Specification of models in large expert systems based on causal probabilistic networks Kistian G. Olesen Steen Andreassen

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Specification of models in large expert systems
based on causal probabilistic networksKistian
G. OlesenSteen Andreassen

• Presented By
• Neeraj Agrawal
• Sujan Pakala

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Introduction

• During the last two decades there has been lot of
  model based expert systems. Causal Probabilistic
  networks (CPN) are one such models for such
  systems.
• For modeling the expert systems using CPN
  probability tables for all nodes have to be
  provided. These conditional probability tables
  can often be described by models that specify the
  nature of interaction between nodes.

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Contd..

• There are two advantages of using these models
  for specifying conditional probabilities,
• The number of parameters in the model is
  proportional to the number of states in the
  parents and the child, while the size of the
  conditional probability grows exponentially with
  the number of states. This provides economy in
  the model-based specification.
• Model based approach allows us to derive
  conditional probabilities for rare conditions by
  extrapolation from more frequently occurring
  conditions

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• Examples of model based expert system.
• MUNIN
• Is the system for diagnosis of
  neuromuscular diseases.
• SWAN
• Is the system for adjustment of insulin
  therapy for diabetes patients.

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Models for causal Interaction

• The construction of CPN model includes
  specificaion of CPT for all nodes in the network.
  This may be a quite formidable task since the
  size of the table is the product of the number of
  states in the node and the number of states in
  each of the parents. In order to reduce the
  amount of numbers that has to be provided, it is
  often possible to specify a model that describes
  the interaction between nodes.

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• Noisy OR gates
• Extended linear models
• Addition models
• Tabulated normal models
• Polynomial models

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Noisy OR Gates
FLU
THROAT INFECTION
FEVER
Soar Throat
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• Given that
• P(Fever Flu,Throat Infection, Other Causes)
  0.9
• P(Fever Flu,Throat Infection, Other Causes)
  0.9
• P(Fever Flu,Throat Infection, Other Causes)
  0.01
• Noisy Or model provides
• P(Fever Flu, Throat Infection, Other Causes)
• 1-(1-0.9)(1-0.9)(1-0.01).9901
• P(Fever Flu, Throat Infection, Other Causes)
• 1-(1-0.9)(1-0.01).90
• P(Fever Flu, Throat Infection, Other Causes)
• 1-(1-0.9)(1-0.01).90
• P(Fever Flu, Throat Infection, Other Causes)
• 1-(1-0.01).01

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Advantages of Noisy Or Model

• The model can be easily expanded for more
  parents. Each new parent node only requires the
  specification of one conditional probability to
  generate an exponentially growing table of
  conditional probabilities for child nodes.
• It provides us the conditional probabilities for
  parents configuration which is normally very
  difficult to find.

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Extended linear models

• These models are related to nodes that are
  continuous by nature.
• Mean(Fever) 37 TF TTi
• TF rise in body temperature because of Flu
• TTi rise in body temperature because of Throat
  Infection
• Variance(Fever) SD2 SDF2 SD2Ti

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• - CPNs have number of process contributing to
  some status variable
• Status at a given time found by adding
  individual contributions
• QUARK example- computing the table
• - constant value contribution from each
  parent r
• - r is then matched with the states of the
  child node.
• If result lies between two states, the
  probability is distributed on the states relative
  to the distance.
• Constraint state values associated with states
  in the child are ordered monotonically.

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Tabulated normal models

• Formulate extended linear models where mean and
  variance of normal distribution for child node
  combine linearly.
• Sometimes necessary to specify normal
  distribution for each parent configuration.
• Computation of tables similar to normal models
  but, mean and standard deviation contributions
  for normal distribution of child are read
  directly.
• These models are not as economic as normal
  models.

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Polynomial models

• Deals with discrete children of continuous
  parents.
• Example involving binomial distribution
• - sequence of independent flips of a coin
• - p probability of getting a head
• - probability of i heads in n trials
• n!
• f(i, n) ---------------- pi (1-p)n-i
• (n-i)! i!
• - Resulting table computed by summation of f(i,
  n) for values specified in child node.

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Handling repeated structures

• CPNs have multiple copies of identical elements.
• Headers provided for ease of specification and
  modification.
• Header specifies elements by a type, identifier
  and actual element.
• Four types of header elements
• - States, tables, models, utilities
• Header element can be simply referenced by its
  name in a model specification.
• The preprocessor expands it to the defined
  structure and checks for structural consistency.
• Fig. 10.

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Conclusion

• Authors present a preprocessor that extends
  HUGINs Net language.
• Increased readability due to extended basic
  syntax.
• Conceptually possible to describe the nature of
  causal interaction between nodes.
• Practically amount of numbers that has to be
  provided is now considerably reduced.
• Future work.