Oleksandr Frei and Murat Apishev - Parallel Non-blocking Deterministic Algorithm for Online Topic Modeling
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This document describes parallel algorithms for topic modeling, including synchronous, asynchronous, and deterministic asynchronous algorithms. The synchronous offline algorithm splits the document collection into batches and has each thread process one batch at a time. The asynchronous online algorithm has processor threads process batches concurrently while a merger thread accumulates and merges results to recalculate model parameters. To make the algorithm deterministic, the deterministic asynchronous approach has each thread process batches and write results directly without a merger thread.
Oleksandr Frei and Murat Apishev - Parallel Non-blocking Deterministic Algorithm for Online Topic Modeling
- 1. Parallel Non-blocking Deterministic Algorithm for Online Topic Modeling Murat Apishev [email protected] Oleksandr Frei [email protected] HSE, MSU, MIPT April 8, 2016
- 2. Contents 1 Introduction Topic modeling ARTM BigARTM 2 Parallel implementation Synchronous algorithms Asynchronous algorithms Comparison 3 Applications The RSF project Conclusions
- 3. Introduction Parallel implementation Applications Topic modeling ARTM BigARTM Topic modeling Topic modeling — an application of machine learning to statistical text analysis. Topic — a specific terminology of the subject area, the set of terms (unigrams or n−grams) frequently appearing together in documents. Topic model uncovers latent semantic structure of a text collection: topic t is a probability distribution p(w|t) over terms w document d is a probability distribution p(t|d) over topics t Applications — information retrieval for long-text queries, classification, categorization, summarization of texts. Murat Apishev [email protected] AIST 2016 3 / 33
- 4. Introduction Parallel implementation Applications Topic modeling ARTM BigARTM Topic modeling task Given: W — set (vocabulary) of terms (unigrams or n−grams), D — set (collection) of text documents d ⊂ W , ndw — how many times term w appears in document d. Find: model p(w|d) = ∑︀ t∈T 𝜑wt 𝜃td with parameters Φ W×T и Θ T×D : 𝜑wt =p(w|t) — term probabilities w in each topic t, 𝜃td =p(t|d) — topic probabilities t in each document d. Criteria log-likelihood maximization: ∑︁ d∈D ∑︁ w∈d ndw ln ∑︁ t∈T 𝜑wt 𝜃td → max 𝜑,𝜃 ; 𝜑wt 0; ∑︀ w 𝜑wt = 1; 𝜃td 0; ∑︀ t 𝜃td = 1. Issue: the problem of stochastic matrix factorization is ill-posed: ΦΘ = (ΦS)(S−1Θ) = Φ′Θ′. Murat Apishev [email protected] AIST 2016 4 / 33
- 5. Introduction Parallel implementation Applications Topic modeling ARTM BigARTM PLSA and EM-algorithm Log-likelihood maximization: ∑︁ d∈D ∑︁ w∈W ndw ln ∑︁ t 𝜑wt 𝜃td → max Φ,Θ EM-algorithm: the simple iteration method for the set of equations E-шаг: M-шаг: ⎧ ⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎩ ptdw = norm t∈T (︀ 𝜑wt 𝜃td )︀ 𝜑wt = norm w∈W (︀ nwt )︀ , nwt = ∑︀ d∈D ndw ptdw 𝜃td = norm t∈T (︀ ntd )︀ , ntd = ∑︀ w∈d ndw ptdw where norm i∈I xi = max{xi ,0}∑︀ j∈I max{xj ,0} Murat Apishev [email protected] AIST 2016 5 / 33
- 6. Introduction Parallel implementation Applications Topic modeling ARTM BigARTM ARTM and regularized EM-algorithm Log-likelihood maximization with additive regularization criterion R: ∑︁ d∈D ∑︁ w∈W ndw ln ∑︁ t 𝜑wt 𝜃td + R(Φ, Θ) → max Φ,Θ EM-algorithm: the simple iteration method for the set of equations E-шаг: M-шаг: ⎧ ⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎩ ptdw = norm t∈T (︀ 𝜑wt 𝜃td )︀ 𝜑wt = norm w∈W (︁ nwt + 𝜑wt 𝜕R 𝜕𝜑wt )︁ , nwt = ∑︀ d∈D ndw ptdw 𝜃td = norm t∈T (︁ ntd + 𝜃td 𝜕R 𝜕𝜃td )︁ , ntd = ∑︀ w∈d ndw ptdw Murat Apishev [email protected] AIST 2016 6 / 33
