Towards Stabilizable Sequential Smoothing Spline Interpolation by Point Forecasting
Keywords: spline interpolation, sequential decision making, stability, controllability, time series forecasting
TL;DR: To the best of our knowledge, we propose the first strategy for stabilizing sequential smoothing spline interpolators under (possibly) delayless regimes and without sacrificing any smoothness of the interpolated trajectory.
Abstract: Sequential smoothing spline interpolators exhibit unstable behavior under low-delay response requirements.
That is, instability issues are observed when a smoothing spline interpolator is forced to provide an interpolated trajectory piece subject to processing only a few to no incoming data points at each time stamp.
Typically, the above instability setback is solved by increasing the delay, sacrificing some degree of smoothness in the interpolated trajectory, or a combination of both.
However, stable sequential smoothing spline interpolation strategies working under low delay and without compromising their degree of smoothness seem vastly unexplored in the literature.
To the best of our knowledge, this work formalizes the internal instability and asserts the controllability of sequential smoothing spline interpolators for the first time.
Specifically, we model the trajectory assembled by a smoothing spline interpolator as a discrete dynamical system of the spline coefficients, facilitating the analysis of its internal instability and controllability.
From these results, we propose a stabilizing strategy based on data point forecasting capable of operating even under delayless regimes and without sacrificing any smoothness of the interpolated trajectory.
Our claims are theoretically confirmed, or experimentally supported by extensive numerical results otherwise.
Supplementary Material: zip
Primary Area: learning on time series and dynamical systems
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Submission Number: 6876
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