Related papers: Kernel Characterisations of Stochastic Orders With…
We formalize a generalized form of the Pareto principle - ``fraction $p$ of inputs yields fraction $1-p$ of outputs'' - as a property of non-negative gain densities $\ell \in L^1([0,1])$, working with the decreasing rearrangement to obtain…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
Comparison of two univariate distributions based on independent samples from them is a fundamental problem in statistics, with applications in a wide variety of scientific disciplines. In many situations, we might hypothesize that the two…
A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions…
We introduce a new partial order on the class of stochastically monotone Markov kernels having a given stationary distribution $\pi$ on a given finite partially ordered state space $\mathcal{X}$. When $K\preceq L$ in this partial order we…
We propose a novel class of kernels to alleviate the high computational cost of large-scale nonparametric learning with kernel methods. The proposed kernel is defined based on a hierarchical partitioning of the underlying data domain, where…
We propose a norm of consistency for a mixed set of defeasible and strict sentences, based on a probabilistic semantics. This norm establishes a clear distinction between knowledge bases depicting exceptions and those containing outright…
We present novel graph kernels for graphs with node and edge labels that have ordered neighborhoods, i.e. when neighbor nodes follow an order. Graphs with ordered neighborhoods are a natural data representation for evolving graphs where…
Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…
For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done…
This paper discusses the problem of marrying structural similarity with semantic relatedness for Information Extraction from text. Aiming at accurate recognition of relations, we introduce local alignment kernels and explore various…
Accurate inference on a scalar interest parameter in the presence of a nuisance parameter may be obtained using an adjusted version of the signed root likelihood ratio statistic, in particular Barndorff-Nielsen's $R^*$ statistic. The…
The likelihood ratio is a crucial quantity for statistical inference in science that enables hypothesis testing, construction of confidence intervals, reweighting of distributions, and more. Many modern scientific applications, however,…
We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these…
Score-based causal discovery methods can effectively identify causal relationships by evaluating candidate graphs and selecting the one with the highest score. One popular class of scores is kernel-based generalized score functions, which…
Machine learning typically presupposes classical probability theory which implies that aggregation is built upon expectation. There are now multiple reasons to motivate looking at richer alternatives to classical probability theory as a…
Stochastic network calculus is a tool for computing error bounds on the performance of queueing systems. However, deriving accurate bounds for networks consisting of several queues or subject to non-independent traffic inputs is…
We derive and prove the path-kernel formula for the linear response (parameter-derivative of averaged statistics) of SDEs. The parameter may affect the drift coefficient, the diffusion coefficient, and the initial condition. The formula…
The majority of popular graph kernels is based on the concept of Haussler's $\mathcal{R}$-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…