Bayesian networks and how they can

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Bayesian networks and how they can help us to
explore fish species interaction in the Northern
gulf of St Lawrence

• Dr Allan Tucker
• Centre for Intelligent Data Analysis
• Brunel University
• West London
• UK

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Talk Outline

• Introduce myself and research group
• Introduce Machine Learning
• Describe Bayesian network models
• Document some preliminary results on fish
  population data
• Conclusions

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Who Am I?

• Research Lecturer at Brunel University, West
  London
• Member of Centre for IDA (est 1994)

X
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What is the ?

• Over 25 members (academics, postdocs, and PhDs)
  with diverse backgrounds (e.g. maths, statistics,
  computing, biology, engineering)
• Over 140 journal publications a dozen research
  council grants since 2001
• Many collaborating partners in UK, Europe, China
  and USA
• Bi Annual Symposia in Europe

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Some Previous Work in

• Machine Learning and Temporal Analysis
• Oil Refinery Models
• Forecasting
• Explanation
• Medical Data Retinal (Visual Field)
• Screening
• Forecasting
• Bioinformatics
• Gene Clusters
• Gene Regulatory Networks

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Some Previous Work in
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Part 1
What is Machine Learning?
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What is Machine Learning?

• (and why not statistics?)
• Data oriented
• Extracting useful info from data
• As automated as possible
• Useful when lots of data and little theory
• Making predictions about the future

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What Can we do with ML?

• Classification and Clustering
• Feature Selection
• Prediction and Forecasting
• Identifying Structure in Data

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E.g. Classification

• Given some labelled data (supervised)
• Build a model to allow us to classify other
  unlabelled data
• e.g. A doctor diagnosing a patient based upon
  previous cases

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Classification e.g. medical

• Scatterplot of patients
• 2 variables
• Measurement of expression of 2 genes

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Classification

• How do we classify them?
• Nearest Neighbour / Linear / Complex Fn?

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Classification

• Trivial case with Cod and Shrimp Data

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The Data

• Northern Gulf (region a)
• Two ships (Needler and Hammond) combined by
  normalising according to overlap year
• Multivariate Spatial Time Series (short)
• Missing Data

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Background

• Northern Gulf considered to be one ecosystem /
  fish community
• Quite heavily fished until about 1990
• Most fish populations collapsed since
• Some say that moved to an alternative stable
  state and unlikely to come back to cod dominated
  community without some chance event beyond human
  control.
• Lots of speculation
• cold water
• large increases in population of predators.
• Examine nature and strength of interactions
  between species in the two periods.
• Ask what if ? questions
• For other parts of community to recover, we would
  need cod to have X strength of interaction with Y
  number of other species?

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ML for Northern Gulf Data

• Network building
• knowledge and data of interactions
• Feature Selection for Classification of relevant
  species to the cod collapse
• State Space / Dynamic models for predicting
  populations
• Hidden variable analysis

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Part 2
Bayesian Networks for Machine Learning
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Bayesian Networks

• Method to model a domain using probabilities
• Easily interpreted by non-statisticians
• Can be used to combine existing knowledge with
  data
• Essentially use independence assumptions to
  model the joint distribution of a domain

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Bayesian Networks

• Simple 2 variable Joint Distribution
• can use it to ask many useful questions
• but requires kN probabilities

P(Collapse1, Collapse2)
Species2 Species2
Species1 0.89 0.01
Species1 0.03 0.07
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Bayesian Network for Toy Domain
SpeciesA
SpeciesB
P(A)
P(B)
.001
.002
A B P(C)
T T .95
T F .94
SpeciesC
F T .29
F F .001
C P(E)
C P(D)
T .70
T .90
F .01
F .05
SpeciesD
SpeciesE
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Bayesian Networks

• Bayesian Network Demo
• Species_Net
• Use algorithms to learn structure and parameters
  from data
• Or build by hand (priors)
• Also continuous nodes (density functions)

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Informative Priors

• To build BNs we can also use prior structures
  and probabilities
• These are then updated with data
• Usually uniform (equal probability)
• Informative Priors used to incorporate existing
  knowledge into BNs

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Bayesian Networks for Classification Feature
Selection

• Node that represents the class label attached to
  the data

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Dynamic Bayesian Networks for Forecasting

• Nodes represent variables at distinct time
  slices
• Links between nodes over time
• Can be used to forecast into the future
• Species_Dynamic_Net

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Hidden Markov Models

• Like a DBN but with hidden nodes
• Often used to model sequences

HT-1
HT
OT-1
OT
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Typical Algorithms for HMMs

• Given an observed sequence and a model, how do
  we compute its probability given the model?
• Given the observed sequence and the model, how
  do we choose an optimal hidden state sequence?
• How do we adjust the model parameters to
  maximise the probability of the observed sequence
  given the model?

