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)
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
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
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