- 7. Introduction Parallel implementation Applications Topic modeling ARTM BigARTM Examples of regularizers Many Bayesian models can be reinterpreted as regularizers in ARTM. Some examples of regularizes: 1 Smoothing Φ / Θ (leads to popular LDA model) 2 Sparsing Φ / Θ 3 Decorrelation of topics in Φ 4 Semi-supervised learning 5 Topic coherence maximization 6 Topic selection 7 . . . Murat Apishev [email protected] AIST 2016 7 / 33
- 8. Introduction Parallel implementation Applications Topic modeling ARTM BigARTM Multimodal Topic Model Multimodal Topic Model finds topical distributions for terms p(w|t), authors p(a|t), time p(y|t), objects of images p(o|t), linked documents p(d′|t), advertising banners p(b|t), users p(u|t), and binds all these modalities into a single topic model. Topics of documents Words and keyphrases of topics doc1: doc2: doc3: doc4: ... Text documents Topic Modeling D o c u m e n t s T o p i c s Metadata: Authors Data Time Conference Organization URL etc. Ads Images Links Users Murat Apishev [email protected] AIST 2016 8 / 33
- 9. Introduction Parallel implementation Applications Topic modeling ARTM BigARTM M-ARTM and multimodal regularized EM-algorithm W m is a vocabulary of terms of m-th modality, m ∈ M, W = W 1 ⊔ W m as a joint vocabulary of all modalities Multimodal log-likelihood maximization with additive regularization criterion R: ∑︁ m∈M 𝜆m ∑︁ d∈D ∑︁ w∈W m ndw ln ∑︁ t 𝜑wt 𝜃td + R(Φ, Θ) → max Φ,Θ EM-algorithm: the simple iteration method for the set of equations E-шаг: M-шаг: ⎧ ⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎩ ptdw = norm t∈T (︀ 𝜑wt 𝜃td )︀ 𝜑wt = norm w∈W m (︁ nwt + 𝜑wt 𝜕R 𝜕𝜑wt )︁ , nwt = ∑︀ d∈D 𝜆m(w)ndw ptdw 𝜃td = norm t∈T (︁ ntd + 𝜃td 𝜕R 𝜕𝜃td )︁ , ntd = ∑︀ w∈d 𝜆m(w)ndw ptdw Murat Apishev [email protected] AIST 2016 9 / 33
- 10. Introduction Parallel implementation Applications Topic modeling ARTM BigARTM BigARTM project BigARTM features: Fast1 parallel and online processing of Big Data; Multimodal and regularized topic modeling; Built-in library of regularizers and quality measures; BigARTM community: Open-source https://github.com/bigartm Documentation http://bigartm.org BigARTM license and programming environment: Freely available for commercial usage (BSD 3-Clause license) Cross-platform — Windows, Linux, Mac OS X (32 bit, 64 bit) Programming APIs: command line, C++, Python 1 Vorontsov K., Frei O., Apishev M., Romov P., Dudarenko M. BigARTM: Open Source Library for Regularized Multimodal Topic Modeling of Large Collections Analysis of Images, Social Networks and Texts. 2015 Murat Apishev [email protected] AIST 2016 10 / 33
- 11. Introduction Parallel implementation Applications Topic modeling ARTM BigARTM BigARTM vs. Gensim vs. Vowpal Wabbit LDA 3.7M articles from Wikipedia, 100K unique words Framework procs train inference perplexity BigARTM 1 35 min 72 sec 4000 LdaModel 1 369 min 395 sec 4161 VW.LDA 1 73 min 120 sec 4108 BigARTM 4 9 min 20 sec 4061 LdaMulticore 4 60 min 222 sec 4111 BigARTM 8 4.5 min 14 sec 4304 LdaMulticore 8 57 min 224 sec 4455 procs = number of parallel threads inference = time to infer 𝜃d for 100K held-out documents perplexity P is calculated on held-out documents P(D) = exp (︂ − 1 n ∑︁ d∈D ∑︁ w∈d ndw ln ∑︁ t∈T 𝜑wt 𝜃td )︂ , n = ∑︁ d nd . Murat Apishev [email protected] AIST 2016 11 / 33
