{"ID":5439480,"CreatedAt":"2026-07-01T01:17:58.482524686Z","UpdatedAt":"2026-07-02T19:06:01.127452785Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.30837","arxiv_id":"2606.30837","title":"A Stationary-Distribution Theory for Triplet-Based Plateau Search in Random Forest Ensemble-Size Selection","abstract":"The number of trees is a central computational parameter in Random Forests: increasing it reduces finite-ensemble variability but increases training and prediction cost. Plateau-based tuning adapts this parameter through local comparisons of out-of-bag scores at a geometric triplet of tree counts. After the remaining hyperparameters have stabilized, however, the central triplet point need not converge to a deterministic value; instead, it fluctuates around a stationary regime. This paper develops a stationary-distribution theory for this process. The central ensemble size $B_t$ is modeled as a birth-death Markov chain on a geometric grid, and its stationary distribution is derived through local balance. Under a leading centered folded-normal approximation, equilibrium equations are obtained for the original update rule and a symmetric modified variant, implying that the stationary center $B_*=O(\\varepsilon^{-2})$ as $\\varepsilon\\downarrow 0$. The stationary spread is also characterized. A local Gaussian approximation and a Fokker-Planck interpretation give grid-level variance constants. After conversion to the ensemble-size scale, $σ_{B,*}=O(\\varepsilon^{-2})$, while the variance is $O(\\varepsilon^{-4})$. The leading relative spread is independent of $\\varepsilon$ and controlled by the scale factor and update rule. These results interpret plateau-based Random Forest tuning as a stochastic process rather than a deterministic stopping rule.","short_abstract":"The number of trees is a central computational parameter in Random Forests: increasing it reduces finite-ensemble variability but increases training and prediction cost. Plateau-based tuning adapts this parameter through local comparisons of out-of-bag scores at a geometric triplet of tree counts. After the remaining h...","url_abs":"https://arxiv.org/abs/2606.30837","url_pdf":"https://arxiv.org/pdf/2606.30837v1","authors":"[\"Andrey A. Dukhovny\",\"Andrey M. Lange\"]","published":"2026-06-29T19:12:29Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"math.PR\",\"stat.ML\"]","methods":"[]","has_code":false}