Putting people into models Social networks and Bayesian networks

1. Putting people into models Social networks and Bayesian networks Ingrid van Putten CSIRO – Marine and Atmospheric research (Hobart- Australia) Jacopo A. Baggio School of Human Evolution &Social Change,Arizona State University What are networks and what are social networks Where did it all start? Small world, random, and scale-free networks Fisheries example – quota trade market Linking qualitative, networks and Bayesian networks How do Bayesian networks work?

2. Leonhard Euler (1707 – 1783) Networks: How did it all start? Commentarii Academiae Scientiarum Imperialis Petropolitanae, vol. 8, pp. 128-140, 1736 The problem, which I am told is widely known, is as follows: in Königsberg in Prussia, there is an island A, called the Kneiphof; the river which surrounds it is divided into two branches, as can be seen in the figure, and these branches are crossed by seven bridges, a, b, c, d, e, f and g. Concerning these bridges, it was asked whether anyone could arrange a route in such a way that he would cross each bridge once and only once.

3. Networks: How did it all start? Definitions (in modern words): A network is a figure of points (vertices/nodes/actors) connected by non-intersecting curves (edges/links/ties). A vertex is called odd if it has an odd number of arcs leading to it. An Euler path is a continuous path that passes through every arc once and only once. Theorems: If a network has more than two odd vertices, it has no Euler paths;if it has two or less odd vertices, there is at least one Euler path.

4. What is a network? An arrangement of intersecting horizontal and vertical lines 1 a network of arteries WEB, lattice, net, matrix, mesh, crisscross, grid, reticulum, reticulation; Anatomy plexus. 2 a network of lanes MAZE, labyrinth, warren, tangle. 3 a network of friends SYSTEM, complex, nexus, web, webwork. What is a SOCIAL network? A social structure that is made up of entities/ agents/ individuals/ or organisations that have ties/ relationships (interactions) between them. Physical networks Ties or relationships could be anything …. Kinship Friendship Informationexchange Marketexchange [http://serialconsign.com/2007/11/we-put-net-network]

5. Physical interaction networks The Blogosphere Biochemical networks Gene-protein networks Food webs: who eats whom The World Wide Web (?) Airline networks Call centre networks Paper citations Social interaction networks Friendships Acquaintances Boards and directors Organizations facebook.com twitter.com

6. node, vertex, actor link, edge, tie V = {v1…vn} Graph G(V,E) E = {e1…en} 1 1 4 2 4 2 3 5 3 5 1 1 2 4 2 4 3 5 3 5 Networks and Matrices Undirected Directed Not symmetrical Symmetrical

7. How did interest in social networks start? ……………. Six degrees of separation ………………… Stanley Milgram (and other researchers) carried out what is now known as “The small world experiment” The experiments are often associated with the phrase "six degrees of separation", although Milgram did not use this term himself. The research was groundbreaking human society is a network characterized byshort path (chain) lengths

8. How did Milgramdo the experiment? 1 Information packets sent to "randomly" selected individuals around USA. Packets had basic information about a target contact person in Boston (Boston stockbroker). This person is the end destination for the packet. If the recipient personally knew the Boston stockbroker described in the letter, they should forward the letter directly. 2 If they did not know the Boston stockbroker personally, then the person was to think of a friend or relative he knew personally who was more likely to know the target. Could only send to someone with whom they were on a first-name basis Recipient was directed to sign his name on a roster and forward the packet to the next person 3 When and if the package eventually reached the contact person in Boston, researchers could examine the roster to count the number of times it had been forwarded from person to person 4 20% of packets reached target Chain length ' 6.5 CSIRO.

9. Milgram’s experiment John Guare wrote a play called Six Degrees of Separation, based on this concept. One of the main character’s lines (Quisa) Chain length ' 6.5 “Everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everybody else on this planet. The president of the United States. A gondolier in Venice… It’s not just the big names. It’s anyone. A native in a rain forest. A Tierra del Fuegan. An Eskimo. I am bound to everyone on this planet by a trail of six people…” CSIRO.