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Summary

• Different learning tasks can be used to solve
  real world problems
• Machine Learning techniques useful when lots of
  data and lots of gaps in knowledge
• Bayesian Networks probabilistic framework that
  can perform most key ML tasks
• Also transparent can incorporate expert
  knowledge

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Part 3
Some Preliminary Results on Northern Gulf Data
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Expert Knowledge

• Ask marine biologists to generate matrices of
  expected relationships
• Can be used to compare models learnt from data
• Also to be used as priors to improve model
  quality

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Results Expert networks
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Results Data networks (BN from correlation)

• 85 conf. imputed from 70 data
• Warning data quality, spurious relations

(Eel pout / Ocean Sun Fish)
Witch Flounder
(Lumpfish)
Cod
Haddock
Shrimp
(Silver Hake)
(Atlantic soft pout / Bristlemouths)
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Example DBN

• Lets look at an example DBN
• NGulfDynamic - range
• Structure Encoded by knowledge
• Updated by data
• Explore with queries
• Supported by previous knowledge
• In the Northern gulf of st. Lawrence, cod (code
  438) and redfish (792,793,794,795,796) collapsed
  to very low levels in the mid 1990s. Subsequently
  the shrimp (8111) increased greatly in biomass so
  one will see this signal in the data. It is
  hypothesised that these are exclusive community
  states where you never get high abundance of both
  at the same time owing to predatory interactions.

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Feature Selection

• Given that we know that from 1990 the cod
  population collapsed
• Can we apply Feature Selection to see what
  species characterise this collapse
• Learn BN and apply CV

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Results 7 Feature Selection with Bootstrap
Filter method using Log Likelihood
Wrapper method using BNs
Redfish
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Results Feature Selection

• Change in Correlation of interactions between
  cod and high ranking species before and after
  1990

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Dynamic Models

• Given that the data is a time-series
• Can we build dynamic models to forecast future
  states?
• Can we use HMM to classify the time-series?

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Multivariate Time Series

• N Gulf is process measured over time
• Autoregressive Correlation Function
• (here cod)
• Cross Correlation Function
• (here hake to cod)

ACF
CCF
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Results 3 Fitting Dynamic Models

• HMM Expert with CCF gt 0.3 (maxlag 5)

LSS 8.3237
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Results 3 Fitting Dynamic Models

• Learning DBN from CCF data

LSS 5.0106
Fluctuation Early Indicator of Collapse?
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Results 4 Examining DBN Net

• Data only Dynamic Links

Hakes
Redfish
Cod
Haddock
Witch Flounder
White Hake
Thorny Skate
Shrimp
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Results 5 Fitting Dynamic Models

• Learning DBN from Expert biased CCF data CCF gt
  0.5 (maxlag5)

LSS 6.1326
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Results 6 Examining DBN Net

• Data Biased Expert Dynamic Links

Cod
Herring
Witch Flounder
Mackerel / Capelin
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Results 7 Linear Dynamic System

• Instead of hidden state, continuous var
• Could be interpreted as measure of fishing?
  Predator population (e.g. seals)? Water
  temperature?

1987
1991
1997
1984
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Conclusions

• Hopefully conveyed the broad idea of machine
  learning
• Shown how it can be used to help analyse data
  like fish population data
• Potentially applicable to other data studied
  here at MLI

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Potential Projects

• Spatio-Temporal Analysis
• Use Spatio-Temporal BNs to model fish stock data.
  Nodes would represent species in specific
  regions
• Combining Expert Knowledge and Data for improved
  Prediction
• Looking for Un/Stable States and the factors that
  influence them
• Machine Learning Techniques for other Data
  generated here at MLI

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E.G. Spatial Analysis

• Spatial Bayesian Network Analysis
• NGulfCodSpatial

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AcknowledgementsDaniel Duplisea for inviting
me
Any Questions?