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Extending Evolutionary Programming to the Learning of
Dynamic Bayesian Networks
Allan Tucker
Xiaohui Liu
Birkbeck College
University of London
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Diagnosis in MTS• Useful to know causes for a given set of
observations within a time series • E.g. Oil Refinery: ‘Why a temperature has become
high whilst a pressure has fallen below a certain value?’
• Possible paradigm to perform Diagnosis is the Bayesian Network
• Evolutionary Methods to learn BNs• Extend work to Dynamic Bayesian Networks
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Dynamic Bayesian Networks
• Static BNs repeated over t time slices
• Contemporaneous / Non-Contemporaneous Links
• Used for Prediction / Diagnosis within dynamic systems
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Assumptions - 1
• Assume all variables take at least one time slice to impose an effect on another.
• The more frequently a system generates data, the more likely this will be true (e.g. every minute, second etc.)
• Contemporaneous Links are excluded from the DBN.
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Representation
• N variables at time slice, t
• P Triples of the form (x,y,lag)
• Each triple represents a link from a node at a previous time slice to a node at time t.
Example: { (0,0,1); (1,1,1); (2,2,1); (3,3,1); (4,4,1); (0,1,3); (2,1,2); (2,4,5); (4,3,4) }
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Search Space• Given the first assumption and proposed
representation Search Space will be:
• E.g. 10 variables, MaxLag = 30
• Make further assumptions to reduce this and speed up the search
MaxLagN 2
2
30002
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Assumptions - 2
• Cross-Description-Length Function (CDLF)
• Exhibits smoothness of Cross Correlation Function (CCF) cousin
• Exploit this smoothness using Swap
300
310
320
330
340
350
360
370
380
390
400
1 11 21 31 41 51
Lag
DL
DL of link(4,6) overdiffering lags
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Assumptions - 3
• Auto-Description-Length Function (ADLF) exhibits the lowest DL with time lag=1
• Automatically insert these links before evaluation 124000
125000
126000
127000
128000
129000
130000
131000
132000
133000
134000
0 20 40 60 80
Lag
DL
ADLF forvariable 2
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Evolutionary Programmingto find Links with Low Description
Length
Evolutionary Program (Swap) to find Dynamic Bayesian Network
with Low Description Length
Dynamic Bayesian Network
MultivariateTime Series
Explanation Algorithm(using Stochastic
Simulation)User
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EP to Find low DL links
• Using an EP approach with self adapting parameters to find a good selection of links with low DL (High Mutual Information)
• Representation: Each individual is a triple (x,y,lag)
• Fitness is DL of triple
• Solution is the resultant population
),0( iii Nxx
)exp( iii ss
)2
1,0(n
Ns
)2
1,0(
nNsi
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Swap Operator
• Select a triple from one parent with equal probability
• Mutate the current lag with a uniform distribution:
• Current Lag + U(-MaxLag/10, MaxLag/10)
(x,y,lag)(x,y,lag)(x,y,lag)(x,y,lag)(x,y,lag)(x,y,lag)(x,y,lag)
(x,y,lag)(x,y,lag)
(x,y,lag)(x,y,lag)(x,y,lag)(x,y,lag)(x,y,lag)(x,y,lag)(x,y,lag)
Lag: 1 MaxLagX
[Lag - MaxLag/10] [Lag + MaxLag/10]
(x,y,lag)
(x,y,lag)(x,y,lag)
(x,y,lag)
(x,y,lag)
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Generating Synthetic Data
t-3 t-2 t-1 t
t-3 t-2 t-1 t t+1
(1)
(2)
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Oil Refinery Data
• Data recorded every minute• Hundreds of variables• Selected 11 interrelated variables• Discretized each variable into 4 states• Large Time Lags (up to 120 minutes between
some variables)
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Parameters
2050080%10%
Population SizeGenerationsOpRate (KGM/Swap)Slide Mutation Rate
EP - DBN Structure Synthetic
30200080%10%
Oil Data
530
Number of VarMaxLag
Data Synthetic
1160
Oil Data
1%2530
Mutation RateLimit (% of all links)ListGenerations
EP - DL Links Synthetic
1%550
Oil Data
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Results 1 - Synthetic Data
1700
1800
1900
2000
2100
2200
2300
2400
1 12 23 34 45 56 67 78 89 100
111
122
133
144
155
166
177
188
199
Generation
DL KGM
Swap
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Results 2 - Oil Refinery Data
66000
66500
67000
67500
68000
68500
69000
69500
70000
70500
1 101 201 301 401 501 601 701 801 901 1001 1101
Generation
DL KGM
Swap
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Results 3
177000
179000
181000
183000
185000
187000
189000
1 9 17 25 33 41 49 57 65 73 81 89 97
Generations
DL
Standard GA
KGM
Swap
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Explanations - using stochastic simulation
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ExplanationsInput:
t - 0 : Tail Gas Flow in_state 0 Reboiler Temperature in_state 3
Output:
t - 7 : Top Temperature in_state 0t - 54 : Feed Rate in_state 1t - 75 : Reactor Inlet Temperature in_state 0
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Future Work
• Exploring the use of different metrics• Improving accuracy
(e.g. different discretization policies, continuous DBNs)
• Learning a library of DBNs in order to classify the current state of a system
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