Related papers: A universal reproducing kernel Hilbert space for l…
The Koopman operator, as a linear representation of a nonlinear dynamical system, has been attracting attention in many fields of science. Recently, Koopman operator theory has been combined with another concept that is popular in data…
In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…
Stochastic configuration networks (SCNs), as a class of randomized learner models, are featured by its way of random parameters assignment in the light of a supervisory mechanism, resulting in the universal approximation property at…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
A major problem in system identification is the incorporation of prior knowledge about the physical properties of the given system, such as stability, positivity and passivity. In this paper, we present first steps towards tackling this…
We introduce a nonparametric algorithm to learn interaction kernels of mean-field equations for 1st-order systems of interacting particles. The data consist of discrete space-time observations of the solution. By least squares with…
In this article, a novel approach to learning a complex function which can be written as the system of linear equations is introduced. This learning is grounded upon the observation that solving the system of linear equations by a…
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…
In this paper, we characterize all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral bi-Carleman operator in $L_2(R)$ with bounded and arbitrarily smooth kernel on $R^2$. In addition, we give…
Modeling dynamical systems with ordinary differential equations implies a mechanistic view of the process underlying the dynamics. However in many cases, this knowledge is not available. To overcome this issue, we introduce a general…
We present a method to construct a chain of reproducing kernel Hilbert spaces controlled by a first-order system of differential equations from a given unimodular function satisfying several conditions. One of the applications of that…
Operator learning is the approximation of operators between infinite dimensional Banach spaces using machine learning approaches. While most progress in this area has been driven by variants of deep neural networks such as the Deep Operator…
In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…
To characterize the function space explored by neural networks (NNs) is an important aspect of learning theory. In this work, noticing that a multi-layer NN generates implicitly a hierarchy of reproducing kernel Hilbert spaces (RKHSs) -…
In kernel methods, temporal information on the data is commonly included by using time-delayed embeddings as inputs. Recently, an alternative formulation was proposed by defining a gamma-filter explicitly in a reproducing kernel Hilbert…
We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…
Suppose H is a space of functions on X. If H is a Hilbert space with reproducing kernel then that structure of H can be used to build distance functions on X. We describe some of those and their interpretations and interrelations. We also…
Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…
This work constructs a hypothesis test for detecting whether an data-generating function $h: R^p \rightarrow R$ belongs to a specific reproducing kernel Hilbert space $\mathcal{H}_0$ , where the structure of $\mathcal{H}_0$ is only…
We study reproducing kernel Hilbert spaces introduced as ranges of generalized Ces\`aro-Hardy operators, in one real variable and in one complex variable. Such spaces can be seen as formed by absolutely continuous functions on the positive…