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Building Trees for Probabilistic Prediction via Scoring Rules (2402.11052v1)

Published 16 Feb 2024 in stat.ME and stat.ML

Abstract: Decision trees built with data remain in widespread use for nonparametric prediction. Predicting probability distributions is preferred over point predictions when uncertainty plays a prominent role in analysis and decision-making. We study modifying a tree to produce nonparametric predictive distributions. We find the standard method for building trees may not result in good predictive distributions and propose changing the splitting criteria for trees to one based on proper scoring rules. Analysis of both simulated data and several real datasets demonstrates that using these new splitting criteria results in trees with improved predictive properties considering the entire predictive distribution.

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References (35)
  1. Recursive partitioning for heterogeneous causal effects. Proceedings of the National Academy of Sciences, 113(27):7353–7360, 2016.
  2. Generalized random forests. The Annals of Statistics, 47(2):1148–1178, 2019.
  3. Bayesian theory. John Wiley & Sons Canada, 2006.
  4. Optimal prescriptive trees. INFORMS Journal on Optimization, 1(2):164–183, 2019.
  5. Towards scalable quantile regression trees. In 2015 IEEE International Conference on Big Data (Big Data), pages 53–60. IEEE, 2015.
  6. Leo Breiman. Some properties of splitting criteria. Machine Learning, 24(1):41–47, 1996.
  7. Classification and regression trees. Chapman and Hall/CRC, 1984.
  8. Arthur Carvalho. An overview of applications of proper scoring rules. Decision Analysis, 13(4):223–242, 2016.
  9. Peter F Christoffersen. Evaluating interval forecasts. International economic review, pages 841–862, 1998.
  10. A Philip Dawid. The geometry of proper scoring rules. Annals of the Institute of Statistical Mathematics, 59(1):77–93, 2007.
  11. Coherent dispersion criteria for optimal experimental design. Annals of Statistics, pages 65–81, 1999.
  12. Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. The Annals of Mathematical Statistics, pages 642–669, 1956.
  13. Statistical methods for eliciting probability distributions. Journal of the American Statistical Association, 100(470):680–701, 2005.
  14. Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association, 102(477):359–378, 2007.
  15. Probabilistic forecasts, calibration and sharpness. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 69(2):243–268, 2007.
  16. Consistent nonparametric regression from recursive partitioning schemes. Journal of Multivariate Analysis, 10(4):611–627, 1980.
  17. Game theory, maximum entropy, minimum discrepancy and robust bayesian decision theory. the Annals of Statistics, 32(4):1367–1433, 2004.
  18. Missing value imputation affects the performance of machine learning: A review and analysis of the literature (2010–2021). Informatics in Medicine Unlocked, 27:100799, 2021.
  19. The elements of statistical learning: data mining, inference, and prediction. New York, NY: Springer, 2009.
  20. Proper scoring rules for evaluating density forecasts with asymmetric loss functions. Journal of Business & Economic Statistics, pages 1–15, 2022.
  21. An introduction to statistical learning, volume 112. Springer, 2013.
  22. Jason Klusowski. Sparse learning with cart. Advances in Neural Information Processing Systems, 33:11612–11622, 2020.
  23. Survival trees by goodness of split. Journal of the American Statistical Association, 88(422):457–467, 1993.
  24. Personalized predictions for unplanned urinary tract infection hospitalizations with hierarchical clustering. In AI and Analytics for Public Health: Proceedings of the 2020 INFORMS International Conference on Service Science, pages 453–465. Springer, 2022.
  25. Pascal Massart. The tight constant in the dvoretzky-kiefer-wolfowitz inequality. The annals of Probability, pages 1269–1283, 1990.
  26. Nicolai Meinshausen. Quantile regression forests. Journal of Machine Learning Research, 7(Jun):983–999, 2006.
  27. Consistency of random forests. The Annals of Statistics, 43(4):1716–1741, 2015.
  28. Maximum likelihood regression trees. Journal of Computational and Graphical Statistics, 13(3):586–598, 2004.
  29. Subgroup analysis via recursive partitioning. Journal of Machine Learning Research, 10(Feb):141–158, 2009.
  30. Calibrated ensemble forecasts using quantile regression forests and ensemble model output statistics. Monthly Weather Review, 144(6):2375–2393, 2016.
  31. Block diagrams and splitting criteria for classification trees. Statistics and Computing, 3(4):147–161, 1993.
  32. Building consistent regression trees from complex sample data. Journal of the American Statistical Association, 106(496):1626–1636, 2011.
  33. Skill of global raw and postprocessed ensemble predictions of rainfall over northern tropical africa. Weather and Forecasting, 33(2):369–388, 2018.
  34. Estimation of the continuous ranked probability score with limited information and applications to ensemble weather forecasts. Mathematical Geosciences, 50(2):209–234, 2018.
  35. Model-based recursive partitioning. Journal of Computational and Graphical Statistics, 17(2):492–514, 2008.

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