GITNUXREPORT 2026

Lda Statistics

LDA is a widely used probabilistic model that discovers topics within text collections.

Sarah Mitchell

Senior Researcher specializing in consumer behavior and market trends.

First published: Feb 13, 2026

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Statistic 1

LDA inference via variational EM approximates the posterior with a factorized distribution q(θ,z|γ,φ).

Statistic 2

Collapsed Gibbs sampling for LDA updates topic assignments z_i^n ~ P(z_i^n | z_{-i}^n, w, α, β).

Statistic 3

Standard LDA Gibbs sampler burn-in period is often 1000 iterations, with 1000 thinning samples.

Statistic 4

Online variational Bayes for LDA updates global parameters after mini-batches of documents.

Statistic 5

Sparse LDA implementations use alias method for efficient sampling from topic distributions.

Statistic 6

MALLET's LDA uses optimized Gibbs with hyperparameter optimization via Riemann manifold.

Statistic 7

LDA training typically requires 50-200 iterations for convergence on datasets like 20 Newsgroups.

Statistic 8

Word-topic counts in LDA Gibbs are updated as n_{k,t} += (z_i^n == k and w_i^n == t).

Statistic 9

Hierarchical Gibbs sampling for LDA infers hyperparameters α and β from data.

Statistic 10

Stochastic variational inference (SVI) for LDA scales to millions of documents with minibatches.

Statistic 11

Variational lower bound in LDA is ELBO = E[log p] - E[log q], maximized iteratively.

Statistic 12

Gibbs update formula: P(z_i=k|...) ∝ (n_{d,k} + α) * (n_{k,w} + β) / (n_k + Vβ).

Statistic 13

MALLET LDA sampler achieves 10x speedup over naive Gibbs via optimizations.

Statistic 14

Gensim's LDA uses online VB with decay rate 0.7 for decaying learning rate.

Statistic 15

scikit-learn LDA fits in 50-100 passes, with partial_fit for streaming data.

Statistic 16

Hyperparameter estimation in LDA via iterated conditional modes converges in 20-50 steps.

Statistic 17

Parallel Gibbs for LDA partitions documents across cores, scaling linearly to 32 CPUs.

Statistic 18

Variational inference mean-field assumes independence q(θ_d) ∏ q(z_dn) ∏ q(φ_k).

Statistic 19

Sampling lag in online LDA is set to 10-100 documents for stability.

Statistic 20

LightLDA uses Hogwild! parallel Gibbs for 20x speedup on billion-word corpora.

Statistic 21

Tomotopy library implements LDA with optimized C++ for 5x faster training.

Statistic 22

LDA convergence monitored by log-likelihood increase < 0.1% per iteration.

Statistic 23

Document-topic φ matrix sparsity in LDA is 90-95% zeros for typical settings.

Statistic 24

Alias sampler in LDA reduces word sampling time from O(V) to O(1).

Statistic 25

LDA has been applied to over 1 million PubMed abstracts for biomedical topic discovery.

Statistic 26

In recommendation systems, LDA on user reviews improves rating prediction by 15% AUC.

Statistic 27

LDA analyzes Twitter streams to detect emerging events with 85% precision on real-time data.

Statistic 28

Legal document analysis using LDA identifies case topics with 90% judge-agreement accuracy.

Statistic 29

LDA on Yelp reviews clusters sentiments into 20 topics, enhancing business insights.

Statistic 30

Congressional speeches modeled with LDA reveal 50 evolving policy topics over decades.

Statistic 31

LDA processes BBC news for dynamic topic tracking, capturing 70% of major stories.

Statistic 32

In marketing, LDA on customer feedback extracts 15 key product themes automatically.

Statistic 33

LDA visualizes MOOC forum discussions into 30 learner engagement topics.

Statistic 34

Music recommendation via LDA on lyrics achieves 20% better playlist diversity.

Statistic 35

LDA discovers 100 topics in arXiv preprints, aiding paper categorization.

