1 / 88

Understanding and Managing Cascades on Large Graphs

Understanding and Managing Cascades on Large Graphs. B. Aditya Prakash Computer Science Virginia Tech. Guest Lecture, 11/6/2012. Networks are everywhere!. Facebook Network [2010]. Gene Regulatory Network [ Decourty 2008]. Human Disease Network [ Barabasi 2007].

uri
Download Presentation

Understanding and Managing Cascades on Large Graphs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Understanding and Managing Cascades on Large Graphs B. Aditya Prakash Computer Science Virginia Tech. Guest Lecture, 11/6/2012

  2. Networks are everywhere! Facebook Network [2010] Gene Regulatory Network [Decourty 2008] Human Disease Network [Barabasi 2007] The Internet [2005] Prakash 2012

  3. Dynamical Processes over networks are also everywhere! Prakash 2012

  4. Why do we care? • Social collaboration • Information Diffusion • Viral Marketing • Epidemiology and Public Health • Cyber Security • Human mobility • Games and Virtual Worlds • Ecology • Localized effects: riots…

  5. Why do we care? (1: Epidemiology) • Dynamical Processes over networks [AJPH 2007] CDC data: Visualization of the first 35 tuberculosis (TB) patients and their 1039 contacts Diseases over contact networks Prakash 2012

  6. Why do we care? (1: Epidemiology) • Dynamical Processes over networks • Each circle is a hospital • ~3000 hospitals • More than 30,000 patients transferred [US-MEDICARE NETWORK 2005] Problem: Given k units of disinfectant, whom to immunize? Prakash 2012

  7. Why do we care? (1: Epidemiology) ~6x fewer! [US-MEDICARE NETWORK 2005] CURRENT PRACTICE OUR METHOD Hospital-acquired inf. took 99K+ lives, cost $5B+ (all per year) Prakash 2012

  8. Why do we care? (2: Online Diffusion) > 800m users, ~$1B revenue [WSJ 2010] ~100m active users > 50m users Prakash 2012

  9. Why do we care? (2: Online Diffusion) • Dynamical Processes over networks Buy Versace™! Followers Celebrity Social Media Marketing Prakash 2012

  10. 3: Water Distribution Network • Given a real city water distribution network • Data on how contaminants spread on network • Problem of interest to many (EPA, etc) S Where should we place the sensors to detect all possible contaminations? Prakash 2012

  11. Why do we care? (4: To change the world?) • Dynamical Processes over networks Social networks and Collaborative Action Prakash 2012

  12. High Impact – Multiple Settings epidemic out-breaks Q. How to squash rumors faster? Q. How do opinions spread? Q. How to market better? products/viruses transmit s/w patches Prakash 2012

  13. Research Theme ANALYSIS Understanding POLICY/ ACTION Managing DATA Large real-world networks & processes Prakash 2012

  14. Research Theme – Public Health ANALYSIS Will an epidemic happen? POLICY/ ACTION How to control out-breaks? DATA Modeling # patient transfers Prakash 2012

  15. Research Theme – Social Media ANALYSIS # cascades in future? POLICY/ ACTION How to market better? DATA Modeling Tweets spreading Prakash 2012

  16. In this lecture Given propagation models: Q1: How do viruses compete? ANALYSIS Understanding Prakash 2012

  17. In this lecture Q2: How to immunize and control out-breaks better? Q3: How to detect outbreaks? POLICY/ ACTION Managing Prakash 2012

  18. In this lecture Q4: How do cascades look like? Q5: How does activity evolve over time? DATA Large real-world networks & processes Prakash 2012

  19. Outline • Motivation • Part 1: Understanding Epidemics (Theory) • Part 2: Policy and Action (Algorithms) • Part 3: Learning Models (Empirical Studies) • Conclusion Prakash 2012

  20. Part 1: Theory • Q1: What happens when viruses compete? • Mutually-exclusive viruses Prakash 2012

  21. Competing Contagions iPhone v Android Blu-ray v HD-DVD v Attack Retreat Biological common flu/avian flu, pneumococcal inf etc Prakash 2012

  22. Details A simple model • Modified flu-like • Mutual Immunity (“pick one of the two”) • Susceptible-Infected1-Infected2-Susceptible Virus 2 Virus 1 Prakash 2012

  23. Question: What happens in the end? green: virus 1 red: virus 2 Number of Infections • Footprint @ Steady State • Footprint @ Steady State = ? ASSUME: Virus 1 is stronger than Virus 2 Prakash 2012

  24. Question: What happens in the end? • Footprint @ Steady State • Footprint @ Steady State green: virus 1 red: virus 2 Number of Infections Strength Strength ?? = 2 Strength Strength ASSUME: Virus 1 is stronger than Virus 2 Prakash 2012

  25. Answer: Winner-Takes-All green: virus 1 red: virus 2 Number of Infections ASSUME: Virus 1 is stronger than Virus 2 Prakash 2012

  26. Our Result: Winner-Takes-All Given our model, and any graph, the weaker virus always dies-out completely Details The stronger survives only if it is above threshold Virus 1 is stronger than Virus 2, if: strength(Virus 1) > strength(Virus 2) Strength(Virus) = λβ / δ same as before! In Prakash+ WWW 2012 Prakash 2012

