using localised ‘gossip’ to structure distributed learning
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Using Localised ‘Gossip’ to Structure Distributed Learning. Bruce Edmonds Centre for Policy Modelling. The Problem. For many problems/situations universal solutions are unreachable - PowerPoint PPT PresentationTRANSCRIPT
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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
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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).
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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
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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
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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
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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
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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
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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
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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
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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
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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!
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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)
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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)
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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)
0%
5%
10%
15%
20%
25%
30%
0 500
00
100
000
1500
00
200
000
250
000
3000
00
3500
00
400
000
450
000
5000
00
Evaluations
Av
era
ge
Lo
ca
lly B
est
E
rro
r
0
1
2
3
4
5
6
Av
erag
e G
ene
Sp
read
Development Phase Analysis Phase
Spread
Error
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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)
0%
5%
10%
15%
20%
25%
30%
0 50
000
10
000
0
150
00
0
200
000
250
000
30
000
0
35
000
0
400
00
0
450
000
500
000
Evaluations
Ave
rag
e L
oca
lly
Bes
t E
rro
r
0
1
2
3
4
5
6
Av
era
ge
Ge
ne
Sp
rea
d
Development Phase Analysis Phase
Spread
Error
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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
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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
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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
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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!)
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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