{"ID":2888484,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.23767","arxiv_id":"2507.23767","title":"Closed-Form Beta Distribution Estimation from Sparse Statistics with Random Forest Implicit Regularization","abstract":"This work advances distribution recovery from sparse data and ensemble classification through three main contributions. First, we introduce a closed-form estimator that reconstructs scaled beta distributions from limited statistics (minimum, maximum, mean, and median) via composite quantile and moment matching. The recovered parameters $(α,β)$, when used as features in Random Forest classifiers, improve pairwise classification on time-series snapshots, validating the fidelity of the recovered distributions. Second, we establish a link between classification accuracy and distributional closeness by deriving error bounds that constrain total variation distance and Jensen-Shannon divergence, the latter exhibiting quadratic convergence. Third, we show that zero-variance features act as an implicit regularizer, increasing selection probability for mid-ranked predictors and producing deeper, more varied trees. A SeatGeek pricing dataset serves as the primary application, illustrating distributional recovery and event-level classification while situating these methods within the structure and dynamics of the secondary ticket marketplace. The UCI handwritten digits dataset confirms the broader regularization effect. Overall, the study outlines a practical route from sparse distributional snapshots to closed-form estimation and improved ensemble accuracy, with reliability enhanced through implicit regularization.","short_abstract":"This work advances distribution recovery from sparse data and ensemble classification through three main contributions. First, we introduce a closed-form estimator that reconstructs scaled beta distributions from limited statistics (minimum, maximum, mean, and median) via composite quantile and moment matching. The rec...","url_abs":"https://arxiv.org/abs/2507.23767","url_pdf":"https://arxiv.org/pdf/2507.23767v2","authors":"[\"Jonathan R. Landers\"]","published":"2025-07-31T17:55:07Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}