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In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…

The nonlinearity of a Boolean function is a key property in deciding its suitability for cryptographic purposes, e.g. as a combining function in stream ciphers, and so the nonlinearity computation is an important problem for applications.…

Our recent work lays out a general framework for inferring information about the parameters and associated dynamics of a differential equation model from a discrete set of data points collected from the system being modeled. Rigorous…

For data-driven iterative learning control (ILC) methods, both the model estimation and controller design problems are converted to parameter estimation problems for some chosen model structures. It is well-known that if the model order is…

Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…

Deep-learning-based nonlinear system identification has shown the ability to produce reliable and highly accurate models in practice. However, these black-box models lack physical interpretability, and a considerable part of the learning…

Objects or structures that are regular take uniform dimensions. Based on the concepts of regular models, our previous research work has developed a system of a regular ontology that models learning structures in a multiagent system for…

In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered…

Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…

In this paper, we introduce a new kernel function which differs from previous functions, and play an important role for generating a new design of primal-dual interior point algorithms for semidefinite linear complementarity problem. Its…

Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…

Kernel-based methods exhibit well-documented performance in various nonlinear learning tasks. Most of them rely on a preselected kernel, whose prudent choice presumes task-specific prior information. Especially when the latter is not…

This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model is completely written in terms of a tensor network, thus…

The damage detection problem becomes a more difficult task when the intrinsically nonlinear behavior of the structures and the natural data variation are considered in the analysis because both phenomena can be confused with damage if…

State estimation is a key ingredient in most robotic systems. Often, state estimation is performed using some form of least squares minimization. Basically, all error minimization procedures that work on real-world data use robust kernels…

How to obtain the desirable representation of a 3D shape is a key challenge in 3D shape retrieval task. Most existing 3D shape retrieval methods focus on capturing shape representation with different neural network architectures, while the…

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…

Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…

Deep Neural Networks (DNNs) have obtained impressive performance across tasks, however they still remain as black boxes, e.g., hard to theoretically analyze. At the same time, Polynomial Networks (PNs) have emerged as an alternative method…

In this paper, we formulate a new generalized reference kernel hoping to improve the original base kernel using a set of reference vectors. Depending on the selected reference vectors, our formulation shows similarities to approximate…