Real-world problems often call for efficient methods to discovery actionable knowledge on which business can directly act [3]. Some works for discovering actionable knowledge [3,5] view actions as behaviors which render a state of an instance into a preferred state, where a state is represented by feature values of the instance and whether a state is preferred is determined by a classifier. Actions usually have many-to-many relations with features of an instance. That is, an action may affect multiple features of an instance, and vise versa, a feature may be influenced by multiple actions. This type of many-to-many relationships between actions and features is prevalent in real-world applications. However, most existing works [3,5] only deal with one-to-one relationship and ignore manyto- many relationship between actions and features. In these works, an action is treated as a behavior with a fixed execution cost. Restricting to a one-to-one relationship between actions and features may not yield an action set (i.e. a set of actions) with the minimal total execution cost. Moreover, one-to-one relationship is simply a special case of many-to-many relationship, and hence the latter will be applicable to more real-world problems. Therefore we aim to extract action sets from a classifier for which the total execution cost is minimal based on many-to-many relationship between actions and features.
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