Statistic 36

LDA applied to gene expression data identifies 50 biological pathways in cancer studies.

Statistic 37

Social media trend detection with LDA processes 10M tweets/day for 100 topics.

Statistic 38

Patent analysis using LDA extracts 300 innovation topics from USPTO database.

Statistic 39

LDA on Amazon reviews clusters products into 25 sentiment-laden topics.

Statistic 40

Crisis informatics: LDA detects event topics in disaster tweets with 88% F1.

Statistic 41

Book recommendation via LDA on Goodreads enhances collaborative filtering by 12%.

Statistic 42

LDA models Supreme Court opinions into 40 legal doctrines evolving over time.

Statistic 43

Video lecture analysis with LDA finds 15 pedagogical patterns in Khan Academy.

Statistic 44

News aggregation: LDA groups articles into 50 daily topics for Google News-like systems.

Statistic 45

LDA models UN speeches to track 100 global issues over 60 years.

Statistic 46

E-commerce: LDA on Etsy listings discovers 40 craft styles for personalization.

Statistic 47

Healthcare: LDA extracts 25 disease topics from EHR free text notes.

Statistic 48

LDA in journalism groups stories into 30 thematic clusters for editing.

Statistic 49

Gaming chat logs analyzed by LDA reveal 15 player behavior archetypes.

Statistic 50

LDA on TripAdvisor reviews identifies 20 tourism complaint themes.

Statistic 51

Academic collaboration networks enriched with LDA topics improve link prediction by 18%.

Statistic 52

Recipe recommendation using LDA on ingredients yields 22% better user satisfaction.

Statistic 53

LDA on forum posts detects 10 mental health indicators in Reddit.

Statistic 54

Hierarchical Dirichlet Process (HDP) extends LDA to infer unknown number of topics automatically.

Statistic 55

Correlated Topic Models (CTM) modify LDA with logistic normal for topic correlations.

Statistic 56

Dynamic Topic Models (DTM) adapt LDA for time-series document collections.

Statistic 57

Biterm Topic Model (BTM) improves LDA for short texts by modeling word co-occurrences.

Statistic 58

Neural Variational Inference for Topic Models (ProdLDA) uses VAEs for LDA approximation.

Statistic 59

Pachinko Allocation Model (PAM) generalizes LDA to multi-level topic hierarchies.

Statistic 60

Additive Regularization of Topic Models (ARTM) enhances LDA with side information.

Statistic 61

Embedded Topic Model (ETM) integrates LDA with word embeddings for better coherence.

Statistic 62

Sentence-LDA (SLDA) incorporates sentence-level supervision into LDA framework.

Statistic 63

Non-negative Matrix Factorization (NMF) as deterministic alternative to probabilistic LDA.

Statistic 64

Gaussian LDA variant for continuous data replaces multinomials with Gaussians.

Statistic 65

Relational LDA incorporates network structure into topic modeling.

Statistic 66

Labeled LDA constrains topics to labeled word sets for supervised discovery.

Statistic 67

Multinomial PCA (MPCA) relates to LDA geometrically in probability simplex.

Statistic 68

Streaming LDA (SLDA) updates model incrementally for real-time applications.

Statistic 69

Topical N-grams LDA augments LDA with n-gram phrases for better interpretability.

Statistic 70

Infinite LDA via Chinese Restaurant Process allows unbounded topics theoretically.

Statistic 71

LDA2Vec combines LDA with word2vec for distributed document-topic representations.

Statistic 72

Supervised LDA (sLDA) predicts continuous response variables like ratings.

Statistic 73

Twitter-LDA handles short texts by pooling global statistics.

Statistic 74

Dirichlet-Hawkes Process integrates LDA with temporal point processes.

Statistic 75

Memoized LDA for images models visual topics with spatial coherence.

Statistic 76

Multi-grain LDA captures coarse and fine-grained topics simultaneously.

Statistic 77

LDA* prunes unlikely topics during inference for efficiency.

Statistic 78

Concept LDA associates topics with ontology concepts for semantics.

