Machine Learning

, Volume 108, Issue 8–9, pp 1613–1634 | Cite as

CaDET: interpretable parametric conditional density estimation with decision trees and forests

  • Cyrus Cousins
  • Matteo RiondatoEmail author
Part of the following topical collections:
  1. Special Issue of the ECML PKDD 2019 Journal Track


We introduce CaDET, an algorithm for parametric Conditional Density Estimation (CDE) based on decision trees and random forests. CaDET uses the empirical cross entropy impurity criterion for tree growth, which incentivizes splits that improve predictive accuracy more than the regression criteria or estimated mean-integrated-square-error used in previous works. CaDET also admits more efficient training and query procedures than existing tree-based CDE approaches, and stores only a bounded amount of information at each tree leaf, by using sufficient statistics for all computations. Previous tree-based CDE techniques produce complicated uninterpretable distribution objects, whereas CaDET may be instantiated with easily interpretable distribution families, making every part of the model easy to understand. Our experimental evaluation on real datasets shows that CaDET usually learns more accurate, smaller, and more interpretable models, and is less prone to overfitting than existing tree-based CDE approaches.


Parametric models Random forests Sufficient statistics 


Supplementary material

10994_2019_5820_MOESM1_ESM.pdf (146 kb)
Supplementary material 1 (pdf 145 KB)


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Copyright information

© The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceBrown UniversityProvidenceUSA
  2. 2.Department of Computer ScienceAmherst CollegeAmherstUSA

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