Combining Divide-And-Conquer And Separate-And-Conquer For Efficient And Effective Rule Induction

Divide-and-Conquer (DAC) and Separate-and-Conquer (SAC) are two strategies for rule induction that have been used extensively. When searching for rules DAC is maximally conservative w.r.t. decisions made during search for previous rules. This results in a very efficient strategy, which however suffers from difficulties in effectively inducing disjunctive concepts due to the replication problem. SAC on the other hand is maximally liberal in the same respect. This allows for a larger hypothesis space to be searched, which in many cases avoids the replication problem but at the cost of lower efficiency. We present a by brid strategy called Reconsider-and-Conquer (RAC), which handles the replication problem more effectively than DAC by reconsidering some of the earlier decisions and allows for more efficient induction than SAC by holding on to some of the decisions. We present experimental results from propositional, numerical and relational domains demonstrating that RAC significantly reduces the replication problem from which DAC suffers and is several times (up to an order of magnitude) faster than SAC.