- 12. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison Offline algorithm The collection is split into batches. Offline algorithm performs scans over the collection. Each thread process one batch at a time, inferring nwt and 𝜃td (using Θ regularization). After each scan algorithm recalculates Φ matrix and apply Φ regularizers according to the equation 𝜑wt = norm w∈W (︁ nwt + 𝜑wt 𝜕R 𝜕𝜑wt )︁ . The implementation never stores the entire Θ matrix at any given time. Murat Apishev [email protected] AIST 2016 12 / 33
- 13. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison Offline algorithm: Gantt chart 0s 4s 8s 12s 16s 20s 24s 28s 32s 36s Main Proc-1 Proc-2 Proc-3 Proc-4 Proc-5 Proc-6 Batch processing Norm This and further Gantt charts were created using the NYTimes dataset: https://archive.ics.uci.edu/ml/datasets/Bag+of+Words. Size of dataset is ≈ 300k documents, but each algorithm was run on some subset (from 70% to 100%) to archive the ≈ 36 sec. working time. Murat Apishev [email protected] AIST 2016 13 / 33
- 14. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison Online algorithm The algorithm is a generalization of Online variational Bayes algorithm for LDA model. Online ARTM improves the convergence rate of the Offline ARTM by re-calculating matrix Φ after every 𝜂 batches. Better suited for large and heterogeneous text collections. Weighted sum of nwt from previous and current 𝜂 batches to control the importance of new information. Issue: all threads has no useful work to do during the update of Φ matrix. Murat Apishev [email protected] AIST 2016 14 / 33
- 15. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison Online algorithm: Gantt chart 0 s. 4 s. 8 s. 12 s. 16 s. 20 s. 24 s. 28 s. 32 s. 36 s. Main Proc-1 Proc-2 Proc-3 Proc-4 Proc-5 Proc-6 Odd batch Even batch Norm Merge Murat Apishev [email protected] AIST 2016 15 / 33
- 16. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison Async: Asynchronous online algorithm Processor threads: ProcessBatch(Db,¡wt)Db ñwt Merger thread: Accumulate ñwt Recalculate ¡wt Queue {Db} Queue {ñwt} ¡wt Sync() Db Faster asynchronous implementation (it was compared with Gensim and VW LDA) Issue: Merger and DataLoader can become a bottleneck. Issue: the result of such algorithm is non-deterministic. Murat Apishev [email protected] AIST 2016 16 / 33
- 17. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison Async: Gantt chart in normal case 0s 4s 8s 12s 16s 20s 24s 28s 32s 36s Merger Proc-1 Proc-2 Proc-3 Proc-4 Proc-5 Proc-6 Odd batch Even batch Norm Merge matrix Merge increments Murat Apishev [email protected] AIST 2016 17 / 33
- 18. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison Async: Gantt chart in bad case 0s 4s 8s 12s 16s 20s 24s 28s 32s 36s Merger Proc-1 Proc-2 Proc-3 Proc-4 Proc-5 Proc-6 Odd batch Even batch Norm Merge matrix Merge increments Murat Apishev [email protected] AIST 2016 18 / 33
- 19. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison DetAsync: Deterministic asynchronous online algorithm To avoid the indeterministic behavior lets replace the update after first 𝜂 batches with update after given 𝜂 batches. Remove Merger and DataLoader threads. Each Processor thread reads batches and writes results into nwt matrix by itself. Processor threads get a set of batches to process, start processing and immediately return a future object to main thread. The main thread can process the updates of Φ matrix while Processor threads work, and then get the result by passing received future object to Await function. Murat Apishev [email protected] AIST 2016 19 / 33
- 20. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison DetAsync: schema MasterModel Processor threads: Db = LoadBatch(b) ProcessBatch(Db,¡wt) Main thread: Recalculate ¡wt nwt¡wt Transform({Db}) FitOffline({Db}) FitOnline({Db}) Murat Apishev [email protected] AIST 2016 20 / 33
