On constrained smoothing and out-of-range prediction using P-splines: A conic optimization approach
Applied Mathematics and Computation, 2023
Abstract
This research addresses the problem of estimating smooth curves which verify structural properties, such as sign, monotonicity, and curvature. The paper introduces a new mathematical optimization formulation for non-negative P-splines, broadens these results to out-of-range prediction, expands the methods to other constraints and multiple curve fitting, and presents a new open-source Python library, cpsplines.
The model has been tested using both simulated and real-life data, including COVID-19 statistics and mortality rates.
A novel method for estimating smooth curves under shape constraints in real-world applications such as pandemic tracking & demographic modelling
Where does it apply?
It is applicable in areas like pandemic tracking and demographic analysis. The method has been applied to map COVID-19’s progression in Aragón, Spain, and to model age-related mortality rates where overlapping of curves is not biologically reasonable.
Why does it matters?
This research introduces a novel method for estimating smooth curves with shape requirements inherent to the nature of the data. The methodology allows the user to incorporate expert knowledge in the fitting procedure, thus yielding coherent estimates of the response.
It supports custom curve fitting to specific needs, providing more insightful results. With its successful use in constrained forecasting, this methodology presents potential for enhancing future data analysis methods.
It is particularly valuable for tracking pandemics or studying demographics, aiding effective decision-making for such aims. Moreover, its future potential in multi-dimensional surfaces and variable selections promises to revolutionize its applications further.
On constrained smoothing and out-of-range prediction using P-splines: A conic optimization approach
Applied Mathematics and Computation, 2023
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