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[2602.14440] CAIRO: Decoupling Order from Scale in Regression
Summary
The paper presents CAIRO, a novel framework that separates the learning of ordering from scale in regression analysis, enhancing robustness against outliers and noise.
Why It Matters
CAIRO addresses limitations in traditional regression methods that conflate ordering and scale, making models vulnerable to outliers. By decoupling these elements, it offers a more robust approach, particularly valuable in fields where data can be noisy or heavy-tailed, such as finance and healthcare.
Key Takeaways
- CAIRO decouples regression into two stages: ranking and scale recovery.
- The framework enhances robustness against outliers and heteroskedastic noise.
- Empirical results show CAIRO matches state-of-the-art performance on tabular data.
- Theoretical foundations include 'Optimal-in-Rank-Order' objectives.
- CAIRO combines neural network representation learning with rank-based statistics.
Statistics > Methodology arXiv:2602.14440 (stat) [Submitted on 16 Feb 2026] Title:CAIRO: Decoupling Order from Scale in Regression Authors:Harri Vanhems, Yue Zhao, Peng Shi, Archer Y. Yang View a PDF of the paper titled CAIRO: Decoupling Order from Scale in Regression, by Harri Vanhems and 3 other authors View PDF HTML (experimental) Abstract:Standard regression methods typically optimize a single pointwise objective, such as mean squared error, which conflates the learning of ordering with the learning of scale. This coupling renders models vulnerable to outliers and heavy-tailed noise. We propose CAIRO (Calibrate After Initial Rank Ordering), a framework that decouples regression into two distinct stages. In the first stage, we learn a scoring function by minimizing a scale-invariant ranking loss; in the second, we recover the target scale via isotonic regression. We theoretically characterize a class of "Optimal-in-Rank-Order" objectives -- including variants of RankNet and Gini covariance -- and prove that they recover the ordering of the true conditional mean under mild assumptions. We further show that subsequent monotone calibration guarantees recovery of the true regression function. Empirically, CAIRO combines the representation learning of neural networks with the robustness of rank-based statistics. It matches the performance of state-of-the-art tree ensembles on tabular benchmarks and significantly outperforms standard regression objectives in regimes with heav...
