This paper analyzes the statistical properties of random forests, a machine learning algorithm introduced by Leo Breiman. The authors show that the random forest model is consistent and adapts to sparsity, meaning its convergence rate depends only on the number of strong features, not on the number of noise variables. The paper provides a detailed analysis of the algorithm, showing that it achieves good performance in high-dimensional settings by effectively handling a large number of input variables without overfitting. The study also discusses the theoretical properties of random forests, including their variance and bias, and demonstrates that the algorithm's performance is influenced by the number of strong features rather than the ambient dimension. The results show that random forests can achieve faster convergence rates in sparse settings, making them a powerful tool for high-dimensional regression problems. The paper also highlights the importance of proper randomization in the algorithm and discusses the implications of using a second sample to induce probability sequences for feature selection. Overall, the analysis confirms that random forests are a robust and effective method for regression tasks, particularly in high-dimensional settings where traditional methods may struggle.This paper analyzes the statistical properties of random forests, a machine learning algorithm introduced by Leo Breiman. The authors show that the random forest model is consistent and adapts to sparsity, meaning its convergence rate depends only on the number of strong features, not on the number of noise variables. The paper provides a detailed analysis of the algorithm, showing that it achieves good performance in high-dimensional settings by effectively handling a large number of input variables without overfitting. The study also discusses the theoretical properties of random forests, including their variance and bias, and demonstrates that the algorithm's performance is influenced by the number of strong features rather than the ambient dimension. The results show that random forests can achieve faster convergence rates in sparse settings, making them a powerful tool for high-dimensional regression problems. The paper also highlights the importance of proper randomization in the algorithm and discusses the implications of using a second sample to induce probability sequences for feature selection. Overall, the analysis confirms that random forests are a robust and effective method for regression tasks, particularly in high-dimensional settings where traditional methods may struggle.