Joey gonzalez, graph lab, m lconf 2013
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Joseph Gonzalez, Co-Founder at GraphLab: Large-Scale Machine Learning on Graphs
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Joey gonzalez, graph lab, m lconf 2013
- 1. Machine Learning on Graphs Joseph Gonzalez Co-Founder, GraphLab Inc. joseph@graphlab.com Postdoc, UC Berkeley AMPLab jegonzal@eecs.berkeley.edu
- 2. Big Data Graphs More Signal More Noise 2!
- 3. Social Media Science Advertising Web Graphs encode relationships between: People Products Ideas Facts Interests Big: billions of vertices and edges & rich metadata Facebook (10/2012): 1B users, 144B friendships Twi>er (2011): 15B follower edges 3
- 4. Graphs are Essential to " Data Mining and Machine Learning Identify influential people and information Find communities Understand people’s shared interests Model complex data dependencies
- 5. Predicting User Behavior ? ? ? Liberal ? ? ? Conservative ? ? ? Post Post ? ? Post Post Post ? Post ? Post Post ? ? ? Post ? Post Post Post ? Conditional Random Field! ? ? ? ? ? ? Belief Propagation! Post ? ? Post Post Post ? ? ? ? 5
- 6. Finding Communities Count triangles passing through each vertex: " 2 3 1 4 Measures “cohesiveness” of local community Fewer Triangles Weaker Community More Triangles Stronger Community
- 8. Recommending Products ≈ Movies f(j) f(i) Movies Iterate: f [i] = arg min w2Rd X j2Nbrs(i) rij f(1) User Factors (U) Users Netflix x f(2) T w f [j] r13 r14 r24 r25 2 f(3) f(4) f(5) Movie Factors (M) Users Low-Rank Matrix Factorization: + ||w||2 2 8
- 10. Identifying Leaders R[i] = 0.15 + X wji R[j] j2Nbrs(i) Rank of user i Weighted sum of neighbors’ ranks Everyone starts with equal ranks Update ranks in parallel Iterate until convergence 10
- 11. Graph-Parallel Algorithms Model / Alg. State Computation depends only on the neighbors 11
- 12. Many More Graph Algorithms • Collaborative Filtering! – – – – • Graph Analytics! Alternating Least Squares! Stochastic Gradient Descent! Tensor Factorization! SVD! • Structured Prediction! – Loopy Belief Propagation! – Max-Product Linear Programs! – Gibbs Sampling! • Semi-supervised ML! – Graph SSL ! – CoEM! – – – – – – PageRank! Shortest Path! Triangle-Counting! Graph Coloring! K-core Decomposition! Personalized PageRank! • Classification! – Neural Networks! – Lasso! …! 12
- 13. How should we program" graph-parallel algorithms? 13
- 14. Structure of Computation Data-Parallel Graph-Parallel Dependency Graph Table Row 6. Before Row Row Result 7. After Row 14 8. After
- 15. How should we program" graph-parallel algorithms? “Think like a Vertex.” - Pregel [SIGMOD’10] 15
- 16. The Graph-Parallel Abstraction A user-defined Vertex-Program runs on each vertex Graph constrains interaction along edges Using messages (e.g. Pregel [PODC’09, SIGMOD’10]) Through shared state (e.g., GraphLab [UAI’10, VLDB’12]) Parallelism: run multiple vertex programs simultaneously 16
- 17. The GraphLab Vertex Program Vertex Programs directly access adjacent vertices and edges GraphLab_PageRank(i) // Compute sum over neighbors total = 0 foreach (j in neighbors(i)): total = total + R[j] * wji // Update the PageRank R[i] = 0.15 + total // Trigger neighbors to run again if R[i] not converged then signal nbrsOf(i) to be recomputed R[4] * w41 4 + 1 + 3 Signaled vertices are recomputed eventually. 2 17
- 18. Num-‐Ver1ces Be>er Convergence of Dynamic PageRank 100000000 51% updated only once! 1000000 10000 100 1 0 10 20 30 40 Number of Updates 50 60 70 18
- 19. Adaptive Belief Propagation Challenge = Boundaries Many Updates Splash Noisy “Sunset” Image Few Updates Cumulative Vertex Updates Algorithm identifies and focuses on hidden sequential structure Graphical Model
- 20. 6. Before Graph-‐parallel Abstrac(ons BeDer for Machine Learning Messaging i Synchronous 7. After 8. After Shared State i Dynamic Asynchronous 20
- 21. Natural Graphs Graphs derived from natural phenomena 21
- 22. Properties of Natural Graphs Regular Mesh Natural Graph Power-Law Degree Distribution 22
- 23. Power-Law Degree Distribution “Star Like” Motif President Obama Followers 23
- 24. Challenges of High-‐Degree VerMces SequenMally process edges Touches a large fracMon of graph CPU 1 CPU 2 Provably Difficult to ParMMon 24
