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 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-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-3

Fitting data globally and piecewise

Data points

Problem Domain

Graph of global candidate model

Graphs of piecewise

models

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

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

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

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

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

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

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

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!

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)

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

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 2nd phase)

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

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

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

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

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

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

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

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

0%

10%

20%

30%

40%

50%

10000 100000 1000000 10000000

Evaluations

Eff

ecti

ve E

rro

r

Global

Local (1, 2)

Local (4, 5)

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)

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erag

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Sp

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Development Phase Analysis Phase

Spread

Error

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)

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Spread

Error

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&2M

ale

Bot

hF

emal

e

Age

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

chol

este

rol

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

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!)

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