Extending Evolutionary Programming to the Learning of Dynamic Bayesian Networks Allan Tucker Xiaohui Liu Birkbeck College University of London

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

Dynamic Bayesian Networks Static BNs repeated over t time slices Contemporaneous / Non-Contemporaneous Links Used for Prediction / Diagnosis within dynamic systems

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.

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) }

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

Assumptions - 2 Cross-Description-Length Function (CDLF) Exhibits smoothness of Cross Correlation Function (CCF) cousin Exploit this smoothness using Swap

Assumptions - 3 Auto-Description-Length Function (ADLF) exhibits the lowest DL with time lag=1 Automatically insert these links before evaluation

Evolutionary Programming to find Links with Low Description Length Evolutionary Program (Swap) to find Dynamic Bayesian Network with Low Description Length Dynamic Bayesian Network Multivariate Time Series Explanation Algorithm (using Stochastic Simulation) User

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

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) Lag: 1 MaxLag X [Lag - MaxLag/10] [Lag + MaxLag/10] (x,y,lag)

Generating Synthetic Data t-3 t-2 t-1 t t-3 t-2 t-1 t t+1 (1) (2)

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)

Parameters % 10% Population Size Generations OpRate (KGM/Swap) Slide Mutation Rate EP - DBN StructureSynthetic % 10% Oil Data 5 30 Number of Var MaxLag DataSynthetic Oil Data 1% Mutation Rate Limit (% of all links) ListGenerations EP - DL LinksSynthetic 1% 5 50 Oil Data

Results 1 - Synthetic Data

Results 2 - Oil Refinery Data

Results 3

Explanations - using stochastic simulation

Explanations Input: t - 0: Tail Gas Flow in_state 0 Reboiler Temperature in_state 3 Output: t - 7: Top Temperature in_state 0 t - 54: Feed Rate in_state 1 t - 75: Reactor Inlet Temperature in_state 0

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