Related papers: Kernel Angle Dependence Measures for Complex Objec…

In recent years, samples of time-varying object data such as time-varying networks that are not in a vector space have been increasingly collected. These data can be viewed as elements of a general metric space that lacks local or global…

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…

We study change-point detection for high-dimensional data in regimes where inference must be performed from small batches of observations. Our primary focus is the high-dimensional, low sample size (HDLSS) regime, where the sequence length…

This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…

We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…

We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…

Human skeleton-based action recognition has long been an indispensable aspect of artificial intelligence. Current state-of-the-art methods tend to consider only the dependencies between connected skeletal joints, limiting their ability to…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…

Recent work on background subtraction has shown developments on two major fronts. In one, there has been increasing sophistication of probabilistic models, from mixtures of Gaussians at each pixel [7], to kernel density estimates at each…

We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…

The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalisation of classical measures of linear dependence (such as the covariance) not…

A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the…

Parametric factor copula models typically work well in modeling multivariate dependencies due to their flexibility and ability to capture complex dependency structures. However, accurately estimating the linking copulas within these models…

In this paper, we consider the problem of estimating the covariance kernel and its eigenvalues and eigenfunctions from sparse, irregularly observed, noise corrupted and (possibly) correlated functional data. We present a method based on…

Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…

Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…

It is well known that the effect of quantum nonlocality, as witnessed by violation of a Bell inequality, can be observed even when relaxing the assumption of measurement independence, i.e. allowing for the source to be partially correlated…

An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…

Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…