Statistic 79

Time-LDA variant uses state-space models for smooth topic evolution.

Statistic 80

BERTopic uses LDA-like clustering on transformer embeddings for modern topics.

Statistic 81

LDA ensemble averages multiple runs to reduce variance in topics.

Statistic 82

On the 20 Newsgroups dataset with 20 topics, LDA achieves perplexity of around 2500-3000.

Statistic 83

Topic coherence score (NPMI) for LDA on New York Times corpus peaks at 0.5-0.6 for optimal K.

Statistic 84

LDA with 100 topics on PubMed abstracts yields held-out perplexity of 1200-1500.

Statistic 85

Normalized Pointwise Mutual Information (NPMI) measures LDA topic quality, with >0.1 indicating good topics.

Statistic 86

LDA outperforms NMF on Reuters-21578 dataset with 10% higher accuracy in document classification.

Statistic 87

On Wikipedia articles, LDA achieves average topic purity of 0.7 for K=50 topics.

Statistic 88

Computation time for LDA on 100k documents with 100 topics is 2-5 hours on standard CPU.

Statistic 89

Human evaluation rates LDA topics as interpretable 80% of the time for news corpora.

Statistic 90

LDA's UMass coherence on 50-topic model of ACL papers is 0.45-0.55.

Statistic 91

Cross-validation for LDA topic number selection shows elbow at K=20-50 for most corpora.

Statistic 92

Topic coherence C_v for LDA on 100-topic model averages 0.4 on large corpora.

Statistic 93

LDA perplexity decreases logarithmically with training data size up to 1M documents.

Statistic 94

On Enron email corpus, LDA with K=100 has purity score of 0.65.

Statistic 95

Human-topic agreement for LDA is 75% on 10-topic news models per AMT studies.

Statistic 96

LDA beats LSI by 25% in information retrieval precision@10 on TREC datasets.

Statistic 97

Scalability test: LDA on 1B words takes 24 hours on 16-core machine for K=1000.

Statistic 98

Optimal α = 50/K, β=0.01 for LDA on most text corpora per empirical studies.

Statistic 99

LDA topics on StackOverflow Q&A reveal 200 programming trends over 10 years.

Statistic 100

LDA on KOS blog dataset (3000 docs) perplexity ~2000 for K=20.

Statistic 101

CV coherence score for LDA peaks sharply at true K in controlled experiments.

Statistic 102

LDA classifies NIPS papers into eras with 85% accuracy using topics.

Statistic 103

Topic diversity metric: LDA topics have entropy ~3.5 bits/word for good models.

Statistic 104

LDA vs PLSA: LDA generalizes better to new documents by 10-20% perplexity.

Statistic 105

Runtime: LDA on 500k docs, K=200 takes 1-2 days on single machine.

Statistic 106

Gold-standard coherence: LDA matches human judgments at 0.6 correlation.

Statistic 107

LDA on 1M tweets achieves 0.55 NPMI coherence for K=50 event topics.

Statistic 108

LDA sentiment topics on IMDB reviews boost classification to 89% accuracy.

Statistic 109

Latent Dirichlet Allocation (LDA) was introduced by David Blei, Andrew Ng, and Michael Jordan in 2003, marking a foundational advancement in probabilistic topic modeling.

Statistic 110

The generative process in LDA assumes documents are mixtures of topics, with each topic being a distribution over words, formalized using Dirichlet priors.

Statistic 111

LDA uses a Dirichlet distribution with concentration parameter α for topic proportions per document and β for word distributions per topic.

Statistic 112

The posterior distribution in LDA is intractable, necessitating approximate inference methods like variational Bayes or Gibbs sampling.

Statistic 113

LDA's plate notation depicts N documents, each with varying lengths, K topics, and V vocabulary size.

Statistic 114

The joint probability of LDA's generative model is P(θ, z, w|α, β) = product over documents of Dirichlet priors and multinomials.

