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Decision tree learning is a widely used approach in machine learning,favoured in applications that require concise and interpretable models.Heuristic methods are traditionally used to quickly produce models withreasonably high accuracy. A commonly criticised point, however, is that theresulting trees may not necessarily be the best representation of the data interms of accuracy and size. In recent years, this motivated the development ofoptimal classification tree algorithms that globally optimise the decision treein contrast to heuristic methods that perform a sequence of locally optimaldecisions. We follow this line of work and provide a novel algorithm forlearning optimal classification trees based on dynamic programming and search.Our algorithm supports constraints on the depth of the tree and number ofnodes. The success of our approach is attributed to a series of specialisedtechniques that exploit properties unique to classification trees. Whereasalgorithms for optimal classification trees have traditionally been plagued byhigh runtimes and limited scalability, we show in a detailed experimental studythat our approach uses only a fraction of the time required by thestate-of-the-art and can handle datasets with tens of thousands of instances,providing several orders of magnitude improvements and notably contributingtowards the practical realisation of optimal decision trees.

MurTree: Optimal Classification Trees via Dynamic Programming and Search