10. Erdős Number (Bacon game for the scientist) Paul Erdős was an influential and itinerant mathematician (often living out of a suitcase boarding with his colleagues). He published more papers during his life (at least 1,525) than any other mathematician in history (with 507 co-authors) Number of links required to connect scholars to Erdős, via co-authorship of papers Paul Erdős (1913-1996) Jerry Grossman’s (Oakland Univ.) website allows mathematicians to compute their Erdos numbers: http://www.oakland.edu/enp/ • Connecting path lengths, among mathematicians only: • average is 4.65 • maximum is 13

11. Random Graphs --- or why does the “small world” phenomena exist? N = nodes (individuals) p= number of nodes with links (A pair of nodes has probability p of being connected) K=number of links (Average degree, k ≈ pN) p=1.0 ; k≈N p=0 ; k=0 N = 12 N = 12 Now put in few random connections Each person is connected to two neighbours either side B Number of steps to get from A to B reduced to two A Takes three steps to get from A to B

12. small-world network L= avg shortest path length C = avg clustering coefficient

13. Most networks are not random but are ‘scale free’ • Tend to have a relatively few nodes of high connectivity (the “Hub” nodes – or “broker” nodes) Our world complies with the Pareto principle (also known as the 80–20 rule, the law of the vital few)

14. Degree Distribution & Power Laws Albert and Barabasi (1999) Many real-world networks exhibit a power-law distribution (also called “Heavy tailed” distribution) P(k) Number of nodes with k links Lots of nodes with only a few links (k) Number of links Power laws in real networks: (a) WWW hyperlinks (b) co-starring in movies (c) co-authorship of physicists (d) co-authorship of neuroscientists (e) Distribution of wealth Power-law distributions are straight lines in log-log space

15. Power Laws ….. Scale-Free Networks CSIRO.

16. Power Laws ….. What happens if you take out a few hubs? Take out 9 centres Take out 7 centres – but target the hubs

17. Epidemic spreading Structure matters: Power law versus random networks Structure matters: what do we know? - Structural properties influence a system strengths and weaknesses. - Structural properties influence diffusion processes such as viruses, pests, communication, information, migration and so on. - There is no golden rule (the “perfect” structure for all systems does not exist)

18. Australian fisheries example of network analysis: Lease quota trade for lobsters Industry structural change after tradeable quota introduced

19. Mapping the lease quota trade • (each line is a trade between two individuals) 1999 (year after the introduction of quota) 2007 (8 years later) New relationships – more brokers / hubs

20. Income supplementer Lease market network Lease quota dependent fisher Investor Quota redistributor Independent fisher Active fishers

21. 25 Portfolio investors D C Ownership characteristics (number of quota units owned by fisher) Concentration of ownership B 75 A Fishing effort (number of quota units fished) Income supplementers (A-C-D) Lease dependent fishers (A-B-C) Investors (A-D) Quota redistributors (A-B-C-D) Independent fishers (A-C) Van Putten(2011)

22. Putting people into models Social networks and Bayesian networks Ingrid van Putten CSIRO – Marine and Atmospheric research (Hobart- Australia) Jacopo A. Baggio School of Human Evolution &Social Change,Arizona State University Linking qualitative, networks and Bayesian networks How do Bayesian networks work?

23. Bayesian models Network models Qualitative models Conditional probabilities p2 p3 N1 N2 Cold (1) Flu (2) + + undirected p1 N3 Fever (3) - Road between power station 1-2, and 1-3, but not between 2-3 If you have a cold (1) there is a chance you have a fever (3), and if you have the flu (2) there is also a chance you have a fever i2 i3 Animal 3 experiences external factors that limit it (self effect). Animal 1 has a positive effect on animal 2, and animal 2 also has a positive effect on animal 3, but animal 2 has no effect on animal 1 (commensalism) directed i1 Cold Flu Fever True False Fever True False 0 0.6 0.1 True 0.7 True Individuals 1-3 are friends with each other, and 1 is friends with 2, but 2 doesn’t feel like 1 is their friend and 2-3 are not friends at all False 0.4 1 False 0.3 0.9

24. Bayes' theorem gives the relationship between the probabilities of Aand B P(A) and P(B) and the conditional probabilities of Agiven B and B given A P(A| B) and P(B | A) Thomas Bayes(1701-1761) A Bayesian network is a directed graph Each node represents a random variable. Each node represents a variable A with parent nodes representing variables B1, B2,..., Bn Each node is assigned a conditional probability table (CPT)

