Related papers: Kernels on fuzzy sets: an overview
This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…
Observables on effect algebras and their fuzzy versions obtained by means of confidence measures (Markov kernels) are studied. It is shown that, on effect algebras with the (E)-property, given an observable and a confidence measure, there…
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…
Efficiency criteria for conformal prediction, such as \emph{observed fuzziness} (i.e., the sum of p-values associated with false labels), are commonly used to \emph{evaluate} the performance of given conformal predictors. Here, we…
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 work we introduce KERNELIZED TRANSFORMER, a generic, scalable, data driven framework for learning the kernel function in Transformers. Our framework approximates the Transformer kernel as a dot product between spectral feature maps…
Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We…
Prediction sets offer a binary inclusion/exclusion for each element at the same fixed confidence level. We generalize to fuzzy prediction sets, which exclude elements at their own data-driven confidence level. Our key insight is that a…
This work concerns the construction and characterization of product kernels for multivariate approximation from a finite set of discrete samples. To this end, we consider composing different component kernels, each acting on a…
We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…
Measuring similarity between incomplete data is a fundamental challenge in web mining, recommendation systems, and user behavior analysis. Traditional approaches either discard incomplete data or perform imputation as a preprocessing step,…
Separation kernels are fundamental software of safety and security-critical systems, which provide to their hosted applications spatial and temporal separation as well as controlled information flows among partitions. The application of…
The purpose of this paper is to study more general real-valued functions of two variables than just metrics on a set X. We concentrate mainly on the classes of distances and almost distances. We also introduce the notion of a bridge on the…
In this short letter we present the construction of a bi-stochastic kernel p for an arbitrary data set X that is derived from an asymmetric affinity function {\alpha}. The affinity function {\alpha} measures the similarity between points in…
The aim of the present work is a comparative study of different persistence kernels applied to various classification problems. After some necessary preliminaries on homology and persistence diagrams, we introduce five different kernels…
Fuzzy logic is a way to argue with boolean predicates for which we only have a confidence value between 0 and 1 rather than a well defined truth value. It is tempting to interpret such a confidence as a probability. We use Markov kernels,…
Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…
Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…
This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing…
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…