  Random forests remain among the most popular off-the-shelf supervised machine
learning tools with a well-established track record of predictive accuracy in
both regression and classification settings. Despite their empirical success as
well as a bevy of recent work investigating their statistical properties, a
full and satisfying explanation for their success has yet to be put forth. Here
we aim to take a step forward in this direction by demonstrating that the
additional randomness injected into individual trees serves as a form of
implicit regularization, making random forests an ideal model in low
signal-to-noise ratio (SNR) settings. Specifically, from a model-complexity
perspective, we show that the mtry parameter in random forests serves much the
same purpose as the shrinkage penalty in explicitly regularized regression
procedures like lasso and ridge regression. To highlight this point, we design
a randomized linear-model-based forward selection procedure intended as an
analogue to tree-based random forests and demonstrate its surprisingly strong
empirical performance. Numerous demonstrations on both real and synthetic data
are provided.