25. Smoking Visit to Asia Tuberculosis Lung Cancer Bronchitis Tuberculosis or Cancer XRay Result Dyspnoea(SOB) Example from Medical Diagnostics Patient Information Medical Difficulties Diagnosis Diagnostic Tests Network represents a knowledge structure between medical difficulties, their causes and effects, patient information and diagnostic tests

26. Smoking Visit to Asia Tuberculosis Lung Cancer Bronchitis Tuberculosis or Cancer XRay Result Dyspnoea (SOB) Example from Medical Diagnostics Dyspnea Bronchitis Medical Difficulties Tub or Can True True False False Bronchitis Present Absent Present Absent Present 0.90 0.70 0.80 0.10 Absent 0.l0 0.30 0.20 0.90 Medical Difficulties CSIRO.

27. Smoking Visit to Asia Tuberculosis Lung Cancer Bronchitis Tuberculosis or Cancer XRay Result Dyspnoea (SOB) Example from Medical Diagnostics CSIRO.

28. We have some information about the patient We know the person has been to Asia From P=1.04 From P=6.48 From P=43.6 From P=11.0 Given evidence about a cause, what are the predicted effects (e.g. you know the person has been to Asia what is the probability that they have tuberculosis?) Predictive reasoning

29. We also can now see the x ray results are normal Increases the probability that it’s not tuberculosis or cancer X-ray results are normal …. Given evidence about an effect (symptom) how does this change our beliefs in the causes? (e.g. I observe there is nothing abnormal about the x-ray– how does that the affect the probability that it’s tuberculosis or cancer?) Diagnostic

30. Australian fisheries example of BBN: Torres Strait (between Papua New Guinea and far northern Australia)

31. Australian Examples: Torres Strait Non-indigenous commercial catch SEC fishery Pre-season survey Lobster abundance Cost related drivers Papuan Price related drivers Hookah ownership Private freezer Season Exchange rate Fuel costs Functional Island freezer Price live Weather Fishing costs Regional Authority ($) Price tails Ease of catching lobster Other lobster available Community business knowledge Socio-cultural drivers Returns from fishing Full time alternative income Community role models Government employment scheme Crew availability Working age men Incidental household payments Social capital Tradition & culture Profit drivers Casual fisher Part time fisher Full time fisher

32. Australian Examples: Torres Strait Non-indigenous commercial catch SEC fishery Pre-season survey Lobster abundance • Objective: more full time indigenous fishers (use olympic quota, ITQ, community quota ?) • Assumed: economic drivers = key • Actually: socio-cultural & infrastructure Cost related drivers Papuan Price related drivers Hookah ownership Private freezer Season Exchange rate Fuel costs Functional Island freezer Price live Weather Fishing costs Regional Authority ($) Price tails Ease of catching lobster Other lobster available Community business knowledge Socio-cultural drivers Returns from fishing Full time alternative income Community role models Government employment scheme Crew availability Working age men Incidental household payments Social capital Tradition & culture Profit drivers Casual fisher Part time fisher Full time fisher

33. Australian Examples: Torres Strait Non-indigenous commercial catch SEC fishery Pre-season survey Lobster abundance • Full time fishers • Economics (profit) is a driver • Social capital important too (crew, freezers) Cost related drivers Papuan Price related drivers Hookah ownership Private freezer Season Exchange rate Fuel costs Functional Island freezer Price live Weather Fishing costs Regional Authority ($) Price tails Ease of catching lobster Other lobster available Community business knowledge Socio-cultural drivers Returns from fishing Full time alternative income Community role models Government employment scheme Crew availability Working age men Incidental household payments Social capital Tradition & culture Profit drivers Casual fisher Part time fisher Full time fisher

34. Australian Examples: Torres Strait Non-indigenous commercial catch SEC fishery Pre-season survey Lobster abundance • Part time fishers • Socio-cultural is key • Ease of access vs other income Cost related drivers Papuan Price related drivers Hookah ownership Private freezer Season Exchange rate Fuel costs Functional Island freezer Weather Price live Fishing costs Ease of catching lobster Regional Authority ($) Price tails Socio-cultural drivers Other lobster available Community business knowledge Returns from fishing Government employment scheme Full time alternative income Community role models Crew availability Incidental household payments Working age men Social capital Tradition & culture Profit drivers Casual fisher Part time fisher Full time fisher