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[2404.07849] Overparameterized Multiple Linear Regression as Hyper-Curve Fitting
Summary
This paper explores the mathematical equivalence of overparameterized multiple linear regression (MLR) to hyper-curve fitting, demonstrating its effectiveness in handling nonlinear data and improving model generalizability.
Why It Matters
Understanding overparameterization in MLR can significantly enhance predictive modeling, especially in complex datasets with nonlinear relationships. This research offers a new perspective on regularization and predictor selection, which is crucial for data scientists and statisticians aiming to improve model performance.
Key Takeaways
- Overparameterized MLR can be reformulated as hyper-curve fitting.
- This approach allows modeling individual predictors as functions of a common parameter.
- Exact predictions can be achieved even with nonlinear dependencies present.
- The method aids in identifying and removing improper predictors that reduce model accuracy.
- Regularization techniques derived from this framework improve generalizability in noisy datasets.
Statistics > Machine Learning arXiv:2404.07849 (stat) [Submitted on 11 Apr 2024 (v1), last revised 25 Feb 2026 (this version, v2)] Title:Overparameterized Multiple Linear Regression as Hyper-Curve Fitting Authors:E. Atza, N. Budko View a PDF of the paper titled Overparameterized Multiple Linear Regression as Hyper-Curve Fitting, by E. Atza and 1 other authors View PDF HTML (experimental) Abstract:This work demonstrates that applying a fixed-effect multiple linear regression (MLR) model to an overparameterized dataset is mathematically equivalent to fitting a hyper-curve parameterized by a single scalar. This reformulation shifts the focus from global coefficients to individual predictors, allowing each to be modeled as a function of a common parameter. We prove that this overparameterized linear framework can yield exact predictions even when the underlying data contains nonlinear dependencies that violate classical linear assumptions. By employing parameterization in terms of the dependent variable and a monomial basis, we validate this approach on both synthetic and experimental datasets. Our results show that the hyper-curve perspective provides a robust framework for regularizing problems with noisy predictors and offers a systematic method for identifying and removing 'improper' predictors that degrade model generalizability. Comments: Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG) Cite as: arXiv:2404.07849 [stat.ML] (or arXiv:2404.07849v2 [stat.ML] ...
