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

2. Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-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).

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

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

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

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

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

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

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

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

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

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

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

14. Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-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 2 nd phase)

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

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

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

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

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

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

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

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

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

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

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

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

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

28. Using localised gossip to structure distributed learning, Bruce Edmonds, SIC@AISB, Univ. of Herts., April 2005, http://cfpm.org/~bruce slide-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!)

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