arXiv subjects

Sunny G. W. Wang

Publications and source records attributed to Sunny G. W. Wang.

5 recordsLinked to original sources

arXiv2026

Learning structured linear dynamical systems from missing observations

We consider the problem of learning structured linear dynamical systems over convex sets $\mathcal{K}$, where only a small subset of the observations are available at each time point. An estimator which minimizes a bias-corrected, potentially non-convex objective function is proposed. Non-asymptotic bounds are obtained for the statistical error, which depend on the local complexity of $\mathcal{K}$, the trajectory length $T$, and the sub-sampling probability $p$. Convergence of the projected gradient descent algorithm is also established. The general theory is applied to settings where (i) $\mathcal{K}$ is a subspace, (ii) $\mathcal{K}$ is the set of bi-isotonic matrices, and (iii) $\mathcal{K}$ is the set of matrices whose rows are formed by sampling Lipschitz functions. We show meaningful recovery of the transition matrix is possible for values of $T$ much smaller than what is required in the unconstrained case, and for $p = o(1)$.

stat.ML↗

arXiv2026

Learning switched non-linear dynamical systems from a single trajectory

We study empirical risk minimization for learning non-linear dynamical systems whose transition dynamics may switch over time. Under stability assumptions, and i.i.d switching over a set of $K$ modes, we derive non-asymptotic bounds on the prediction risk expressed in terms of the metric entropy of the underlying function class. We instantiate our general result for Hölder and linear function classes, obtaining explicit convergence rates that depend on the effective sample size $Tp_i$, where $T$ is the trajectory length and $p_i$ is the probability of observing mode $i$. Numerical simulations support our theoretical findings. To the best of our knowledge, these results are the first non-asymptotic guarantees for learning switched nonlinear dynamical systems from a single trajectory.

stat.ML↗

arXiv2026

Structural adaptation and rate accelerated estimation in bivariate functional data

We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity additionally views anisotropy through the lens of directions. We show that faster rates of convergence for smoothing can be obtained through a change-of-basis by adapting to the anisotropy of a bivariate process. An algorithm for the estimation and identification of the change-of-basis matrix is constructed, made possible due to the replication structure of functional data. Non-asymptotic bounds are provided for our algorithm, supplemented by numerical evidence from an extensive simulation study. Finally, a real-world rainfall measurement dataset is analyzed with our methods.

stat.ME↗

arXiv2025

Adaptive functional principal components analysis

Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference, data-driven methods for selecting these parameters are not well-developed, frustrated by the difficulty of using all the information shared by curves while being computationally efficient. On the one hand, smoothing individual curves in an isolated, albeit sophisticated way, ignores useful signals present in other curves. On the other hand, bandwidth selection by automatic procedures such as cross-validation after pooling all the curves together quickly become computationally unfeasible due to the large number of data points. In this paper we propose a new data-driven, adaptive kernel smoothing, specifically tailored for functional principal components analysis through the derivation of sharp, explicit risk bounds for the eigen-elements. The minimization of these quadratic risk bounds provide refined, yet computationally efficient bandwidth rules for each eigen-element separately. Both common and independent design cases are allowed. Rates of convergence for the estimators are derived. An extensive simulation study, designed in a versatile manner to closely mimic the characteristics of real data sets supports our methodological contribution. An illustration on a real data application is provided.

stat.ME↗

arXiv2025

Rate accelerated inference for integrals of multivariate random functions

The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo integration literature, we propose effective unbiased estimation and inference procedures for integrals of uni- and multivariate random functions. Several applications to key problems in functional data analysis involving random design points are studied and illustrated. In the absence of noise, the proposed estimates converge faster than the sample mean and the usual algorithms for numerical integration. Moreover, the proposed estimator facilitates effective inference by generally providing better coverage with shorter confidence and prediction intervals, in both noisy and noiseless setups.

stat.ME↗