# Comments on Leo Breiman's paper 'Statistical Modeling: The Two Cultures' (Statistical Science, 2001, 16(3), 199-231)

arXiv: https://arxiv.org/abs/2103.11327 · HTML: https://mlsanity.com/paper/2103.11327/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 54 references that are in the map.
- First posted on arXiv 21 Mar 2021.

## Builds on (most cited first, 24 of 24)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Two models of double descent for weak features](https://mlsanity.com/paper/1903.07571/) (2019)
- [To understand deep learning we need to understand kernel learning](https://mlsanity.com/paper/1802.01396/) (2018)
- [The Power of Interpolation: Understanding the Effectiveness of SGD in Modern Over-parametrized Learning](https://mlsanity.com/paper/1712.06559/) (2017)
- [Stability](https://mlsanity.com/paper/1310.0150/) (2013)
- [Implicit Regularization in Deep Learning May Not Be Explainable by Norms](https://mlsanity.com/paper/2005.06398/) (2020)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [Harnessing the Power of Infinitely Wide Deep Nets on Small-data Tasks](https://mlsanity.com/paper/1910.01663/) (2019)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Veridical Data Science](https://mlsanity.com/paper/1901.08152/) (2019)
- [Universal Inference](https://mlsanity.com/paper/1912.11436/) (2019)
- [Geometry of Optimization and Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1705.03071/) (2017)
- [Semi-supervised Inference: General Theory and Estimation of Means](https://mlsanity.com/paper/1606.07268/) (2016)
- [On the infinite width limit of neural networks with a standard parameterization](https://mlsanity.com/paper/2001.07301/) (2020)
- [Local nearest neighbour classification with applications to semi-supervised learning](https://mlsanity.com/paper/1704.00642/) (2017)
- [Sparsity Double Robust Inference of Average Treatment Effects](https://mlsanity.com/paper/1905.00744/) (2019)
- [Minimax Semiparametric Learning With Approximate Sparsity](https://mlsanity.com/paper/1912.12213/) (2019)
- [Testability of high-dimensional linear models with non-sparse structures](https://mlsanity.com/paper/1802.09117/) (2018)
- [Significance testing in non-sparse high-dimensional linear models](https://mlsanity.com/paper/1610.02122/) (2016)

## Abstract (arXiv)

Breiman challenged statisticians to think more broadly, to step into the unknown, model-free learning world, with him paving the way forward. Statistics community responded with slight optimism, some skepticism, and plenty of disbelief. Today, we are at the same crossroad anew. Faced with the enormous practical success of model-free, deep, and machine learning, we are naturally inclined to think that everything is resolved. A new frontier has emerged; the one where the role, impact, or stability of the it learning algorithms is no longer measured by prediction quality, but an inferential one -- asking the questions of it why and it if can no longer be safely ignored.