{"ID":2850377,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22419","arxiv_id":"2510.22419","title":"A PyTorch Framework for Scalable Non-Crossing Quantile Regression","abstract":"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.","short_abstract":"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 enforc...","url_abs":"https://arxiv.org/abs/2510.22419","url_pdf":"https://arxiv.org/pdf/2510.22419v2","authors":"[\"Kaihua Chang\"]","published":"2025-10-25T19:39:07Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}