# Understanding overfitting in random forest for probability estimation: a visualization and simulation study

arXiv: https://arxiv.org/abs/2402.18612 · HTML: https://mlsanity.com/paper/2402.18612/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 28 Feb 2024.

## Builds on (most cited first, 10 of 10)

- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [A Random Forest Guided Tour](https://mlsanity.com/paper/1511.05741/) (2015)
- [Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation](https://mlsanity.com/paper/2105.14368/) (2021)
- [Hyperparameters and Tuning Strategies for Random Forest](https://mlsanity.com/paper/1804.03515/) (2018)
- [Using simulation studies to evaluate statistical methods](https://mlsanity.com/paper/1712.03198/) (2017)
- [Explaining the Success of AdaBoost and Random Forests as Interpolating Classifiers](https://mlsanity.com/paper/1504.07676/) (2015)
- [To tune or not to tune the number of trees in random forest?](https://mlsanity.com/paper/1705.05654/) (2017)
- [Randomization as Regularization: A Degrees of Freedom Explanation for Random Forest Success](https://mlsanity.com/paper/1911.00190/) (2019)
- [Stability of clinical prediction models developed using statistical or machine learning methods](https://mlsanity.com/paper/2211.01061/) (2022)
- [There is no Double-Descent in Random Forests](https://mlsanity.com/paper/2111.04409/) (2021)

## Built on by (most cited first, 1 of 1)

- [Uncertainty-Driven Modeling of Microporosity and Permeability in Clastic Reservoirs Using Random Forest](https://mlsanity.com/paper/2503.16957/) (2025)

## Abstract (arXiv)

Random forests have become popular for clinical risk prediction modelling. In a case study on predicting ovarian malignancy, we observed training c-statistics close to 1. Although this suggests overfitting, performance was competitive on test data. We aimed to understand the behaviour of random forests by (1) visualizing data space in three real world case studies and (2) a simulation study. For the case studies, risk estimates were visualised using heatmaps in a 2-dimensional subspace. The simulation study included 48 logistic data generating mechanisms (DGM), varying the predictor distribution, the number of predictors, the correlation between predictors, the true c-statistic and the strength of true predictors. For each DGM, 1000 training datasets of size 200 or 4000 were simulated and RF models trained with minimum node size 2 or 20 using ranger package, resulting in 192 scenarios in total. The visualizations suggested that the model learned spikes of probability around events in the training set. A cluster of events created a bigger peak, isolated events local peaks. In the simulation study, median training c-statistics were between 0.97 and 1 unless there were 4 or 16 binary predictors with minimum node size 20. Median test c-statistics were higher with higher events per variable, higher minimum node size, and binary predictors. Median training slopes were always above 1, and were not correlated with median test slopes across scenarios (correlation -0.11). Median test slopes were higher with higher true c-statistic, higher minimum node size, and higher sample size. Random forests learn local probability peaks that often yield near perfect training c-statistics without strongly affecting c-statistics on test data. When the aim is probability estimation, the simulation results go against the common recommendation to use fully grown trees in random forest models.