- 21. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison DetAsync: Gantt chart 0s 4s 8s 12s 16s 20s 24s 28s 32s 36s Main Proc-1 Proc-2 Proc-3 Proc-4 Proc-5 Proc-6 Odd batch Even batch Norm Merge Murat Apishev [email protected] AIST 2016 21 / 33
- 22. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison Experiments Datasets: Wikipedia (|D| = 3.7M articles, |W | = 100K words), Pubmed (|D| = 8.2M abstracts, |W | = 141K words). Node: Intel Xeon CPU E5-2650 v2 system with 2 processors, 16 physical cores in total (32 with hyper-threading). Metric: perplexity P value achieved in the allotted time. Time: each algorithm was time-boxed to run for a 30 minutes. Peak memory usage (Gb): |T| Offline Online DetAsync Async (v0.6) Pubmed 1000 5.17 4.68 8.18 13.4 Pubmed 100 1.86 1.62 2.17 3.71 Wiki 1000 1.74 2.44 3.93 7.9 Wiki 100 0.54 0.53 0.83 1.28 Murat Apishev [email protected] AIST 2016 22 / 33
- 23. Introduction Parallel implementation Applications Synchronous algorithms Asynchronous algorithms Comparison Reached perplexity value 0 5 10 15 20 25 30 2,000 2,200 2,400 Time (min) Perplexity Offline Online Async DetAsync 10 15 20 25 30 35 3,800 4,000 4,200 4,400 4,600 4,800 5,000 Time (min) Perplexity Offline Online Async DetAsync Wikipedia (left), Pubmed (right). DetAsync achives best perplexity in given time-box. Murat Apishev [email protected] AIST 2016 23 / 33
- 24. Introduction Parallel implementation Applications The RSF project Conclusions Mining ethnic-related content from blogosphere Development of concept and methodology for multi-level monitoring of the state of inter-ethnic relations with the data from social media. The objectives of Topic Modeling in this project: 1 Identify ethnic topics in social media big data 2 Identify event and permanent ethnic topics 3 Identify spatio-temporal patterns of the ethnic discourse 4 Estimate the sentiment of the ethnic discourse 5 Develop the monitoring system of inter-ethnic discourse The Russian Science Foundation grant 15-18-00091 (2015–2017) (Higher School of Economics, St. Petersburg School of Social Sciences and Humanities, Internet Studies Laboratory LINIS) Murat Apishev [email protected] AIST 2016 24 / 33
- 25. Introduction Parallel implementation Applications The RSF project Conclusions Example ethnonyms for semi-supervised topic modeling османский русич восточноевропейский сингапурец эвенк перуанский швейцарская словенский аланский вепсский саамский ниггер латыш адыги литовец сомалиец цыганка абхаз ханты-мансийский темнокожий карачаевский нигериец кубинка лягушатник гагаузский камбоджиец Murat Apishev [email protected] AIST 2016 25 / 33
- 26. Introduction Parallel implementation Applications The RSF project Conclusions Regularization for finding ethnic topics smoothing ethnonyms in ethnic topics sparsing ethnonyms in background topics Murat Apishev [email protected] AIST 2016 26 / 33
- 27. Introduction Parallel implementation Applications The RSF project Conclusions Regularization for finding ethnic topics smoothing ethnonyms in ethnic topics sparsing ethnonyms in background topics smoothing non-ethnonyms for background topics Murat Apishev [email protected] AIST 2016 27 / 33
- 28. Introduction Parallel implementation Applications The RSF project Conclusions Regularization for finding ethnic topics smoothing ethnonyms in ethnic topics sparsing ethnonyms in background topics smoothing non-ethnonyms in background topics decorrelating ethnic topics Murat Apishev [email protected] AIST 2016 28 / 33