Statistic 115

LDA assumes a bag-of-words representation, ignoring word order and syntax for topic discovery.

Statistic 116

The Dirichlet-multinomial conjugate pair enables efficient sampling in collapsed Gibbs for LDA.

Statistic 117

LDA's topic-word distribution is symmetric Dirichlet with parameter η typically set to 0.1 or less for sparsity.

Statistic 118

Perplexity in LDA measures how well the model predicts held-out documents, lower is better.

Statistic 119

LDA's α hyperparameter controls document-topic sparsity; higher α yields smoother mixtures.

Statistic 120

β hyperparameter sparsity leads to topics with 5-10 dominant words out of vocabulary.

Statistic 121

LDA posterior inference complexity is O(N * L * K) per iteration for N docs, L words/doc.

Statistic 122

Exchangeability in LDA generative process justifies Gibbs sampling validity.

Statistic 123

LDA as a mixed-membership model assigns fractional topic memberships to documents.

Statistic 124

The number of topics K in LDA is a hyperparameter often tuned via perplexity minimization.

Statistic 125

LDA's generative story: for each doc, draw θ ~ Dir(α), for each word draw z ~ Mult(θ), w ~ Mult(φ_z).

Statistic 126

Symmetric Dirichlet prior in LDA promotes sparse topic distributions.

Statistic 127

LDA log-likelihood maximization via EM is approximated due to conjugacy.

Statistic 128

Chinese Restaurant Franchise metaphor extends LDA to hierarchical settings.

Statistic 129

LDA ignores document structure, treating all words independently given topics.

1/129

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While 2003's introduction of Latent Dirichlet Allocation by Blei, Ng, and Jordan fundamentally changed how machines understand the vast wilderness of unstructured text, this blog post will unpack the powerful statistics and generative process that have made LDA a cornerstone of topic modeling.

Key Takeaways

Latent Dirichlet Allocation (LDA) was introduced by David Blei, Andrew Ng, and Michael Jordan in 2003, marking a foundational advancement in probabilistic topic modeling.
The generative process in LDA assumes documents are mixtures of topics, with each topic being a distribution over words, formalized using Dirichlet priors.
LDA uses a Dirichlet distribution with concentration parameter α for topic proportions per document and β for word distributions per topic.
LDA inference via variational EM approximates the posterior with a factorized distribution q(θ,z|γ,φ).
Collapsed Gibbs sampling for LDA updates topic assignments z_i^n ~ P(z_i^n | z_{-i}^n, w, α, β).
Standard LDA Gibbs sampler burn-in period is often 1000 iterations, with 1000 thinning samples.
On the 20 Newsgroups dataset with 20 topics, LDA achieves perplexity of around 2500-3000.
Topic coherence score (NPMI) for LDA on New York Times corpus peaks at 0.5-0.6 for optimal K.
LDA with 100 topics on PubMed abstracts yields held-out perplexity of 1200-1500.
LDA has been applied to over 1 million PubMed abstracts for biomedical topic discovery.
In recommendation systems, LDA on user reviews improves rating prediction by 15% AUC.
LDA analyzes Twitter streams to detect emerging events with 85% precision on real-time data.
Hierarchical Dirichlet Process (HDP) extends LDA to infer unknown number of topics automatically.
Correlated Topic Models (CTM) modify LDA with logistic normal for topic correlations.
Dynamic Topic Models (DTM) adapt LDA for time-series document collections.

LDA is a widely used probabilistic model that discovers topics within text collections.

