The confidence of an association rule A => B is defined as?

The confidence of an association rule A => B is defined as the probability of event B occurring given that event A has occurred. This concept is fundamental in association rule learning, which seeks to identify relationships between variables in large datasets.

When evaluating the confidence of the rule, it measures how often items in B appear in transactions that contain A. Mathematically, confidence can be expressed as P(B|A), which quantifies the likelihood of occurrence of B in transactions that are known to include A.

This definition is critical for making actionable insights in data mining contexts, such as market basket analysis, where businesses might want to understand how purchasing one product (A) could influence the sale of another product (B). High confidence implies that the presence of A strongly suggests the presence of B, thus providing valuable information for decision-making.

In contrast, other options reflect different concepts that do not specifically address the relationship defined by confidence. For instance, the probability of A occurring pertains solely to the occurrence of A without considering B, and the probability of A and B occurring together does not measure the conditional likelihood of B given A. Lastly, the ratio of successful predictions does not relate to the direct association expressed in the confidence metric. Hence, the probability of B