MurTree: Optimal Decision Trees via Dynamic Programming and Search

By Emir Demirovi'c, Anna Lukina, Emmanuel Hebrard, Jeffrey Chan, James Bailey, C. Leckie, Kotagiri Ramamohanarao, Peter James Stuckey. 2020

89 citations recorded by the source corpus.

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 with reasonably high accuracy. A commonly criticised point, however, is that the resulting trees may not necessarily be the best representation of the data in terms of accuracy and size. In recent years, this motivated the development of optimal classification tree algorithms that globally optimise the decision tree in contrast to heuristic methods that perform a sequence of locally optimal decisions. We follow this line of work and provide a novel algorithm for learning optimal classification trees based on dynamic programming and search. Our algorithm supports constraints on the depth of the tree and number of nodes. The success of our approach is attributed to a series of specialised techniques that exploit properties unique to classification trees. Whereas algorithms for optimal classification trees have traditionally been plagued by high runtimes and limited scalability, we show in a detailed experimental study that our approach uses only a fraction of the time required by the state-of-the-art and can handle datasets with tens of thousands of instances, providing several orders of magnitude improvements and notably contributing towards the practical realisation of optimal decision trees.

Subfields: Artificial Intelligence, Optimization & Training, Algorithms & Complexity

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Citations in the corpus

Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges (2021, methodology): “, 321, 114, 228], and (3) customized dynamic programming algorithms that incorporate branchand-bound techniques for reducing the size of the search space [131, 185, 222, 78].”
Optimal Decision Trees for Nonlinear Metrics (2020, methodology): “See (Demirović et al. 2020) for a formulation that additionally allows constraining the number of nodes, however such a formulation is not necessary for understanding our main contributions.”