  27. Real Examples [Google Search Trends data] Reddit v Digg Blu-Ray v HD-DVD Prakash 2012

  28. Outline • Motivation • Part 1: Understanding Epidemics (Theory) • Part 2: Policy and Action (Algorithms) • Part 3: Learning Models (Empirical Studies) • Conclusion Prakash 2012

  29. Part 2: Algorithms • Q2: Whom to immunize? • Q3: How to detect outbreaks? Prakash 2012

  30. Full Static Immunization Given: a graph A, virus prop. model and budget k; Find: k ‘best’ nodes for immunization (removal). ? ? k = 2 ? ? Prakash 2012

  31. Part 2: Algorithms • Q3: Whom to immunize? • Full Immunization (Static Graphs) • Fractional Immunization • Q4: How to detect outbreaks? • Q5: Who are the culprits? Prakash 2012

  32. Challenges Given a graph A, budget k, Q1(Metric) How to measure the ‘shield-value’ for a set of nodes (S)? Q2(Algorithm) How to find a set of k nodes with highest ‘shield-value’? Prakash 2012

  33. Proposed vulnerability measure λ λ is the epidemic threshold “Safe” “Vulnerable” “Deadly” Increasing λ Increasing vulnerability Prakash 2012

  34. A1: “Eigen-Drop”: an ideal shield value Eigen-Drop(S) Δ λ = λ - λs 9 Δ 9 9 11 10 10 2 1 1 4 4 8 8 6 2 7 3 7 3 5 5 6 Without {2, 6} Original Graph Prakash 2012

  35. (Q2) - Direct Algorithm too expensive! • Immunize k nodes which maximize Δλ S = argmaxΔλ • Combinatorial! • Complexity: • Example: • 1,000 nodes, with 10,000 edges • It takes 0.01 seconds to compute λ • It takes2,615 yearsto find 5-best nodes! Prakash 2012

  36. A2: Our Solution In Tong+ ICDM 2010 • Part 1: Shield Value • Carefully approximate Eigen-drop (Δλ) • Matrix perturbation theory • Part 2: Algorithm • Greedily pick best node at each step • Near-optimal due to submodularity • NetShield(linear complexity) • O(nk2+m) n = # nodes; m = # edges Prakash 2012

  37. Details Our Solution: Part 1 u(i) A u u = λ . • Approximate Eigen-drop (Δλ) • Δλ ≈SV(S) = • Result using Matrix perturbation theory • u(i) == ‘eigenscore’ ~~ pagerank(i) Prakash 2012

  38. Details P1: node importance P2: set diversity Original Graph Prakash 2012 Select by P1 Select by P1+P2

  39. Our Solution: Part 2: NetShield Corollary: Greedy algorithm works 1. NetShield is near-optimal (w.r.t. max SV(S)) 2. NetShield is O(nk2+m) We prove that: SV(S) is sub-modular (& monotone non-decreasing) NetShield: Greedily add best node at each step Prakash 2012 Footnote: near-optimal means SV(S NetShield) >= (1-1/e) SV(S Opt)

  40. Experiment: Immunization quality Log(fraction of infected nodes) PageRank Betweeness (shortest path) Degree Lower is better Acquaintance Eigs (=HITS) NetShield Time Prakash 2012

  41. Fractional Immunization of Networks B. Aditya Prakash, LadaAdamic, Theodore Iwashyna (M.D.), Hanghang Tong, Christos Faloutsos Under Submission Prakash 2012

  42. Previously: Full Static Immunization Given: a graph A, virus prop. model and budget k; Find: k ‘best’ nodes for immunization (removal). k = 2 ? ? Prakash 2012

  43. Fractional Asymmetric Immunization # antidotes = 3 Fractional Effect [ f(x) = ] Asymmetric Effect Prakash 2012

  44. Now: Fractional Asymmetric Immunization # antidotes = 3 Fractional Effect [ f(x) = ] Asymmetric Effect Prakash 2012

  45. Fractional Asymmetric Immunization # antidotes = 3 Fractional Effect [ f(x) = ] Asymmetric Effect Prakash 2012

  46. Fractional Asymmetric Immunization Drug-resistant Bacteria (like XDR-TB) Another Hospital Hospital Prakash 2012

  47. Fractional Asymmetric Immunization = f Drug-resistant Bacteria (like XDR-TB) Another Hospital Hospital Prakash 2012

  48. Fractional Asymmetric Immunization Problem: Given k units of disinfectant, how to distribute them to maximize hospitals saved? Another Hospital Hospital Prakash 2012

  49. Our Algorithm “SMART-ALLOC” ~6x fewer! [US-MEDICARE NETWORK 2005] • Each circle is a hospital, ~3000 hospitals • More than 30,000 patients transferred CURRENT PRACTICE SMART-ALLOC Prakash 2012

  50. Running Time Wall-Clock Time > 1 week ≈ > 30,000x speed-up! Lower is better 14 secs Simulations SMART-ALLOC Prakash 2012

More Related