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Decision Trees are accessible, interpretable, and well-performingclassification models. A plethora of variants with increasing expressivenesshas been proposed in the last forty years. We contrast the two families ofunivariate DTs, whose split functions partition data through axis-parallelhyperplanes, and multivariate DTs, whose splits instead partition data throughoblique hyperplanes. The latter include the former, hence multivariate DTs arein principle more powerful. Surprisingly enough, however, univariate DTsconsistently show comparable performances in the literature. We analyze thereasons behind this, both with synthetic and real-world benchmark datasets. Ourresearch questions test whether the pre-processing phase of removingcorrelation among features in datasets has an impact on the relativeperformances of univariate vs multivariate DTs. We find that existing benchmarkdatasets are likely biased towards favoring univariate DTs.

Correlation and Unintended Biases on Univariate and Multivariate Decision Trees