Specification of models in large expert systems based on causal probabilistic

networks

Kistian G. OlesenSteen Andreassen

Presented By:

Neeraj Agrawal

Sujan Pakala

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.

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

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.

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.

• Noisy OR gates

• Extended linear models

• Addition models

• Tabulated normal models

• Polynomial models

Noisy OR Gates

FEVER

FLU THROAT INFECTION

Soar Throat

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

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.

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 + SD2

Ti

• - 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.

- 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.

Tabulated normal models

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) = ---------------- p^i (1-p)^n-i

(n-i)! i!

- Resulting table computed by summation of f(i, n) for values specified in child node.

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.

Conclusion

- Authors present a preprocessor that extends HUGIN’s

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.