropy variables divergence mutual
0.19 probabilistic bayesian prior posterior
0.11 bayesian posterior prior bayes
0.15 mixture mixtures experts latent
0.14 mixture mixtures experts hierarchical

reinforcement sutton barto actions policy
0.12 transition states reinforcement reward
0.10 reinforcement policy reward states
0.14 trajectory trajectories path adaptive
0.12 actions action control controller agent
0.09 sutton barto td critic moore

HLTA topics have sizes, HLDA/LDA topics do not

HLTA produces better hierarchy

HLTA gives better topic characterizations
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Measure of Topic Quality

Suppose a topic t is described using M words

The topic coherence score for t is:

Idea


The words for a topic would tend to co-occur.

Given a list of words, the more often the words co-occur, than the better the list is
as a definition of a topic.
Note:

Score decreases with M.

Topics be compared should be described using the same number of words
D. Mimno, H. M. Wallach, E. Talley, M. Leenders, and A. McCallum. Optimizing semantic
coherence in topic models. In Proceedings of the Conference on Empirical Methods in
AAAI
2014 Tutorial
Nevin2011
L. Zhang
41
Natural Language Processing
, pages
262–272,
. HKUST
HLTA Found More Coherent Topics than LDA and HLDA

HLTA (L3-L4): All non-background topics from Levels 3 and 4: 47
HLTA (L2-L3-L4): All non-background topics from Levels 2, 3 and 4: 140

LDA was instructed to find two sets of topics with 47 and140 topics

HLDA found more 179.
HLDA-s: A subset of the HLDA topics were sampled for fair comparison.


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Comparisons in Terms of Model Fit

Regard LDA, HLDA and HLTA as methods for text modeling


Evaluation:



Build a probabilistic model for the corpus
Per-document held-out loglikelihood (-log(perplexity)).
Measure performance of model on predicting unseen data
Data:



NIPS:
1,740 papers from NIPS, 1,000 words,
JACM:
536 abstracts from J of ACM, 1,809 words.
NEWSGROUP: 20,000 newsgroup posts, 1,000 words.
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
HLTA results robust w.r.t UD-test threshold
 The values 1, 3, 5 are from literature on Bayes factor (see Part III)

LDA produced by far worst models in all cases.
HLTA out-performed HLDA on NIPS, tied on JACP, and beaten on
Newsgroup
Caution: Better model does not implies better topics



Running time on NIPS:
 LDA – 3.6 hours, HLTA – 17 hours, HLDA – 68 hours.
Summary
HLTA


LDA, HLDA

Topic: collection of documents

Topic: Distribution over vocabulary

Have sizes

Don’t have sizes

Characterization: Words occur with
high probability in topic, low
probability in other documents

Characterization: Words occur with
high probability in topic

Document: A member of topic, can
belong to multiple topics with
probability 1.

Document: A mixture of topics

HLTA produces better hierarchy than HLDA

HLTA produce more coherent topics than LDA and HLDA
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Part III: Applications

Approximate Inference in Bayesian networks

Analysis of social survey data

Topic detection

Analysis of medical symptom survey data

Software
AAAI 2014 Tutorial Nevin L. Zhang HKUST
46
Background of Research

Common practice in China, increasingly in Western world
 Patients of a WM disease divided into several TCM classes
 Different classes are treated differently using TCM treatments.

Example:
 WM disease: Depression
 TCM Classes:

Liver-Qi Stagnation (肝气郁结). Treatment principle: 疏肝解郁, Prescription:
柴胡疏肝散

Deficiency of Liver Yin and Kidney Yin (肝肾阴虚):Treatment principle: 滋肾养
肝, Prescription: 逍遥散合六味地黄丸

Vacuity of both heart and spleen (心脾两虚). Treatment principle: 益气健脾,
Prescription: 归脾汤

….
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Key Question

How should patients of a WM disease be divided into
subclasses from the TCM perspective?
 What TCM classes?
 What are the characteristics of each TCM class?
 How to differentiate different TCM classes?

Important for
 Clinic practice
 Research


Randomized controlled trials for efficacy

Modern biomedical understanding of TCM concepts
No consensus. Different doctors/researchers use different
schemes. Key weakness of TCM.
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Key Idea

Our objective:
 Provide an evidence-based method for TCM patient classification

Key Idea
 Cluster analysis of symptom data => empirical partition of patients
 Check to see whether it corresponds to TCM class concept

Key technology: Multidimensional clustering
 Motivation for developing latent tree analysis
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Symptoms Data of Depressive Patients

Subjects:



604 depressive patients aged between 19 and 69 from 9 hospitals
Selected using the Chinese classification of mental disorder clinic
guideline CCMD-3
Exclusion:


(Zhao et al. JACM 2014)
Subjects we took anti-depression drugs within two weeks prior to the survey;
women in the gestational and suckling periods, .. etc
Symptom variables




From the TCM literature on depression between 1994 and 2004.
Searched with the phrase “抑郁 and 证” on the CNKI (China National
Knowledge Infrastructure) data
Kept only those on studies where patients were selected using the ICD-9,
ICD-10, CCMD-2, or CCMD-3 guidelines.
143 symptoms reported in those studies altogether.
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The Depression Data

Data as a table
 604 rows, each for a patient
 143 columns, each for a symptom
 Table cells: 0 – symptom not present, 1 – symptom present

Removed: Symptoms occurring <10 times

86 symptoms variables entered latent tree analysis.

