Related papers: On the Consistency of Kernel Methods with Dependen…

Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…

The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…

As a promising step, the performance of data analysis and feature learning are able to be improved if certain pattern matching mechanism is available. One of the feasible solutions can refer to the importance estimation of instances, and…

Quantum kernel methods (QKMs) have emerged as a prominent framework for supervised quantum machine learning. Unlike variational quantum algorithms, which rely on gradient-based optimisation and may suffer from issues such as barren…

Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert…

Ensemble methods such as boosting combine multiple learners to obtain better prediction than could be obtained from any individual learner. Here we propose a principled framework for directly constructing ensemble learning methods from…

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

Imbalanced response variable distribution is a common occurrence in data science. In fields such as fraud detection, medical diagnostics, system intrusion detection and many others where abnormal behavior is rarely observed the data under…

Evaluation and validation of complicated control systems are crucial to guarantee usability and safety. Usually, failure happens in some very rarely encountered situations, but once triggered, the consequence is disastrous. Accelerated…

We propose a kernel-based nonparametric estimator for the causal effect when the cause is corrupted by error. We do so by generalizing estimation in the instrumental variable setting. Despite significant work on regression with measurement…

Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite…

Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…

This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…

Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While…

Data-driven techniques for analysis, modeling, and control of complex dynamical systems are on the uptake. Koopman theory provides the theoretical foundation for the popular kernel extended dynamic mode decomposition (kEDMD). In this work,…

Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…

We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…

We apply kernel mean embedding methods to sample-based stochastic optimization and control. Specifically, we use the reduced-set expansion method as a way to discard sampled scenarios. The effect of such constraint removal is improved…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…