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: 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 2 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 3 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? AAAI 2014 Tutorial Nevin L. Zhang HKUST 4 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 5 Empirical Evaluations Alternatives Original networks 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST 6 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 dense 7 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 8 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 …. AAAI 2014 Tutorial Nevin L. Zhang HKUST 9 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 10 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST 11 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 12 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST 13 Part III: Applications Approximate Inference Analysis of social survey data Topic detection (Analysis of text data) Analysis of medical symptom survey data Software AAAI 2014 Tutorial Nevin L. Zhang HKUST 14 Latent Tree Models for Topic Detection Basics Aggregation of miniature topics Topic extraction and characterization Empirical results AAAI 2014 Tutorial Nevin L. Zhang HKUST 15 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 17 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 19 Latent Tree Model for a Subset of Newsgroup Data Latent variable give miniature topics. Intuitively, more interesting topics can be detected if we combine 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST 20 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 21 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) AAAI 2014 Tutorial Nevin L. Zhang HKUST 22 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST 23 Latent Tree Models for Topic Detection Basics Aggregation of miniature topics Topic extraction and characterization Empirical results AAAI 2014 Tutorial Nevin L. Zhang HKUST 24 Semantic Base Interpreting states of Z21 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST 25 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%. AAAI 2014 Tutorial Nevin L. Zhang HKUST 26 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 Topic Z22=s1 characterized using words 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST 28 Latent Tree Models for Topic Detection Basics Aggregation of miniature topics Topic extraction and characterization Empirical results AAAI 2014 Tutorial Nevin L. Zhang HKUST 29 Empirical Results Show the results of HLTA on real-world data Compare HLTA with HLDA and LDA AAAI 2014 Tutorial Nevin L. Zhang HKUST 30 NIPS Data 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 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 31 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST 37 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 … AAAI 2014 Tutorial Nevin L. Zhang HKUST 39 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 40 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST 42 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST 43 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 45 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 …. AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 47 47 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 48 48 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 49 49 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 50 50 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 51 51 Model Obtained for a Depression Data (Top) AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 52 52 Model obtained for a Depression Data (Bottom) AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 53 53 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 54 54 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) AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 55 55 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 56 56 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 57 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 58 58 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) Page 59 AAAI 2014 Tutorial Nevin L. Zhang HKUST 59 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’. AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 60 60 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 61 61 (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. AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 62 62 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. AAAI 2014 Tutorial Nevin L. Zhang HKUST Page 63 63 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 64 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 AAAI 2014 Tutorial Nevin L. Zhang HKUST 65