Related papers: Positive Definite Multi-Kernels for Scattered Data…

Coherent, continuous spatial representations are critical for synthesizing physical and perceptual phenomena into a single representational space. Radial basis kernels provide a path forward for this type of distributed representation. In…

Deep networks are nowadays becoming popular in many computer vision and pattern recognition tasks. Among these networks, deep kernels are particularly interesting and effective, however, their computational complexity is a major issue…

In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in reproducing kernel Hilbert spaces. Using the orthogonality of…

We provide a characterization for the continuous positive definite kernels on $\mathbb R^d$ that are invariant to linear isometries, i.e. invariant under the orthogonal group $O(d)$. Furthermore, we provide necessary and sufficient…

Motivated by applications, we consider here new operator theoretic approaches to Conditional mean embeddings (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and…

We prove that the optimal assignment kernel, proposed recently as an attempt to embed labeled graphs and more generally tuples of basic data to a Hilbert space, is in fact not always positive definite.

Reproducing kernel Hilbert spaces provide a foundational framework for kernel-based learning, where regularization and interpolation problems admit finite-dimensional solutions through classical representer theorems. Many modern learning…

In statistical learning theory, interpolation spaces of the form $[\mathrm{L}^2,H]_{\theta,r}$, where $H$ is a reproducing kernel Hilbert space, are in widespread use. So far, however, they are only well understood for fine index $r=2$. We…

We discuss the structure of positive definite kernels in terms of operator models. In particular, we introduce two models, one of Hessenberg type and another one that we call near triangular. These models produce parametrizations of the…

Perceptrons are neuronal devices capable of fully discriminating linearly separable classes. Although straightforward to implement and train, their applicability is usually hindered by non-trivial requirements imposed by real-world…

This paper focuses on learning rate analysis of distributed kernel ridge regression for strong mixing sequences. Using a recently developed integral operator approach and a classical covariance inequality for Banach-valued strong mixing…

Predicting tensorial properties with machine learning models typically requires carefully designed tensorial descriptors. In this work, we introduce an alternative strategy for learning tensorial quantities based on scalar descriptors. We…

We propose a kernelized classification layer for deep networks. Although conventional deep networks introduce an abundance of nonlinearity for representation (feature) learning, they almost universally use a linear classifier on the learned…

Multivariate associated kernel estimators, which depend on both target point and bandwidth matrix, are appropriate for partially or totally bounded distributions and generalize the classical ones as Gaussian. Previous studies on…

The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…

We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…

Minkowski tensors, also known as tensor valuations, provide robust $n$-point information for a wide range of random spatial structures. Local estimators for point clouds, e.g., representing voxelized data, however, are unavoidably biased…

Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that…

Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…

$C^*$-algebra-valued kernels could pave the way for the next generation of kernel machines. To further our fundamental understanding of learning with $C^*$-algebraic kernels, we propose a new class of positive definite kernels based on the…