The below mentioned article provides a note on decision-theoretic expert systems.
The field of decision analysis, which got evolved in the 1950s and 1980s studies the application of decision theory of actual decision problems. It is used to help make rational decisions in important domains where the stakes are high, such as business, government law, military strategy, medical diagnosis and public health, engineering design and resource management.
The process involves a careful study of the possible actions and outcomes, as well as the preferences placed on each outcome. It is traditional in decision analysis to talk about two roles: decision maker and decision analyst the decision maker states preferences between outcomes, and the decision analyst enumerates the possible action and outcomes and elicits preferences from the decision maker to determine the best course of action.
Until 1980s, the main purpose of decision analysis was to help humans make decisions which actually reflect their own preferences. These days more and more decision processes are automated and decision analysis is used to ensure that the automated processes are behaving as desired.
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Early expert system research concentrated on answering questions rather than on making decisions. Those systems which did recommend actions rather than providing opinions on matters of fact, generally did so using antecedent-action rules, rather than with explicit relationships of outcomes and preferences.
The emergence of Bayesian networks in the late 1980s made it possible to build large scale systems which generated sound probabilistic inferences from evidence. The addition of decision networks means that expert systems can be developed which recommended optimal decisions reflecting the preferences of the user as well as the available evidence.
Systems which incorporate utilities can avoid one of the most common pit falls associated with the consultation process: confusing likelihood and importance. A common strategy in early medical expert systems, for example, was to rank possible diagnosis in order of likelihood and report the most likely outcome.
Unfortunately this can be disastrous! For majority of patients in general practice, the two most likely diagnoses are usually, “There is nothing wrong with you” and “you have a bad cold”, but if the third most-likely diagnosis for a given patient is lung cancer, that is a serious matter. Obviously, a testing or treatment plan should depend both on probabilities and utilities. Probability theory describes what an agent should believe on the basis of evidence, utility theory describes what an agent wants.
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The utility theory combined with probability theory yields a decision-theoretic agent-an agent which can make rational decisions based on what it believes and what it wants. Such an agent can make decisions in domains or situations where uncertainty and conflicting goal reign supreme and the logical process is left with no way to decide. In effect, a goal based agent has a binary distinction between good (goal) and bad (non-goal) states, while a decision-theoretic agent has a continuous measures of state quality. The basic principle of decision theory is the maximisation of expected utility.
The choice between the good and bad states in problem solving depends upon utility function, which is a single index of expressing the desirability of a state. The utilities are combined with outcome probabilities of actions to give an expected utility for each action. The expected utility of a non-deterministic action A, given the evidence, E(U) (A | E), is given by
where, P(Result (A) | D0 (A), E is the probability assigned to each outcome.
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U (S) is the utility of the state S
E is the available evidence about the world of consideration.
D0 (A) is the proposition that action A is executed in the current state. Index i ranges over the different outcomes.
The principle of Maximum Expected Utility (MEU) states that a rational agent should choose an action which maximises the agent’s expected utility. Although the MEU defines the right action to be taken in a decision problem the computation involved can be prohibitive and it is sometime difficult even to formulate the problem completely. Knowing the initial state of the paradigm requires perception, learning, knowledge representation and inference.
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Computing [P (Resulti (A) | D0 (A), (E)] requires complete causal model of the world and inference in Bayesian network. Computing the utility of each state U[Resulti (A)] often requires search or planning because an agent does not know how good a state is until it knows where it can get to from that state.
So decision theory alone is not a panacea which can, solve the AI problems. However, it does provide a frame work into which we can fit in the components of the an expert system as a component of the decision. System, giving rise to what is called a Decision Theoretic Expert System. So it is worth considering the design of a decision, theoretic expert system.
For example, we shall consider the problem of selecting a medical treatment for a kind of congenital heart disease in children.
About 1% children in the world are born with a heart anomaly the most common being aortic coarctation (a constriction of the aorta). It can be treated with surgery, angioplasty or medication. The problem is to decide what treatment to use and when to do it: the younger the child the greater the risks of certain treatments but for infinitely long time cannot be waited. A decision theoretic expert system for this problem can be created by a team consisting of one domain expert (a pediatric cardiologist) and one knowledge engineer.
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The process can be broken down into the following steps:
1. Create a Causal Model:
Determine what are the possible symptoms, disorders, treatments and outcomes. Then draw arcs between them indicating what disorders. Some of these will be well known to the domain expert, and some will come from literature. Often the model will match well with the informal descriptions given in the medical literature.
2. Simplification of the Decision Model:
Since we are using the model of making treatment decisions and not for other purposes (such as determining the joint probability of certain symptom/disorder combinations), we can often simplify by removing variables which are not involved in treatment decisions. Sometimes variables will have to be split or joined to match the expert’s intuitions.
3. Assignment of Probabilities:
Probabilities can come from patient’s data bases, literature studies or expert’s subjective assessments. In cases where the wrong kinds of probabilities are given in the literature techniques such as Bayes’ rules and marginalization can be used to compute the desired probabilities. It has been found that experts are best able to assess the probability of an effect given a cause.
4. Assignment of Utilities:
When there are small number of possible outcomes, they can be enumerated and evaluated individually. For more outcomes, as in the case of medical expert system are would create a scale from best to worst outcome and give each a numeric value, say-1000 for death and 0 for complete recovery. Other outcomes on this scale, can be placed which can of course, be done by the expert. But it is better if the patient’s parents (if he is infant) or the patient himself can be involved, because different people have different preferences.
If there are exponentially many outcomes there is a need to combine them using multi-attribute utility functions.
5. Verification and Refinement of the Model:
To evaluate the system we need a set of correct (input, output) pairs-called gold standard, to compare against. For medical expert systems this usually means assembling the best available doctors, presenting them with a few cases and asking for their diagnosis and the treatment plan. It is seen how fairly the expert system compares with their recommendations. If it does poorly, the parts which are going wrong are fixed. It can be useful to run the system “backwards”. In that case the system is presented with the diagnosis (instead of asking for diagnosis after giving the symptoms).
6. Sensitivity Analysis Performance:
This step checks whether the best decision is sensitive to small changes in the assigned probabilities and utilities by systematically varying those parameters and running the evaluation again. If small changes lead to significantly different decisions then data is collected again.
Sensitivity analysis is particularly important because one of the criticisms of probabilistic approaches to expert systems is that it is too difficult to assess the numerical probabilities required. Sensitivity analysis often reveals that many of the numbers need be specified only very approximately.
Thus, Decision-theoretic expert systems offer a mathematically sound collection of formalisms for building knowledge-based (expert) systems for domains in which uncertainty is of central concern. The main applications of such formalisms are in classification (for example diagnosis) and in decision making under uncertainty (for example optimal treatment management of a patient).
For example, we might be uncertain about the prior probability, and we try many different values for this probability and in each case the recommended action of influence diagram more commonly called decision networks. They combine Bayesian networks with nodes for actions and utilities is the same then we can be less concerned about our ignorance. Sensitivity analysis in such a case provides a better understanding of the model and the problem it purports to analyze or solve.
It may increase the confidence of the users in the model, especially when the model is not so sensitive to changes. A sensitive model means that small changes in conditions dictate a different solution. In a non-sensitive model, changes in conditions do not significantly change the recommended solution which means that the chances for a solution to succeed are very high.