Structure of the latent tree model obtained on the next two slides.
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Model Obtained for a Depression Data (Top)
AAAI 2014 Tutorial Nevin L. Zhang HKUST
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Model obtained for a Depression Data (Bottom)
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The Empirical Partitions

The first cluster (Y29= s0) consists of 54% of the patients and while the cluster
(Y29= s1) consists of 46% of the patients.

The two symptoms ‘fear of cold’ and ‘cold limbs’ do not occur often in the first
cluster

While they both tend to occur with high probabilities (0.8 and 0.85) in the
second cluster.
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Probabilistic Symptom co-occurrence pattern

Probabilistic symptom co-occurrence pattern:
The table indicates that the two symptoms ‘fear of cold’ and ‘cold limbs’ tend
to co-occur in the cluster Y29= s1



Pattern meaningful from the TCM perspective.

TCM asserts that YANG DEFICIENCY (阳虚) can lead to, among other
symptoms, ‘fear of cold’ and ‘cold limbs’

So, the co-occurrence pattern suggests the TCM symdrome type (证型)
YANG DEFICIENCY (阳虚).
The partition Y29 suggests that

Among depressive patients, there is a subclass of
patient with YANG DEFICIENCY.

In this subclass, ‘fear of cold’ and ‘cold limbs’
co-occur with high probabilities (0.8 and 0.85)
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Probabilistic Symptom co-occurrence pattern

Y28= s1 captures the probabilistic co-occurrence of ‘aching lumbus’, ‘lumbar pain
like pressure’ and ‘lumbar pain like warmth’.

This pattern is present in 27% of the patients.

It suggests that

Among depressive patients, there is a subclass that correspond to the TCM
concept of KIDNEY DEPRIVED OF NOURISHMENT (肾虚失养)

Characteristics of the subclass given by distributions for Y28= s1
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Probabilistic Symptom co-occurrence pattern

Y27= s1 captures the probabilistic co-occurrence of ‘weak lumbus and knees’ and ‘cumbersome
limbs’.

This pattern is present in 44% of the patients

It suggests that,


Among depressive patients, there is a subclass that correspond to the TCM concept of
KIDNEY DEFICIENCY (肾虚)

Characteristics of the subclass given by distributions for Y 27= s1
Y27, Y28, Y29 together provide evidence for defining KIDNEY YANG DEFICIENCY
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Probabilistic Symptom co-occurrence pattern

Pattern Y21= s1: evidence for defining STAGNANT QI TURNING INTO FIRE
(气郁化火)

Y15= s1 : evidence for defining QI DEFICIENCY

Y17 = s1 : evidence for defining HEART QI DEFICIENCY

Y16= s1 : evidence for defining QI STAGNATION

Y19= s1: evidence for defining QI STAGNATION IN HEAD
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Probabilistic Symptom co-occurrence pattern

Y9= s1 :evidence for defining DEFICIENCY OF BOTH QI AND YIN (气阴两虚)

Y10= s1: evidence for defining YIN DEFICIENCY (阴虚)

Y11= s1: evidence for defining DEFICIENCY OF STOMACH/SPLEEN YIN (脾胃
阴虚)
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Symptom Mutual-Exclusion Patterns

Some empirical partitions reveal
symptom exclusion patterns

Y1 reveals the mutual exclusion of
‘white tongue coating’, ‘yellow tongue
coating’ and ‘yellow-white tongue
coating’

Y2 reveals the mutual exclusion of ‘thin
tongue coating’, ‘thick tongue coating’
and ‘little tongue coating’.
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Summary of TCM Data Analysis

By analyzing 604 cases of depressive patient data using latent tree models
we have discovered a host of probabilistic symptom co-occurrence patterns
and symptom mutual-exclusion patterns.

Most of the co-occurrence patterns have clear TCM syndrome connotations,
while the mutual-exclusion patterns are also reasonable and meaningful.

The patterns can be used as evidence for the task of defining TCM classes
in the context of depressive patients and for differentiating between those
classes.
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(Zhang et al. JACM 2008)
Another Perspective: Statistical Validation of TCM Postulates
…..
…..
Y28 = s1
Kidney deprived of
nourishment
Y29 = s1
Yang Deficiency

TCM terms such as Yang Deficiency were introduced to explain symptom cooccurrence patterns observed in clinic practice.
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Value of Work in View of Others

D. Haughton and J. Haughton. Living Standards Analytics:
Development through the Lens of Household Survey Data.
Springer. 2012

Zhang et al. provide a very interesting application of latent class
(tree) models to diagnoses in traditional Chinese medicine
(TCM).

The results tend to confirm known theories in Chinese traditional
medicine.

This is a significant advance, since the scientific bases for these
theories are not known.

The model proposed by the authors provides at least a statistical
justification for them.
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Part III: Applications

Approximate Inference in Bayesian networks

Analysis of social survey data

Topic detection

Analysis of medical symptom survey data

Software
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Software

http://www.cse.ust.hk/faculty/lzhang/ltm/index.htm




Implementation of LTM learning algorithms: EAST, BI
Tool for manipulate LTMs: Lantern
LTM for topic detection: HLTA
Implementation of other LTM learning algorithms
BIN-A, BIN-G, CL and LCM:
http://people.kyb.tuebingen.mpg.de/harmeling/code/ltt-1.4.tar
 CFHLC:
https://sites.google.com/site/raphaelmouradeng/home/programs
 NJ, RG, CLRG and regCLRG:
http://people.csail.mit.edu/myungjin/latentTree.html
 − NJ (fast implementation):
http://nimbletwist.com/software/ninja

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