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Kernel ridge regression (KRR) is a well-known and popular nonparametric regression approach with many desirable properties, including minimax rate-optimality in estimating functions that belong to common reproducing kernel Hilbert spaces…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

We study the kernel instrumental variable (KIV) algorithm, a kernel-based two-stage least-squares method for nonparametric instrumental variable regression. We provide a convergence analysis covering both identified and non-identified…

Many existing two-phase kernel-based hypothesis transfer learning algorithms employ the same kernel regularization across phases and rely on the known smoothness of functions to obtain optimality. Therefore, they fail to adapt to the…

Implicit layer deep learning techniques, like Neural Differential Equations, have become an important modeling framework due to their ability to adapt to new problems automatically. Training a neural differential equation is effectively a…

The $\chi^2$-principle generalizes the Morozov discrepancy principle (MDP) to the augmented residual of the Tikhonov regularized least squares problem. Weighting of the data fidelity by a known Gaussian noise distribution on the measured…

Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system…

We study reinforcement learning (RL) with linear function approximation where the underlying transition probability kernel of the Markov decision process (MDP) is a linear mixture model (Jia et al., 2020; Ayoub et al., 2020; Zhou et al.,…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

Recovering a function or high-dimensional parameter vector from indirect measurements is a central task in various scientific areas. Several methods for solving such inverse problems are well developed and well understood. Recently, novel…

In current synthetic aperture radar (SAR) object classification, one of the major challenges is the severe overfitting issue due to the limited dataset (few-shot) and noisy data. Considering the advantages of knowledge distillation as a…

We consider nonlinear inverse problems arising in the context of parameter identification for parabolic partial differential equations (PDEs). For stable reconstructions, regularization methods such as the iteratively regularized…

The Arnoldi-Tikhonov method is a well-established regularization technique for solving large-scale ill-posed linear inverse problems. This method leverages the Arnoldi decomposition to reduce computational complexity by projecting the…

We consider the problem of simultaneous variable selection and estimation of the corresponding regression coefficients in an ultra-high dimensional linear regression models, an extremely important problem in the recent era. The adaptive…

We systematically investigated the limited inverse discrete Fourier transform of the quasi distributions from the perspective of inverse problem theory. This transformation satisfies two of Hadamard's well-posedness criteria, existence and…

Real-world data (RWD) gains growing interests to provide a representative sample of the population for selecting the optimal treatment options. However, existing complex black box methods for estimating individualized treatment rules (ITR)…

Being motivated by the multilayer RECOS (REctified-COrrelations on a Sphere) transform, we develop a data-driven Saak (Subspace approximation with augmented kernels) transform in this work. The Saak transform consists of three steps: 1)…

In complex-valued coherent inverse problems such as synthetic aperture radar (SAR), one may often have prior information only on the magnitude image which shows the features of interest such as strength of reflectivity. In contrast, there…

The numerical solution of parameter identification inverse problems for kinetic equations can exhibit high computational and memory costs. In this paper, we propose a dynamical low-rank scheme for the reconstruction of the scattering…

We introduce an adaptive L2 regularization mechanism in the setting of person re-identification. In the literature, it is common practice to utilize hand-picked regularization factors which remain constant throughout the training procedure.…