- 25. ment. While fast and easy to implement, placement cuts most of the edges: Random ParMMoning em 5.1. If vertices random (hashed) assigne are randomly • GraphLab resorts to parMMoning on natural graphs nes then the expected fraction of edges cut |Edges Cut| E =1 |E| 1 p 10 Machines ! 90% of edges cut example if just two machines are used, hal 100 Machines ! 99% of edges cut! Machine 1 Machine 2 es will be cut requiring order |E| /2 commun 25
- 26. Program For This Run on This Machine 1 Machine 2 • Split High-‐Degree verMces • New Abstrac1on ! Equivalence on Split Ver(ces 26
- 27. A Common Pattern in Vertex Programs GraphLab_PageRank(i) // Compute sum over neighbors total = 0 Gather Informa1on foreach( j in neighbors(i)): About Neighborhood total = total + R[j] * wji // Update the PageRank Update Vertex R[i] = total // Trigger neighbors to run again priority = |R[i] – oldR[i]| Signal Neighbors & if R[i] not converged then Modify Edge Data signal neighbors(i) with priority 27
- 28. GAS Decomposition Machine 1 Machine 2 Master Gather Apply Sca>er Y’ Y’ Y’ Y’ Σ1 Σ Σ2 + + + Mirror Y Σ3 Σ4 Mirror Machine 3 Mirror Machine 4 28
- 29. Minimizing Communication in PowerGraph Y Communication is linear in " the number of machines " each vertex spans A vertex-cut minimizes " machines each vertex spans Percolation theory suggests that power law graphs have good vertex cuts. [Albert et al. 2000] 29
- 30. Machine Learning and Data-Mining Toolkits Graph AnalyMcs Graphical Models Computer Vision Clustering Topic Modeling CollaboraMve Filtering GraphLab2 System MPI/TCP-‐IP PThreads HDFS EC2 HPC Nodes http://graphlab.org Apache 2 License
- 31. PageRank on Twitter Follower Graph Natural Graph with 40M Users, 1.4 Billion Links Run1me Per Itera1on 0 50 100 150 200 Hadoop GraphLab Twister Piccolo Order of magnitude by exploiting properties of Natural Graphs PowerGraph Hadoop results from [Kang et al. '11] Twister (in-memory MapReduce) [Ekanayake et al. ‘10] 31
- 32. GraphLab2 is Scalable Yahoo Altavista Web Graph (2002): One of the largest publicly available web graphs 1.4 Billion Webpages, 6.6 Billion Links 7 Seconds per Iter. 1B links Nodes processed per second 64 HPC 1024 Cores (2048 30 lines of user code HT) 32
- 33. Topic Modeling English language Wikipedia – 2.6M Documents, 8.3M Words, 500M Tokens – Computationally intensive algorithm Million Tokens Per Second 0 Smola et al. PowerGraph 20 40 60 80 100 120 140 160 100 Yahoo! Machines Specifically engineered for this task 64 cc2.8xlarge EC2 Nodes 200 lines of code & 4 human hours 33
- 34. Triangle Counting on Twitter 40M Users, 1.4 Billion Links Counted: 34.8 Billion Triangles Hadoop [WWW’11] 1536 Machines 423 Minutes 64 Machines 15 Seconds 1000 x Faster 34 S. Suri and S. Vassilvitskii, “CounMng triangles and the curse of the last reducer,” WWW’11
- 35. 7. After 8. After By exploiting common patterns in graph data and computation: New ways to represent real-world graphs New ways execute graph algorithms Machine 1 Machine 2 Orders of magnitude improvements over existing systems
- 37. Exciting Time to Work in ML J Unique opportunities to change the world!! With ML, I will cure cancer!!! With ML I will find true love. Why won’t ML read my mind??? L Building scalable learning system requires experts …
- 38. But… Even basics of scalable ML can be challenging ML key to any new service we want to build 6 months from prototype to producMon State-‐of-‐art ML algorithms trapped in research papers Goal of GraphLab 3: Make large-scale machine learning accessible to all! J
- 39. Adding a Python Layer Python API Graph AnalyMcs Graphical Models Computer Vision Clustering Topic Modeling CollaboraMve Filtering GraphLab2 System MPI/TCP-‐IP PThreads EC2 HPC Nodes HDFS
- 40. Learning ML with GraphLab Notebook https://beta.graphlab.com/examples!
- 41. Prototype to Production with Python GraphLab: Easily install prototype locally Deploy to the cluster in one step
- 42. Learn: GraphLab Notebook Prototype: pip install graphlab è local prototyping Production: Same code scales to EC2 cluster
- 43. GraphLab Toolkits Highly scalable, state-of-the-art machine learning straight from python Graph Analytics Graphical Models Computer Vision Clustering Topic Modeling Collaborative Filtering
- 44. Machine Learning on Graphs partners@graphlab.com NIPS Workshop on Big Learning: biglearn.org Lake Tahoe, December 9th Joseph Gonzalez Co-Founder, GraphLab Inc. joseph@graphlab.com