AI Decision Making under Uncertainty

Study Notes

Representing Uncertainty with Probability

Partial knowledge of the world leads to uncertainty, making it essential to make optimal decisions with limited information.
Probability uncertainty can be represented as a number of events and their likelihood.

Possible Worlds and Probability Notation

Every possible situation can be thought of as a world, represented by the lowercase Greek letter omega (ω).
The probability of a certain world is represented as P(ω).

Axioms in Probability

0 < P(ω) < 1: every value representing probability must range between 0 and 1.
Zero represents an impossible event, while one represents a certain event.
The higher the value, the more likely the event is to happen.
The probabilities of every possible event, when summed together, are equal to 1.

Summing Probabilities

The probability of rolling a number R with a standard die is P(R) = 1/6, due to six equally likely possible worlds.
When rolling two dice, there are 36 possible events, which are equally likely to happen.

Calculating Probability

To get the probability of an event, divide the number of worlds in which it occurs by the number of total possible worlds.
Example: P(12) = 1/36, the probability of rolling two dice and getting a sum of 12.
Example: P(7) = 6/36 = 1/6, the probability of rolling two dice and getting a sum of 7.

Unconditional and Conditional Probability

Unconditional probability is the degree of belief in a proposition in the absence of any other evidence.
Conditional probability is the degree of belief in a proposition given some evidence that has already been revealed.
Conditional probability is expressed as P(a | b), meaning "the probability of event a occurring given that we know event b to have occurred."

Conditional Probability Formula

P(a | b) = P(a, b) / P(b): the probability of a given b is equal to the probability of a and b being true, divided by the probability of b.

Description

Learn how AI systems make decisions with partial knowledge, managing uncertainty and making predictions in scenarios like weather forecasting. Explore the concepts and techniques used to make informed decisions in uncertain environments.