interpolation methods

Reconstructing kinematically consistent vehicle state sequences (position, velocity, acceleration, heading) from noisy, position-only trajectory observations—while enforcing integral relationships (e.g., velocity as the integral of acceleration) and directional motion constraints (i.e., motion strictly along the heading direction). Method: We propose an end-to-end trajectory reconstruction framework that jointly models B-spline parameterization, physics-based regularization (embedding numerical integration and orientation-driven motion constraints), and supervised feature regression. Contribution/Results: To our knowledge, this is the first approach unifying these three components in a single differentiable architecture. We release a configurable Python library implementing the method. Experiments on real-world data demonstrate significant improvements in trajectory accuracy—yielding reconstructions substantially closer to ground truth—and enhanced performance in downstream machine learning tasks reliant on high-fidelity reference trajectories.

This study addresses the challenges posed by potentially infinite-dimensional covariates and non-mixing dependence structures in spatiotemporal data by proposing a nonparametric regression framework conditioned on second-order stationary covariates. The work innovatively replaces conventional mixing assumptions with a polynomially decaying moment contraction (PMC) condition, enabling effective modeling of infinite-dimensional spatiotemporal covariates. Employing kernel estimation techniques, the authors establish statistical consistency of the mean function estimator under the PMC condition and construct simultaneous confidence intervals based on a central limit theorem. Comprehensive theoretical analysis, simulation studies, and applications to two real-world datasets demonstrate that the proposed method exhibits strong finite-sample performance and is suitable for hypothesis testing regarding the functional form of the mean.

This work addresses the challenge of reconstructing continuous trajectories from cross-sectional point-cloud observations across time in dynamic processes—such as cellular evolution—where topological changes (e.g., splitting and merging) occur. We propose a trajectory reconstruction method in Wasserstein space that explicitly supports such topological transitions. Our core innovation is the first integration of Wasserstein intrinsic continuous averaging with B-splines, yielding an optimal-transport-based geodesic subdivision interpolation framework. This framework ensures geometric awareness, adaptive smoothness, and controllable reconstruction accuracy. We establish theoretical convergence guarantees for the method. Empirical evaluation on simulated single-cell data featuring branching and merging events demonstrates that our approach significantly outperforms state-of-the-art methods, while rigorously preserving the intrinsic geometry of the data and consistency with Wasserstein transport distances.

This paper addresses the challenge of spectral modeling for multivariate inhomogeneous spatial point processes—particularly second-order intensity-reweighted stationary processes. Methodologically, it introduces a novel spectral analysis framework centered on the definition and estimation of a “pseudo-spectrum”: a matrix-valued, locally interpretable spectral density estimator that inherits the asymptotic properties of the classical stationary spectrum. The work extends periodogram asymptotics—previously established only for stationary settings—to multivariate nonstationary spatial point processes, yielding a consistent pseudo-spectrum estimator. It further proposes two data-driven, adaptive bandwidth selection strategies. The approach integrates kernel smoothing, spectral-domain modeling, and rigorous asymptotic analysis. Extensive simulation studies and application to real-world tropical forest tree species distribution data demonstrate the method’s effectiveness and robustness, substantially advancing the frequency-domain analysis capability for nonstationary spatial point processes.

In spatial linear models, conventional confidence intervals severely under-cover nominal levels (e.g., 95%) when model misspecification co-occurs with distributional shift, as they ignore estimation bias induced by spatial dependence. To address this, we propose the first inference framework for spatial data that replaces the inapplicable i.i.d. assumption with a Lipschitz continuity assumption on the spatially varying coefficients. Our method explicitly models the bias structure under spatial smoothness constraints and constructs bias-aware confidence intervals with theoretical guarantees on nominal coverage. Theoretical analysis and empirical evaluation across diverse spatial dependence settings demonstrate that our 95% confidence intervals achieve actual coverage rates of 94.8–95.3%, substantially outperforming existing approaches. The core innovation lies in integrating Lipschitz spatial regularization into the inferential foundation—enabling interpretable, correctable, and theoretically guaranteed bias control in spatial statistical inference.

This work addresses the limited adoption of Gaussian processes (GPs) in continuous-time state estimation—primarily hindered by their high theoretical barrier—by introducing a GP modeling approach formulated within a factor graph framework. By re-expressing the GP motion prior using factor graph semantics, the proposed method naturally supports asynchronous multi-sensor fusion and trajectory interpolation while yielding smooth, continuous trajectories. The authors provide three open-source implementations built on GTSAM, significantly lowering the practical entry barrier for employing GP-based continuous-time estimation and thereby facilitating its real-world deployment and application in robotic systems.

This work addresses the challenge of accurately attributing detected change points in multivariate time series to specific subsets of variables. The authors propose a post-hoc, nonparametric testing framework that, after an offline change point has been identified, determines whether the change occurs in one of two pre-specified coordinate blocks or in both. Built upon two-sample nonparametric hypothesis testing, the method offers rigorous theoretical guarantees for Type I error control. Empirical evaluations on both synthetic and real-world datasets demonstrate that the proposed approach achieves high attribution accuracy and strong robustness in identifying the components responsible for the change.

This work proposes a nonparametric method for testing separability of the covariance structure in spatio-temporal second-order stationary processes without assuming normality or relying on spectral analysis. By constructing a discrepancy measure between the empirical covariance estimator and its separable approximation, and leveraging domain expansion combined with infill asymptotic theory, the authors derive inferential tools whose limiting distributions are nonstandard. Corresponding hypothesis tests and confidence intervals are established under both asymptotic frameworks, providing rigorous theoretical guarantees. This approach constitutes the first fully nonparametric procedure capable of formally validating separability, thereby substantially reducing modeling and computational complexity while maintaining statistical rigor.

This study addresses the stability of the solution operator with respect to perturbations in the input parameter distribution within the framework of nonparametric Bayesian computer model calibration. By integrating nonparametric Bayesian inference, weak convergence theory of probability measures, and total variation metric analysis, the work establishes—for the first time—a systematic continuity theory for the solution operator in this calibration setting. The primary contributions include proving the uniform continuity of the solution operator under the total variation metric and demonstrating its continuity under the weak topology for a broad class of prior distributions. These results provide a rigorous theoretical foundation for the robustness of nonparametric Bayesian calibration methods in complex scientific applications.

This work addresses the performance instability and data sparsity issues arising from random trajectory selection in trajectory data augmentation by proposing a scalable framework that systematically evaluates five trajectory selection strategies—abnormality, diversity, representativeness, uncertainty, and randomness—for the first time. Integrating geometric perturbation-based augmentation with Optuna-driven hyperparameter optimization, the framework is validated across multiple domains. Experimental results demonstrate that abnormality- and uncertainty-based strategies significantly enhance model stability and repair topological fragmentation in sparse data, yet may introduce noise when applied to dense, high-quality datasets. The efficacy of augmentation is shown to be highly dependent on data density and quality, while also revealing inherent physical limitations of standard perturbation methods in highly dynamic scenarios.