# Closed-Form Beta Distribution Estimation from Sparse Statistics with Random Forest Implicit Regularization

arXiv: https://arxiv.org/abs/2507.23767 · HTML: https://mlsanity.com/paper/2507.23767/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 31 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Bake off redux: a review and experimental evaluation of recent time series classification algorithms](https://mlsanity.com/paper/2304.13029/) (2023)
- [Multistep Distillation of Diffusion Models via Moment Matching](https://mlsanity.com/paper/2406.04103/) (2024)
- [Explaining the Success of AdaBoost and Random Forests as Interpolating Classifiers](https://mlsanity.com/paper/1504.07676/) (2015)
- [Randomization as Regularization: A Degrees of Freedom Explanation for Random Forest Success](https://mlsanity.com/paper/1911.00190/) (2019)
- [Distributional GFlowNets with Quantile Flows](https://mlsanity.com/paper/2302.05793/) (2023)
- [Beta Diffusion](https://mlsanity.com/paper/2309.07867/) (2023)
- [QUANT: A Minimalist Interval Method for Time Series Classification](https://mlsanity.com/paper/2308.00928/) (2023)
- [Moment Matching Denoising Gibbs Sampling](https://mlsanity.com/paper/2305.11650/) (2023)
- [Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Features](https://mlsanity.com/paper/2407.00584/) (2024)
- [Towards black-box parameter estimation](https://mlsanity.com/paper/2303.15041/) (2023)
- [Dataset Condensation with Latent Quantile Matching](https://mlsanity.com/paper/2406.09860/) (2024)
- [Automatic model training under restrictive time constraints](https://mlsanity.com/paper/2104.10746/) (2021)
- [Roughness regularization for functional data analysis with free knots spline estimation](https://mlsanity.com/paper/2407.05159/) (2024)

## Abstract (arXiv)

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.