AI: Belief Networks

Belief Networks

Acting
Its a process in which planning systems must face up to the awful prospect of actually having to take their own advice.

Conditional planning
Also known as contingency planning.
Conditional planning deals with incomplete information by constructing a conditional plan that accounts for each possible situation or contingency that could arise.
The agent finds out which part of the plan to execute by including sensing actions in the plan to test for the appropriate conditions.

A method for constructing belief networks
Choose the set of relevant variables X, that describe the domain.
Choose an ordering for the variables.
While there are variables left:(a) Pick a variable X,- and add a node to the network for it.(b) Set Parents(Xi) to some minimal set of nodes already in the net such that the conditionalindependence property is satisfied.(c) Define the conditional probability table for Xi

Types of Distribution
Canonical distributions distributions fit some standard pattern. In such cases, the complete table can be specified by naming the pattern and perhaps supplying a few parameters.
A deterministic node has its value specified exactly by the values of its parents, with no uncertainty.

Inference in multi connected belief network
A multi connected graph is one in which two nodes are connected by more than one path. There exists three basic classes of algorithms for evaluating multi connected networks
Clustering methods
Conditioning methods
Stochastic simulation methods

Approach to knowledge engineering for probabilistic reasoning systems
Decide what to talk about.
Decide on a vocabulary of random variables
Encode general knowledge about the dependence between variables
Encode a description of the specific problem instance.
Pose queries to the inference procedure and get answers

Other approaches to uncertainty reasoning
Default reasoning
Rule-based methods for uncertain reasoning
Representing ignorance: Dempster-Shafer theory
Representing vagueness: Fuzzy sets and fuzzy logic

The axioms of utility theory
Ordcrability
Transitivity
Continuity
Substitutability
Monotonicity
Decomposability
Utility principle
Maximum Expected Utility principle

What is Utility Function?Utility is a function that maps from states to real numbers.
What is Multi attribute utility functions?
Decision making in the field of public policy involves both millions of dollars and life and death.
What is Dominance?
Suppose that airport site S1 costs less, generates less noise pollution, and is safer than site S2. One would not hesitate to reject S2. We say that there is strict dominance of S1 over S2

How to Evaluating decision networks
Set the evidence variables for the current state.
For each possible value of the decision node:(a) Set the decision node to that value.(b) Calculate the posterior probabilities for the parent nodes of the utility node, using astandard probabilistic inference algorithm.(c) Calculate the resulting utility for the action.
Return the action with the highest utility.

How to build Decision Theoretic Expert Systems?
Determine the scope of the problem
Lay out the topology.
Assign probabilities.
Assign utilities.
Enter available evidence.
Evaluate the diagram.
Obtain new evidence.
Perform sensitivity analysis.

What is Dynamic belief network?
The environment is modeled by the conditional probability distribution P(X,Y,A), which describes how the state depends on the previous state and the action of the agent. As with the sensor model, we make a stationary assumption: the conditional probabilities are the same for all time.

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AI: Belief Networks

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