Bootstrap Sampling Rate Greater than 1.0 May Improve Random Forest Performance

Random forests (RFs) utilize bootstrap sampling to generate individual training sets for each component tree by sampling with replacement, with the sample size typically equal to that of the original training set ($N$). Previous research indicates that drawing fewer than $N$ observations can also yield satisfactory results. The ratio of the number of observations in each bootstrap sample to the total number of training instances is referred to as the bootstrap rate (BR). Sampling more than $N$ observations (BR $>$ 1.0) has been explored only to a limited extent and has generally been considered ineffective. In this paper, we revisit this setup using 36 diverse datasets, evaluating BR values ranging from 1.2 to 5.0. Contrary to previous findings, we show that higher BR values can lead to statistically significant improvements in classification accuracy compared to standard settings (BR $\leq$ 1.0). Furthermore, we analyze how BR affects the leaf structure of decision trees within the RF and investigate factors influencing the optimal BR. Our results indicate that the optimal BR is primarily determined by the characteristics of the data set rather than the RF hyperparameters.