Closed-Form Beta Distribution Estimation from Sparse Statistics with Random Forest Implicit Regularization
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915603546112000 |
|---|---|
| author | Landers, Jonathan R. |
| author_facet | Landers, Jonathan R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23767 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Closed-Form Beta Distribution Estimation from Sparse Statistics with Random Forest Implicit Regularization Landers, Jonathan R. Machine Learning 68T05, 62H30, 62F10, 68Q32 F.2.2; I.2.6; I.5.2; G.3 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. |
| title | Closed-Form Beta Distribution Estimation from Sparse Statistics with Random Forest Implicit Regularization |
| topic | Machine Learning 68T05, 62H30, 62F10, 68Q32 F.2.2; I.2.6; I.5.2; G.3 |
| url | https://arxiv.org/abs/2507.23767 |