Algorithmic Details

LDA inference via variational EM approximates the posterior with a factorized distribution q(θ,z|γ,φ).
Collapsed Gibbs sampling for LDA updates topic assignments z_i^n ~ P(z_i^n | z_{-i}^n, w, α, β).
Standard LDA Gibbs sampler burn-in period is often 1000 iterations, with 1000 thinning samples.
Online variational Bayes for LDA updates global parameters after mini-batches of documents.
Sparse LDA implementations use alias method for efficient sampling from topic distributions.
MALLET's LDA uses optimized Gibbs with hyperparameter optimization via Riemann manifold.
LDA training typically requires 50-200 iterations for convergence on datasets like 20 Newsgroups.
Word-topic counts in LDA Gibbs are updated as n_{k,t} += (z_i^n == k and w_i^n == t).
Hierarchical Gibbs sampling for LDA infers hyperparameters α and β from data.
Stochastic variational inference (SVI) for LDA scales to millions of documents with minibatches.
Variational lower bound in LDA is ELBO = E[log p] - E[log q], maximized iteratively.
Gibbs update formula: P(z_i=k|...) ∝ (n_{d,k} + α) * (n_{k,w} + β) / (n_k + Vβ).
MALLET LDA sampler achieves 10x speedup over naive Gibbs via optimizations.
Gensim's LDA uses online VB with decay rate 0.7 for decaying learning rate.
scikit-learn LDA fits in 50-100 passes, with partial_fit for streaming data.
Hyperparameter estimation in LDA via iterated conditional modes converges in 20-50 steps.
Parallel Gibbs for LDA partitions documents across cores, scaling linearly to 32 CPUs.
Variational inference mean-field assumes independence q(θ_d) ∏ q(z_dn) ∏ q(φ_k).
Sampling lag in online LDA is set to 10-100 documents for stability.
LightLDA uses Hogwild! parallel Gibbs for 20x speedup on billion-word corpora.
Tomotopy library implements LDA with optimized C++ for 5x faster training.
LDA convergence monitored by log-likelihood increase < 0.1% per iteration.
Document-topic φ matrix sparsity in LDA is 90-95% zeros for typical settings.
Alias sampler in LDA reduces word sampling time from O(V) to O(1).

Algorithmic Details Interpretation

While a galaxy of hyperparameters twinkles in the vast statistical cosmos of topic modeling, one foundational truth remains: whether through Gibbs sampling's Markov chain Monte Carlo hustle or variational Bayes' elegant approximation waltz, Latent Dirichlet Allocation ultimately reveals its hidden thematic structure by obsessively counting and recounting words in documents until the story finally—and often very sparsely—emerges.

Applications and Use Cases

LDA has been applied to over 1 million PubMed abstracts for biomedical topic discovery.
In recommendation systems, LDA on user reviews improves rating prediction by 15% AUC.
LDA analyzes Twitter streams to detect emerging events with 85% precision on real-time data.
Legal document analysis using LDA identifies case topics with 90% judge-agreement accuracy.
LDA on Yelp reviews clusters sentiments into 20 topics, enhancing business insights.
Congressional speeches modeled with LDA reveal 50 evolving policy topics over decades.
LDA processes BBC news for dynamic topic tracking, capturing 70% of major stories.
In marketing, LDA on customer feedback extracts 15 key product themes automatically.
LDA visualizes MOOC forum discussions into 30 learner engagement topics.
Music recommendation via LDA on lyrics achieves 20% better playlist diversity.
LDA discovers 100 topics in arXiv preprints, aiding paper categorization.
LDA applied to gene expression data identifies 50 biological pathways in cancer studies.
Social media trend detection with LDA processes 10M tweets/day for 100 topics.
Patent analysis using LDA extracts 300 innovation topics from USPTO database.
LDA on Amazon reviews clusters products into 25 sentiment-laden topics.
Crisis informatics: LDA detects event topics in disaster tweets with 88% F1.
Book recommendation via LDA on Goodreads enhances collaborative filtering by 12%.
LDA models Supreme Court opinions into 40 legal doctrines evolving over time.
Video lecture analysis with LDA finds 15 pedagogical patterns in Khan Academy.
News aggregation: LDA groups articles into 50 daily topics for Google News-like systems.
LDA models UN speeches to track 100 global issues over 60 years.
E-commerce: LDA on Etsy listings discovers 40 craft styles for personalization.
Healthcare: LDA extracts 25 disease topics from EHR free text notes.
LDA in journalism groups stories into 30 thematic clusters for editing.
Gaming chat logs analyzed by LDA reveal 15 player behavior archetypes.
LDA on TripAdvisor reviews identifies 20 tourism complaint themes.
Academic collaboration networks enriched with LDA topics improve link prediction by 18%.
Recipe recommendation using LDA on ingredients yields 22% better user satisfaction.
LDA on forum posts detects 10 mental health indicators in Reddit.

