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Ouyang Ruofei Topic Model Latent Dirichlet Allocation Ouyang Ruofei May LDA

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Introduction Ouyang Ruofei LDA Parameters: 2 Inference: data = latent pattern + noise

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Introduction Ouyang Ruofei LDA Parametric Model: 3 Nonparametric Model: Number of parameters is fixed w.r.t. sample size Number of parameters grows with sample size Infinite dimensional parameter space ProblemParameter Density Estimation Distributions RegressionFunctions ClusteringPartitions

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Clustering Ouyang Ruofei LDA 4 1.Ironman2.Thor3.Hulk Indicator variable for each data point

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Dirichlet process Ouyang Ruofei LDA 5 Ironman: 3 times Thor: 2 times Hulk: 2 times Without the likelihood, we know that: 1. There are three clusters 2. The distribution over three clusters New data

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Dirichlet process Ouyang Ruofei LDA 6 Dirichlet distribution: pdf: mean: Example: Dir(Ironman,Thor,Hulk)

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Dirichlet process Ouyang Ruofei LDA 7 Dirichlet distribution: Multinomial distribution: Conjugate prior Posterior: Example:IronmanThorHulkPrior322 Likelihood Posterior Pseudo count

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Dirichlet process Ouyang Ruofei LDA 8 In our Avengers model, K=3 (Ironman, Thor, Hulk) Dirichlet process: However, this guy comes… Dirichlet distribution can’t model this stupid guy K = infinity Nonparametrics here mean infinite number of clusters

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Dirichlet process Ouyang Ruofei LDA 9 α: Pseudo counts in each cluster G 0 : Base distribution of each cluster A distribution over distributions Dirichlet process: Given any partition Distribution template

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Dirichlet process Ouyang Ruofei LDA 10 Construct Dirichlet process by CRP In a restaurant, there are infinite number of tables. Chinese restaurant process: Costumer 1 seats at an unoccupied table with p=1. Costumer N seats at table k with p=

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Dirichlet process Ouyang Ruofei LDA 11

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Dirichlet process Ouyang Ruofei LDA 12

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Dirichlet process Ouyang Ruofei LDA 13

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Dirichlet process Ouyang Ruofei LDA 14

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Dirichlet process Ouyang Ruofei LDA 15 Customers : data Tables : clusters

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Dirichlet process Ouyang Ruofei LDA 16 Train the model by Gibbs sampling

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Dirichlet process Ouyang Ruofei LDA 17 Train the model by Gibbs sampling

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Gibbs sampling Ouyang Ruofei LDA 18 Gibbs sampling is a MCMC method to obtain a sequence of observations from a multivariate distribution The intuition is to turn a multivariate problem into a sequence of univariate problem. Multivariate: Univariate: In Dirichlet process,

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Gibbs sampling Ouyang Ruofei LDA 19 Gibbs sampling pseudo code:

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Topic model Ouyang Ruofei LDA 20 Document Mixture of topics we can read words Latent variable But, topics words

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Topic model Ouyang Ruofei LDA 21

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Topic model Ouyang Ruofei LDA 22

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Topic model Ouyang Ruofei LDA 23 word/topic counttopic/doc count topic of x ij observed word other topics other words

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Topic model Ouyang Ruofei LDA 24 Apply Dirichlet process in topic model Topic 1 Topic 2 Topic 3 Document P1P1P1P1 P2P2P2P2 P3P3P3P3 Topic 1 Topic 2 Topic 3 Word Q1Q1Q1Q1 Q2Q2Q2Q2 Q3Q3Q3Q3 Learn the distribution of topics in a document Learn the distribution of topics for a word

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Topic model Ouyang Ruofei LDA 25 t1t2t3 d1 t1t2t3 d2 t1t2t3 d3 w1w2w3w4 t1 t2 t3 topic/doc table word/topic table

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Topic model Ouyang Ruofei LDA 26 Latent Dirichlet allocation: Dirichlet mixture model:

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LDA Example Ouyang Ruofei LDA 27 w: ipad apple itunes mirror queen joker ladygaga t1: product t2: story t3: poker d1: ipad apple itunes d2: apple mirror queen d3: queen joker ladygaga d4: queen ladygaga mirror In fact, the topics are latent

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LDA example Ouyang Ruofei LDA 28 d1: ipad apple itunes d2: apple mirror queen d3: queen joker ladygaga d4: queen ladygaga mirror ipadappleitunesmirrorqueenjokerladygaga t1112 t2212 t3111 sum t1t2t3 d1111 d2120 d3102 d

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LDA example Ouyang Ruofei LDA 29 d1: ipad apple itunes d2: apple mirror queen d3: joker ladygaga d4: queen ladygaga mirror ipadappleitunesmirrorqueenjokerladygaga t1112 t2212 t3111 sum t1t2t3 d1111 d2120 d3102 d queen

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LDA example Ouyang Ruofei LDA 30 d1: ipad apple itunes d2: apple mirror queen d3: joker ladygaga d4: queen ladygaga mirror ipadappleitunesmirrorqueenjokerladygaga t1112 t2212 t sum t1t2t3 d1111 d2120 d d queen

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LDA example Ouyang Ruofei LDA 31 d1: ipad apple itunes d2: apple mirror queen d3: joker ladygaga d4: queen ladygaga mirror ipadappleitunesmirrorqueenjokerladygaga t1112 t2212 t3101 sum t1t2t3 d1111 d2120 d3101 d queen

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LDA example Ouyang Ruofei LDA 32 d1: ipad apple itunes d2: apple mirror queen d3: joker ladygaga d4: queen ladygaga mirror ipadappleitunesmirrorqueenjokerladygaga t1112 t t3101 sum t1t2t3 d1111 d2120 d d queen 2

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Further Ouyang Ruofei LDA 33 Dirichlet distribution prior: K topics Alpha mainly controls the probability of a topic with few training data in the document. Dirichlet process prior: infinite topics Beta mainly controls the probability of a topic with few training data in the words. Supervised Unsupervised

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Further Ouyang Ruofei LDA 34 Unrealistic bag of words assumption Lose power law behavior TNG, biLDA Pitman Yor language model David Blei has done an extensive survey on topic model

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Q&A Ouyang Ruofei LDA

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