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Using Localised ‘Gossip’ to Structure Distributed Learning

Using Localised ‘Gossip’ to Structure Distributed Learning. Bruce Edmonds Centre for Policy Modelling. The Problem. For many problems/situations universal solutions are unreachable

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Using Localised ‘Gossip’ to Structure Distributed Learning

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  1. Using Localised ‘Gossip’ to Structure Distributed Learning Bruce EdmondsCentre for Policy Modelling Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-1

  2. The Problem • For many problems/situations universal solutions are unreachable …in such situations one has to seek partial solutions (i.e. solutions that are valid/effective only in a subdomain). • Sometimes the relevant subdomains seem obvious (e.g. biology vs. physics) …but in many other situations the best way to subdivide a situation also needs to be discovered (entangled with solution types). Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-2

  3. Graphs of piecewise models Graph of global candidate model Fitting data globally and piecewise Data points Problem Domain Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-3

  4. Solution source • Both ecology and human society inhabit situations where universal solutions are not reachable • Even closely related species are successful in different regions and niches • Human techniques for dealing with the environment have spread over the areas where these techniques work Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-4

  5. Cavalli-Sforza, Menozzi, and Piazza 1994 p. 257 – Cultural Diffusion Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-5

  6. Beef Cows in the USA 2002 Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-6

  7. Milk Cows in the USA 2002 Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-7

  8. Change in the use of irrigation in USA 1997-2002 Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-8

  9. Different ranges of different species Greenstriped grasshopper Striped grasshopper Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-9

  10. Distribution of terms for soft drinks in the USA – Matthew Campbell’s map Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-10

  11. …like homo sapiens! Only occasionally do global parasites arise… Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-11

  12. D 3.7 2.1 0.9 2.2 Some Space of Characteristics An Illustration of the Basic Algorithm p (Learning Domain & Content) Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-12

  13. The algorithm outline (generic version) Initialise space with a random set of genes Repeat ForEachgene from 1 to popSize Randomly select a locality randomly select from locality a set of sample genes evaluate set in the locality chose two bestfrom set ifrandomNum < probCrossover then cross two best -> newInd elsebest -> newInd Nextgene New population composed of newInds Until finished Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-13

  14. Two phases of this approach • When species successfully propagate over regions they tend to “speciate” into many varieties • Information learnt is spread over the population not in a single best individual • Thus if you want to understand the results it is helpful to add an “analysis” phase …which does a sort of “cluster analysis” of the locally best solutions in the population • I do this by: turning off variation; allowing only one solution per location; and massive but strictly local propagation to nearby locations (in this 2nd phase) Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-14

  15. An application to the Cleveland Heart Disease Data Set Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-15

  16. Cleveland Heart Disease Data Set – the processed sub-set used In processed sub-set: • 281 entries • 14 attributes numeric or numerically coded • Attribute 14 is the outcome (0, 1, 2, 3, 4) • Some attributes: 1 - age, 2 - sex, 4 - resting blood pressure (trestpbs), 5 - cholesterol (chol) • Available at the repository of Machine Learning Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-16

  17. Why this particular data set? • It is fairly large • It is quite complex • I know hardly anything about the causes of heart disease • Its accessible • ML techniques so far have not found a very high performing global solution • It seemed a vaguely useful thing to do Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-17

  18. The Solution Form • Solutions are a set of 5 numeric functions (one for each outcome), each coded as tree expressions • E.g. Outcome 0 has weight calculated by: [TIMES [MIN [CONST -0.6] [INPUT 8]] [SAFEDIVIDE [INPUT 1] [CONST 0.5]]] • Which simplifies to: 2 * V8 * V1 • Each of 5 functions evaluated (given 13 inputs) • Function with highest value gives prediction • Functions: MIN, MAX, IGZ, TIMES, MINUS, PLUS, SAFEDIVIDE • Leaves: inputs 1,2,…,13 and constants -1, -.9,.., 1 Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-18

  19. The space of characteristics • Is essentially the 281 points in the data set …with the distance structure determined by the cartesian distance within the chosen space of characteristics Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-19

  20. The 3 sets of runs (12 runs each) • Global: a standard GP approach, evaluation against 10% random sample, population of 281, 90% crossover • Local: set of solutions evaluated at a point in the space, taken from point plus some from neighbouring localities, population 800, 20% crossover • Local (1, 2): space defined by age and sex • Local (4, 5): space defined by restbps and chol Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-20

  21. Measuring the success • Cost of each approach measured in terms of the number of evaluations of a solution at a point in the space, since this dominates the computational time • Effective error is: Global runs: the average error (over all points) of the best solution in the population Local runs: the average of the error of set of the best solution at each point evaluated at that point Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-21

  22. Comparison of global and local runs Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-22

  23. Error and Spread in Local(1, 2) Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-23

  24. Error and Spread in Local(4, 5) Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-24

  25. Spread of solutions using items 1&2 Female Both Male Age Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-25

  26. Spread of solutions using items 4&5 cholesterol resting blood pressure Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-26

  27. Related Work • Local Regression (or the slightly more general locally weighted learning) • Clustering techniques • ‘Demes’ in GP • Evolving parts of a problem separately (DCCGA etc.) • Decision tree induction (e.g. C4.5) • Ecological models Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-27

  28. Conclusion • Memetic/ecological processes that combine local propagation and solution development can find and exploit niches in complex problems …but this does not lead to neat global solutions (in cases I have tried) …and can be sensitive to the selection of the space over which propagation occurs (although am investigating systems where this is also discovered, so wish me luck!) Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-28

  29. The End Bruce Edmonds bruce.edmonds.name Centre for Policy Modelling cfpm.org Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-29

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