- 29. Introduction Parallel implementation Applications The RSF project Conclusions Regularization for finding ethnic topics smoothing ethnonyms in ethnic topics sparsing ethnonyms in background topics smoothing non-ethnonyms in background topics decorrelating ethnic topics adding ethnonyms modality and decorrelating their topics Murat Apishev [email protected] AIST 2016 29 / 33
- 30. Introduction Parallel implementation Applications The RSF project Conclusions Experiment LiveJournal collection: 1.58M of documents 860K of words in the raw vocabulary after lemmatization 90K of words after filtering out short words with length 2, rare words with nw < 20 including: non-Russian words 250 ethnonyms Murat Apishev [email protected] AIST 2016 30 / 33
- 31. Introduction Parallel implementation Applications The RSF project Conclusions Semi-supervised ARTM for ethnic topic modeling The number of ethnic topics found by the model: model ethnic |S| background |B| ++ +− −+ coh20 2 tfidf20 PLSA 400 12 15 17 -1447 -1012 LDA 400 12 15 17 -1540 -1121 ARTM-4 250 150 21 27 20 -1651 -1296 ARTM-5 250 150 38 42 30 -1342 -908 ARTM-4: ethnic topics: sparsing and decorrelating, ethnonyms smoothing background topics: smoothing, ethnonyms sparsing ARTM-5: ARTM-4 + ethnonyms as additional modality 2 Coherence and TF-IDF coherence are metrics that match the human judgment of topic quality. The topic is better if it has higher coherence value. Murat Apishev [email protected] AIST 2016 31 / 33
- 32. Introduction Parallel implementation Applications The RSF project Conclusions Ethnic topics examples (русские): русский, князь, россия, татарин, великий, царить, царь, иван, император, империя, грозить, государь, век, московская, екатерина, москва, (русские): акция, организация, митинг, движение, активный, мероприятие, совет, русский, участник, москва, оппозиция, россия, пикет, протест, проведение, националист, поддержка, общественный, проводить, участие, (славяне, византийцы): славянский, святослав, жрец, древние, письменность, рюрик, летопись, византия, мефодий, хазарский, русский, азбука, (сирийцы): сирийский, асад, боевик, район, террорист, уничтожать, группировка, дамаск, оружие, алесио, оппозиция, операция, селение, сша, нусра, турция, (турки): турция, турецкий, курдский, эрдоган, стамбул, страна, кавказ, горин, полиция, премьер-министр, регион, курдистан, ататюрк, партия, (иранцы): иран, иранский, сша, россия, ядерный, президент, тегеран, сирия, оон, израиль, переговоры, обама, санкция, исламский, (палестинцы): террорист, израиль, терять, палестинский, палестинец, террористический, палестина, взрыв, территория, страна, государство, безопасность, арабский, организация, иерусалим, военный, полиция, газ, (ливанцы): ливанский, боевик, район, ливан, армия, террорист, али, военный, хизбалла, раненый, уничтожать, сирия, подразделение, квартал, армейский, (ливийцы): ливан, демократия, страна, ливийский, каддафи, государство, алжир, война, правительство, сша, арабский, али, муаммар, сирия, (евреи): израиль, израильский, страна, израил, война, нетаньяху, тель-авив, время, сша, сирия, египет, случай, самолет, еврейский, военный, ближний, Murat Apishev [email protected] AIST 2016 32 / 33
- 33. Introduction Parallel implementation Applications The RSF project Conclusions Conclusions BigARTM is an open-source library supporting multimodal ARTM theory. Fast implementation of the underlying online EM-algorithm was even more improved. Memory usage was reduced. Combination of 8 regularizers in the task of ethnic topics extraction showed the supirity of ARTM approach. BigARTM is using to process more than 20 collections in several different projects. Join our comunity! Contacts: bigartm.org, [email protected] Murat Apishev [email protected] AIST 2016 33 / 33