Related papers: Regularized Nonparametric Volterra Kernel Estimati…
In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…
Recent contributions have framed linear system identification as a nonparametric regularized inverse problem. Relying on $\ell_2$-type regularization which accounts for the stability and smoothness of the impulse response to be estimated,…
Regularized nonlinear acceleration (RNA) estimates the minimum of a function by post-processing iterates from an algorithm such as the gradient method. It can be seen as a regularized version of Anderson acceleration, a classical…
Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…
Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the…
We make an attempt to understanding convolutional neural network by exploring the relationship between (deep) convolutional neural networks and Volterra convolutions. We propose a novel approach to explain and study the overall…
This paper focuses on the systems theory of bilinear dynamical systems using the Volterra series representation. The main contributions are threefold. First, we gain an input-output representation in the frequency domain, where the Laplace…
Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive…
The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…
We provide a new estimator of integral operators with smooth kernels, obtained from a set of scattered and noisy impulse responses. The proposed approach relies on the formalism of smoothing in reproducing kernel Hilbert spaces and on the…
In this paper, a new two-parameter family of regularized kernels is introduced, suitable for applying high-order time stepping to N-body systems. These high-order kernels are derived by truncating a Taylor expansion of the non-regularized…
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…
This study aims to discuss the existence and uniqueness of solution of fuzzy Volterra integral equation with piecewise continuous kernel. Such problems appears in many balance problems for hereditary dynamic systems, e.g. in electric load…
A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
The numerical method for solution of the weakly regular scalar Volterra integral equation of the 1st kind is proposed. The kernels of such equations have jump discontinuities on the continuous curves which starts at the origin. The…
This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…
Dynamic systems characterized by second-order nonlinear ordinary differential equations appear in many fields of physics and engineering. To solve these kinds of problems, time-consuming step-by-step numerical integration methods and…
We propose a kernel-based nonparametric framework for mean-variance optimization that enables inference on economically motivated shape constraints in finance, including positivity, monotonicity, and convexity. Many central hypotheses in…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…