Presentation on theme: "Latent Tree Models Part IV: Applications Nevin L. Zhang Dept. of Computer Science & Engineering The Hong Kong Univ. of Sci. & Tech."— Presentation transcript:
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 AAAI 2014 Tutorial
AAAI 2014 Tutorial Nevin L. Zhang HKUST2 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 Market survey data, social survey, medical survey data Analysis of text data Topic detection Approximate probabilistic inference Applications of Latent Tree Analysis (LTA)
AAAI 2014 Tutorial Nevin L. Zhang HKUST3 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 HKUST4 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? LTMs for Probabilistic Modelling
AAAI 2014 Tutorial Nevin L. Zhang HKUST5 In a Bayesian network over observed variables, exact inference can be computationally prohibitive. Two-phase approximate inference: Offline Sample data set from the original network Learn a latent tree model (secondary representation) Online Make inference using the latent tree model. (Fast) Approximate Inference in Bayesian Networks (Wang et al. AAAI 2008) Sample Learn LTM
AAAI 2014 Tutorial Nevin L. Zhang HKUST6 Alternatives 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) Original networks ALARM, INSURANCE, MILDEW, BARLEY, etc. Evaluation: 500 random queries Quality of approximation measured using KL from exact answer. Empirical Evaluations
AAAI 2014 Tutorial Nevin L. Zhang HKUST7 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 Empirical Results sparse dense
AAAI 2014 Tutorial Nevin L. Zhang HKUST8 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 HKUST10 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 HKUST11 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 HKUST12 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 HKUST13 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 HKUST14 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 HKUST15 Basics Aggregation of miniature topics Topic extraction and characterization Empirical results Latent Tree Models for Topic Detection
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. What is a topic in LTA? LTM for toy text data
AAAI 2014 Tutorial Nevin L. Zhang HKUST17 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. How are topics and documents are related? D97, D115, D205, D528 are documents from the toy text data Table shows: l D97 is a web page on OOP from U of Wisconsin Madison l D528 is a web page on AI from U of Texas Austin
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 LTA Differs from Latent Dirichlet Allocation (LDA)
AAAI 2014 Tutorial Nevin L. Zhang HKUST19 Basics Aggregation of miniature topics Topic extraction and characterization Empirical results Latent Tree Models for Topic Detection
AAAI 2014 Tutorial Nevin L. Zhang HKUST20 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. Latent Tree Model for a Subset of Newsgroup Data
AAAI 2014 Tutorial Nevin L. Zhang HKUST21 Convert the latent variables into observed one via hard assignment. Afterwards, Z11-Z19 become observed. Run BI on Z11-Z19 Hierarchical Latent Tree Analysis (HLTA)
AAAI 2014 Tutorial Nevin L. Zhang HKUST22 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) Hierarchical Latent Tree Analysis (HLTA)
AAAI 2014 Tutorial Nevin L. Zhang HKUST23 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. Hierarchical Latent Tree Analysis (HLTA)
AAAI 2014 Tutorial Nevin L. Zhang HKUST24 Basics Aggregation of miniature topics Topic extraction and characterization Empirical results Latent Tree Models for Topic Detection
AAAI 2014 Tutorial Nevin L. Zhang HKUST25 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. Semantic Base
AAAI 2014 Tutorial Nevin L. Zhang HKUST26 Semantic base might be too large to handle. Effective base: Subset of semantic base that matters. Sort variables X i from semantic base in descending of I(Z; X i ). I(Z; X 1, …, X i ): Mutual information between Z and first i-th variables Estimated via sampling, increases with i. I(Z; X 1, …, X m ): Mutual information between Z and all m variables in semantic base Information coverage of the first i-th variable I(Z; X 1, …, X i )/ I(Z; X 1, …, X m ): Effective semantic base: Set of leading variables with information coverage higher than a certain level, i.e., 95%. Effective Semantic Base Chen et al. AIJ 2012
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. Z22: Upper: Information coverage Lower: Mutual Information
AAAI 2014 Tutorial Nevin L. Zhang HKUST28 HLTA characterizes Latent state (topics) using probabilities of words from effective semantic base NOT sorted according to probability, but mutual information Topic Z22=s1 characterized using words 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. Topic Characterizations
AAAI 2014 Tutorial Nevin L. Zhang HKUST29 Basics Aggregation of miniature topics Topic extraction and characterization Empirical results Latent Tree Models for Topic Detection
AAAI 2014 Tutorial Nevin L. Zhang HKUST30 Show the results of HLTA on real-world data Compare HLTA with HLDA and LDA Empirical Results
AAAI 2014 Tutorial Nevin L. Zhang HKUST31 1,740 papers published at NIPS between 1988 – 1999. Vocabulary: 1,000 words selected using average TF-IDF. 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 Topic characterizations, topic sizes, Topic groups, topic group labels. For details: http://www.cse.ust.hk/~lzhang/ltm/index.htm NIPS Data
AAAI 2014 Tutorial Nevin L. Zhang HKUST37 Level 1: 279 latent variables Many capture trivial word co-occurrence patterns Level 2: 72 latent variables Meaningful topics, and meaningful topic groups Level 3 : 21 latent variables Meaningful topics, and meaningful topic groups More general than Level 2 topics Level 4: 8 latent variables Meaningful topics, very general Level 5: 2 latent variables 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. Summary of HLTA Results on NIPS Data
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 HLDA Topics 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 ….