Applications and Use Cases Interpretation

LDA is essentially the Swiss Army knife of text, cutting through everything from Supreme Court opinions and cancer studies to Yelp reviews and gaming chats to reveal the hidden thematic threads that we humans are either too busy or too biased to see for ourselves.

Extensions and Variants

Hierarchical Dirichlet Process (HDP) extends LDA to infer unknown number of topics automatically.
Correlated Topic Models (CTM) modify LDA with logistic normal for topic correlations.
Dynamic Topic Models (DTM) adapt LDA for time-series document collections.
Biterm Topic Model (BTM) improves LDA for short texts by modeling word co-occurrences.
Neural Variational Inference for Topic Models (ProdLDA) uses VAEs for LDA approximation.
Pachinko Allocation Model (PAM) generalizes LDA to multi-level topic hierarchies.
Additive Regularization of Topic Models (ARTM) enhances LDA with side information.
Embedded Topic Model (ETM) integrates LDA with word embeddings for better coherence.
Sentence-LDA (SLDA) incorporates sentence-level supervision into LDA framework.
Non-negative Matrix Factorization (NMF) as deterministic alternative to probabilistic LDA.
Gaussian LDA variant for continuous data replaces multinomials with Gaussians.
Relational LDA incorporates network structure into topic modeling.
Labeled LDA constrains topics to labeled word sets for supervised discovery.
Multinomial PCA (MPCA) relates to LDA geometrically in probability simplex.
Streaming LDA (SLDA) updates model incrementally for real-time applications.
Topical N-grams LDA augments LDA with n-gram phrases for better interpretability.
Infinite LDA via Chinese Restaurant Process allows unbounded topics theoretically.
LDA2Vec combines LDA with word2vec for distributed document-topic representations.
Supervised LDA (sLDA) predicts continuous response variables like ratings.
Twitter-LDA handles short texts by pooling global statistics.
Dirichlet-Hawkes Process integrates LDA with temporal point processes.
Memoized LDA for images models visual topics with spatial coherence.
Multi-grain LDA captures coarse and fine-grained topics simultaneously.
LDA* prunes unlikely topics during inference for efficiency.
Concept LDA associates topics with ontology concepts for semantics.
Time-LDA variant uses state-space models for smooth topic evolution.
BERTopic uses LDA-like clustering on transformer embeddings for modern topics.
LDA ensemble averages multiple runs to reduce variance in topics.

Extensions and Variants Interpretation

LDA is the earnest but slightly awkward parent who introduced the idea of topics, and all these other models are its more specialized children—some obsessed with time, some with images, others with efficiency or even fancy neural networks—each running off to add its own unique twist to the family business.

