Related papers: Reservoir kernels and Volterra series
The combination of machine learning and quantum computing has emerged as a promising approach for addressing previously untenable problems. Reservoir computing is an efficient learning paradigm that utilizes nonlinear dynamical systems for…
In this paper we consider the problem of approximating vector-valued functions over a domain $\Omega$. For this purpose, we use matrix-valued reproducing kernels, which can be related to Reproducing kernel Hilbert spaces of vectorial…
Hilbertian kernel methods and their positive semidefinite kernels have been extensively used in various fields of applied mathematics and machine learning, owing to their several equivalent characterizations. We here unveil an analogy with…
We are concerned with nonparametric hypothesis testing of time series functionals. It is known that the popular autoregressive sieve bootstrap is, in general, not valid for statistics whose (asymptotic) distribution depends on moments of…
A reservoir computer is a way of using a high dimensional dynamical system for computation. One way to construct a reservoir computer is by connecting a set of nonlinear nodes into a network. Because the network creates feedback between…
Quantum reservoir computing (QRC) harnesses driven quantum dynamics for time-series processing, yet the mechanisms behind the differing performance levels across its many implementations remain unclear. We show that apparently unrelated…
Kernels are often developed and used as implicit mapping functions that show impressive predictive power due to their high-dimensional feature space representations. In this study, we gradually construct a series of simple feature maps that…
The paradigm of reservoir computing exploits the nonlinear dynamics of a physical reservoir to perform complex time-series processing tasks such as speech recognition and forecasting. Unlike other machine-learning approaches, reservoir…
Reservoir Computing (RC) has become popular in recent years thanks to its fast and efficient computational capabilities. Standard RC has been shown to be equivalent in the asymptotic limit to Recurrent Kernels, which helps in analyzing its…
A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…
Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and…
This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about…
Reservoir computing is a popular approach to design recurrent neural networks, due to its training simplicity and approximation performance. The recurrent part of these networks is not trained (e.g., via gradient descent), making them…
This work defines and studies one-dimensional convolution kernels that preserve nonnegativity. When the past dynamics of a process is integrated with a convolution kernel like in Stochastic Volterra Equations or in the jump intensity of…
A new machine learning scheme, termed versatile reservoir computing, is proposed for sustaining the dynamics of heterogeneous complex networks. We show that a single, small-scale reservoir computer trained on time series from a subset of…
Quantum machine learning represents a promising avenue for data processing, also for purposes of sequential temporal data analysis, as recently proposed in quantum reservoir computing (QRC). The possibility to operate on several platforms…
Quantum reservoir computing is a computing approach which aims at utilising the complexity and high-dimensionality of small quantum systems, together with the fast trainability of reservoir computing, in order to solve complex tasks. The…
In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of…
We introduce a novel framework of reservoir computing. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells and nonlinear computation is performed on…