Finite-sample guarantees for classical random forests

Establish rigorous finite-sample performance guarantees for Breiman’s classical random forest algorithm under i.i.d. sampling, providing non-asymptotic results that quantify prediction error or risk behavior in finite samples.

Background

The paper notes that, even for i.i.d. data, the theory of classical random forests remains challenging, with important aspects not fully resolved. In particular, while asymptotic properties have been studied, non-asymptotic (finite-sample) guarantees are scarce, leaving a gap in understanding the behavior of random forests in realistic sample sizes.

This unresolved issue matters for both methodological development and practical deployment, as finite-sample guarantees underpin reliable inference, calibration, and robustness claims for widely used tree-ensemble methods.

References

Moreover, many questions remain open, for instance regarding finite-sample guarantees or extensions to dependent data.

— Distributional Random Forests for Complex Survey Designs on Reproducing Kernel Hilbert Spaces  (2512.08179 - Zou et al., 9 Dec 2025) in Section 1 (Introduction)

We conjecture, and the simulations of Section~\ref{sec:simulation} examine, that the leading order of eq:relative-cost is unchanged under minimum-node-size and bounded-depth conditions of the type used by \citet{mcconville2019}: the additional randomness of the structure can increase $V_2$ but operates on the same cells-of-size-$n/H$ scale. A rigorous treatment of the adaptive case is left open; the results above should be read as conditional on the realized structure, the reading legitimized by the poststratification interpretation of \citet{mcconville2019}.

— Model-assisted estimation with a training subsample: a two-phase sampling approach with design-based variance estimation  (2609.04082 - Riaño, 3 Sep 2026) in Remark 2, “Adaptive cell structure,” Section 4.3