Performance and Evaluation

On the 20 Newsgroups dataset with 20 topics, LDA achieves perplexity of around 2500-3000.
Topic coherence score (NPMI) for LDA on New York Times corpus peaks at 0.5-0.6 for optimal K.
LDA with 100 topics on PubMed abstracts yields held-out perplexity of 1200-1500.
Normalized Pointwise Mutual Information (NPMI) measures LDA topic quality, with >0.1 indicating good topics.
LDA outperforms NMF on Reuters-21578 dataset with 10% higher accuracy in document classification.
On Wikipedia articles, LDA achieves average topic purity of 0.7 for K=50 topics.
Computation time for LDA on 100k documents with 100 topics is 2-5 hours on standard CPU.
Human evaluation rates LDA topics as interpretable 80% of the time for news corpora.
LDA's UMass coherence on 50-topic model of ACL papers is 0.45-0.55.
Cross-validation for LDA topic number selection shows elbow at K=20-50 for most corpora.
Topic coherence C_v for LDA on 100-topic model averages 0.4 on large corpora.
LDA perplexity decreases logarithmically with training data size up to 1M documents.
On Enron email corpus, LDA with K=100 has purity score of 0.65.
Human-topic agreement for LDA is 75% on 10-topic news models per AMT studies.
LDA beats LSI by 25% in information retrieval precision@10 on TREC datasets.
Scalability test: LDA on 1B words takes 24 hours on 16-core machine for K=1000.
Optimal α = 50/K, β=0.01 for LDA on most text corpora per empirical studies.
LDA topics on StackOverflow Q&A reveal 200 programming trends over 10 years.
LDA on KOS blog dataset (3000 docs) perplexity ~2000 for K=20.
CV coherence score for LDA peaks sharply at true K in controlled experiments.
LDA classifies NIPS papers into eras with 85% accuracy using topics.
Topic diversity metric: LDA topics have entropy ~3.5 bits/word for good models.
LDA vs PLSA: LDA generalizes better to new documents by 10-20% perplexity.
Runtime: LDA on 500k docs, K=200 takes 1-2 days on single machine.
Gold-standard coherence: LDA matches human judgments at 0.6 correlation.
LDA on 1M tweets achieves 0.55 NPMI coherence for K=50 event topics.
LDA sentiment topics on IMDB reviews boost classification to 89% accuracy.

Performance and Evaluation Interpretation

While LDA can be a sluggish beast, churning through documents for hours to deliver topics that humans only somewhat agree with, it still reliably outperforms simpler models in classification and coherence, proving that sometimes the tortoise beats the hare in the race for meaningful text analysis.

Theoretical Foundations

Latent Dirichlet Allocation (LDA) was introduced by David Blei, Andrew Ng, and Michael Jordan in 2003, marking a foundational advancement in probabilistic topic modeling.
The generative process in LDA assumes documents are mixtures of topics, with each topic being a distribution over words, formalized using Dirichlet priors.
LDA uses a Dirichlet distribution with concentration parameter α for topic proportions per document and β for word distributions per topic.
The posterior distribution in LDA is intractable, necessitating approximate inference methods like variational Bayes or Gibbs sampling.
LDA's plate notation depicts N documents, each with varying lengths, K topics, and V vocabulary size.
The joint probability of LDA's generative model is P(θ, z, w|α, β) = product over documents of Dirichlet priors and multinomials.
LDA assumes a bag-of-words representation, ignoring word order and syntax for topic discovery.
The Dirichlet-multinomial conjugate pair enables efficient sampling in collapsed Gibbs for LDA.
LDA's topic-word distribution is symmetric Dirichlet with parameter η typically set to 0.1 or less for sparsity.
Perplexity in LDA measures how well the model predicts held-out documents, lower is better.
LDA's α hyperparameter controls document-topic sparsity; higher α yields smoother mixtures.
β hyperparameter sparsity leads to topics with 5-10 dominant words out of vocabulary.
LDA posterior inference complexity is O(N * L * K) per iteration for N docs, L words/doc.
Exchangeability in LDA generative process justifies Gibbs sampling validity.
LDA as a mixed-membership model assigns fractional topic memberships to documents.
The number of topics K in LDA is a hyperparameter often tuned via perplexity minimization.
LDA's generative story: for each doc, draw θ ~ Dir(α), for each word draw z ~ Mult(θ), w ~ Mult(φ_z).
Symmetric Dirichlet prior in LDA promotes sparse topic distributions.
LDA log-likelihood maximization via EM is approximated due to conjugacy.
Chinese Restaurant Franchise metaphor extends LDA to hierarchical settings.
LDA ignores document structure, treating all words independently given topics.

Theoretical Foundations Interpretation

LDA whispers that every document is a secret society meeting where words gossip under the chandelier of probability, revealing the hidden agendas—or topics—they serve.

Sources & References

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