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We present a greedy method for simultaneously performing local bandwidth selection and variable selection in nonparametric regression. The method starts with a local linear estimator with large bandwidths, and incrementally decreases the…
This paper considers the problem of closed-loop identification of linear scalar systems with Gaussian process noise, where the system input is determined by a deterministic state feedback policy. The regularized least-square estimate (LSE)…
This paper studies the finite-horizon robust optimal control of constrained linear systems subject to model mismatch and additive stochastic disturbances. Utilizing the system level synthesis (SLS) parameterization, we propose a novel SLS…
This paper investigates the control of nonlinear systems using a piecewise linear approximation framework. The proposed approach combines a PID controller with locally linearized models obtained by partitioning the nonlinear function into…
We investigate transient radiation processes in the non-linear superradiance (SR) regime of the Doppler broadened Maxwell-Bloch equations when the velocity distribution is of total bandwidth greatly exceeding that of the transient process…
Multivariate time series forecasting is a challenging task because the data involves a mixture of long- and short-term patterns, with dynamic spatio-temporal dependencies among variables. Existing graph neural networks (GNN) typically model…
Many real-world relational systems, such as social networks and biological systems, contain dynamic interactions. When learning dynamic graph representation, it is essential to employ sequential temporal information and geometric structure.…
The Bandwidth Problem seeks for a simultaneous permutation of the rows and columns of the adjacency matrix of a graph such that all nonzero entries are as close as possible to the main diagonal. This work focuses on investigating novel…
Nonlinear Fourier transform (NFT) and eigenvalue communication with the use of nonlinear signal spectrum (both discrete and continuous), have been recently discussed as a promising transmission method to combat fiber nonlinearity…
Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…
The generation of rogue waves is investigated via a nonlocal nonlinear Schrodinger (NLS) equation. In this system, modulation instability is suppressed and is usually expected that rogue wave formation would also be limited. On the…
This paper characterizes a new parametrization of nonlinear networked incrementally $L_2$-bounded operators in discrete time. The distinctive novelty is that our parametrization is \emph{free} -- that is, a sparse large-scale operator with…
Spectral analysis of neighborhood graphs is one of the most widely used techniques for exploratory data analysis, with applications ranging from machine learning to social sciences. In such applications, it is typical to first encode…
Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still…
This paper proposes a novel formulation of frequency response for nonlinear systems in the Koopman operator framework. This framework is a promising direction for the analysis and synthesis of systems with nonlinear dynamics based on…
We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and non-null cases. The intricate nonlinear interaction of different quantities in SST is…
We systematically study the spectrum of kernel-based graph Laplacian (GL) constructed from high-dimensional and noisy random point cloud in the nonnull setup. The problem is motived by studying the model when the clean signal is sampled…
The throughput gains of extending the optical transmission bandwidth to the S+C+L-band are quantified using a Gaussian Noise model that accounts for inter-channel stimulated Raman scattering (ISRS). The impact of potential ISRS mitigation…
Spectral graph neural networks learn graph filters, but their behavior with increasing depth and polynomial order is not well understood. We analyze these models in the graph Fourier domain, where each layer becomes an element-wise…
Multimodal regression estimation methods are introduced for regression models involving circular response and/or covariate. The regression estimators are based on the maximization of the conditional densities of the response variable over…