Research map / Learning theory and algorithms / Kernels and regression theory
Fast Nonlinear Vector Quantile Regression
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| nonlinear embedding of covariates (NL-VQR) instead of linear specification | VQR · Conditional banana | QFD: 70% lower error than linear VQR | Helped |
| nonlinear embedding of covariates (NL-VQR) instead of linear specification | VQR · Rotating stars | KDE-L1 and qualitative fit: outperforms CVAE and linear VQR by a large margin | Helped |
| NL-VQR instead of CVAE | conditional generative modeling · Conditional banana | KDE-L1: outperforms CVAE by 23% | Helped |
| NL-VQR instead of separable QR baselines for distribution-free confidence sets | uncertainty estimation · Four real datasets | alpha-confidence set size: 34-60% smaller than second-best method | Helped |
| stochastic mini-batch sampling of both data points and quantile levels in the relaxed dual solver | VQR solver · Scale experiment (MVN) | memory footprint and runtime: constant memory; runtime linear in N, quadratic in T | Helped |
| vector monotone rearrangement (VMR) post-processing | NL-VQR estimated CVQF · Synthetic experiments | co-monotonicity violations and strong representation: violations completely eliminated; strong representation strictly improves | Helped |
| SGD with mini-batches vs full-batch relaxed dual (ablation) | VQR solver · Optimization experiments | optimization error: negligible optimization error added | No clear effect |
| NL-VQR vs linear VQR on rotating stars with CVAE training time | training cost · Rotating stars | training time: under 4 minutes vs 35 minutes for CVAE | Helped |
Closest papers by meaning
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- QuEst: Enhancing Estimates of Quantile-Based Distributional Measures Using Model Predictions (ICML 2025 · similarity 0.85)
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- Optimal Kernel Quantile Learning with Random Features (ICML 2024 · similarity 0.84)
- Efficient Analytic Uncertainty Quantification for Multimodal Regression (NeurIPS 2026 · similarity 0.84)
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