Dynamic Feature Inference from Sparse Empirical Trajectories: A Reference-Free Framework for Assessing Reconstruction-Model Dependence

Sparse longitudinal monitoring requires dynamic characteristics to be inferred without a continuous reference for the unobserved evolution between measurements. This study introduces a reference-free framework for quantifying reconstruction-model dependence and its response to limited process information. The framework was evaluated using empirical competency-development data from 96 participants and seven reconstruction approaches: PCHIP, cubic smoothing splines, Gaussian processes, cubic radial basis functions, and three regularized Laguerre/Kautz representations. Trajectory-level U measures quantified disagreement across the observation domain and within and outside prolonged gaps, while Dk and Rk assessed feature-level disagreement and its magnitude relative to between-participant variability. Stabilization effects were evaluated using changes in trajectory disagreement, spatial contrast C, and the feature-change measures Qk, W1, and Pchange. Cross-model disagreement was concentrated in weakly observed regions and generally greater for local and derivative-dependent characteristics than for broader descriptors. For 37 trajectories with prolonged gaps, process-informed stabilization reduced disagreement predominantly within these intervals, while most continuous characteristics changed little relative to between-participant variability. The framework provides a model-agnostic methodology with potential applicability to other sparse longitudinal monitoring problems lacking continuous reference trajectories.