AAAI 2014 Tutorial Nevin L. Zhang HKUST39 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 LDA Topics 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 HKUST40 HLTA Topics 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 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 Comparisons between HLTA and HLDA HLDA Topics 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 HLTA topics have sizes, HLDA/LDA topics do not HLTA produces better hierarchy HLTA gives better topic characterizations
AAAI 2014 Tutorial Nevin L. Zhang HKUST41 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 Measure of Topic Quality 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 Natural Language Processing, pages 262–272, 2011.
AAAI 2014 Tutorial Nevin L. Zhang HKUST42 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. HLTA Found More Coherent Topics than LDA and HLDA
AAAI 2014 Tutorial Nevin L. Zhang HKUST43 Regard LDA, HLDA and HLTA as methods for text modeling Build a probabilistic model for the corpus Evaluation: 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. Comparisons in Terms of Model Fit
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.
AAAI 2014 Tutorial Nevin L. Zhang HKUST45 HLTA Topic: collection of documents Have sizes Characterization: Words occur with high probability in topic, low probability in other documents Document: A member of topic, can belong to multiple topics with probability 1. Summary LDA, HLDA Topic: Distribution over vocabulary Don’t have sizes Characterization: Words occur with high probability in topic 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 HKUST46 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 HKUST47 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 …. Page 47
AAAI 2014 Tutorial Nevin L. Zhang HKUST48 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. Page 48
AAAI 2014 Tutorial Nevin L. Zhang HKUST49 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 Page 49
AAAI 2014 Tutorial Nevin L. Zhang HKUST50 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: 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. Page 50 (Zhao et al. JACM 2014)
AAAI 2014 Tutorial Nevin L. Zhang HKUST51 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. Page 51
AAAI 2014 Tutorial Nevin L. Zhang HKUST52 Model Obtained for a Depression Data (Top) Page 52
AAAI 2014 Tutorial Nevin L. Zhang HKUST53 Model obtained for a Depression Data (Bottom) Page 53
AAAI 2014 Tutorial Nevin L. Zhang HKUST54 The Empirical Partitions Page 54 The first cluster (Y 29 = s 0 ) consists of 54% of the patients and while the cluster (Y 29 = s 1 ) 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 HKUST55 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 Y 29 = s 1 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). Page 55 l The partition Y 29 suggests that n Among depressive patients, there is a subclass of patient with YANG DEFICIENCY. n 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 HKUST56 Probabilistic Symptom co-occurrence pattern Page 56 Y 28 = s 1 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 Y 28 = s 1
AAAI 2014 Tutorial Nevin L. Zhang HKUST57 Probabilistic Symptom co-occurrence pattern Y 27 = s 1 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 = s 1 Y27, Y28, Y29 together provide evidence for defining KIDNEY YANG DEFICIENCY
AAAI 2014 Tutorial Nevin L. Zhang HKUST58 Probabilistic Symptom co-occurrence pattern Pattern Y 21 = s 1 : evidence for defining STAGNANT QI TURNING INTO FIRE （气郁化火） Y 15 = s 1 : evidence for defining QI DEFICIENCY Y 17 = s 1 : evidence for defining HEART QI DEFICIENCY Y 16 = s 1 : evidence for defining QI STAGNATION Y 19 = s 1 : evidence for defining QI STAGNATION IN HEAD Page 58
AAAI 2014 Tutorial Nevin L. Zhang HKUST59 Probabilistic Symptom co-occurrence pattern Y 9 = s 1 :evidence for defining DEFICIENCY OF BOTH QI AND YIN (气阴两虚) Y 10 = s 1 : evidence for defining YIN DEFICIENCY (阴虚) Y 11 = s 1 : evidence for defining DEFICIENCY OF STOMACH/SPLEEN YIN (脾胃 阴虚) Page 59
AAAI 2014 Tutorial Nevin L. Zhang HKUST60 Symptom Mutual-Exclusion Patterns Some empirical partitions reveal symptom exclusion patterns Y 1 reveals the mutual exclusion of ‘white tongue coating’, ‘yellow tongue coating’ and ‘yellow-white tongue coating’ Y 2 reveals the mutual exclusion of ‘thin tongue coating’, ‘thick tongue coating’ and ‘little tongue coating’. Page 60
AAAI 2014 Tutorial Nevin L. Zhang HKUST61 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. Page 61
AAAI 2014 Tutorial Nevin L. Zhang HKUST62 Another Perspective: Statistical Validation of TCM Postulates Page 62 (Zhang et al. JACM 2008) Yang Deficiency Y29 = s1 Kidney deprived of nourishment Y28 = s1 TCM terms such as Yang Deficiency were introduced to explain symptom co- occurrence patterns observed in clinic practice. …..
AAAI 2014 Tutorial Nevin L. Zhang HKUST63 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. Page 63
AAAI 2014 Tutorial Nevin L. Zhang HKUST64 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 HKUST65 http://www.cse.ust.hk/faculty/lzhang/ltm/index.htm 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 Software
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