A PyTorch Framework for Scalable Non-Crossing Quantile Regression
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917143667277824 |
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| author | Chang, Kaihua |
| author_facet | Chang, Kaihua |
| contents | Quantile regression is fundamental to distributional modeling, yet independent estimation of multiple quantiles frequently produces crossing -- where estimated quantile functions violate monotonicity, implying impossible negative probability densities. While Constrained Joint Quantile Regression (CJQR) elegantly enforces non-crossing by construction, existing formulations via Linear Programming exhibit $O((qn)^3)$ complexity, rendering them impractical for large-scale applications. We present the first scalable solution using PyTorch automatic differentiation: \textbf{CJQR-ALM}, combining the \textbf{Augmented Lagrangian Method} with \textbf{differentiable pinball loss} and \textbf{L-BFGS} optimization. Our approach reduces computational complexity to $O(n)$, achieving near-zero crossing rates on datasets exceeding 70,000 observations within minutes. The differentiable formulation naturally extends to neural network architectures for non-linear conditional quantile estimation. Application to Student Growth Percentile calculations demonstrates practical utility for educational assessment, while simulation studies show negligible accuracy cost (RMSE increase $\approx 2.4$ points) relative to unconstrained estimation -- a favorable trade-off for applications requiring valid probability statements across finance, healthcare, and engineering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22419 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A PyTorch Framework for Scalable Non-Crossing Quantile Regression Chang, Kaihua Machine Learning Quantile regression is fundamental to distributional modeling, yet independent estimation of multiple quantiles frequently produces crossing -- where estimated quantile functions violate monotonicity, implying impossible negative probability densities. While Constrained Joint Quantile Regression (CJQR) elegantly enforces non-crossing by construction, existing formulations via Linear Programming exhibit $O((qn)^3)$ complexity, rendering them impractical for large-scale applications. We present the first scalable solution using PyTorch automatic differentiation: \textbf{CJQR-ALM}, combining the \textbf{Augmented Lagrangian Method} with \textbf{differentiable pinball loss} and \textbf{L-BFGS} optimization. Our approach reduces computational complexity to $O(n)$, achieving near-zero crossing rates on datasets exceeding 70,000 observations within minutes. The differentiable formulation naturally extends to neural network architectures for non-linear conditional quantile estimation. Application to Student Growth Percentile calculations demonstrates practical utility for educational assessment, while simulation studies show negligible accuracy cost (RMSE increase $\approx 2.4$ points) relative to unconstrained estimation -- a favorable trade-off for applications requiring valid probability statements across finance, healthcare, and engineering. |
| title | A PyTorch Framework for Scalable Non-Crossing Quantile Regression |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.22419 |