Related papers: Bayesian Kernel and Mutual $k$-Nearest Neighbor Re…
Gaussian processes offers a convenient way to perform nonparametric reconstructions of observational data assuming only a kernel which describes the covariance between neighbouring points in a data set. We approach the ambiguity in the…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and…
Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting…
A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…
The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm…
Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear…
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…
Nonlinear Bayesian update for a prior ensemble is proposed to extend traditional ensemble Kalman filtering to settings characterized by non-Gaussian priors and nonlinear measurement operators. In this framework, the observed component is…
Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised…
Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised…
We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…
Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…
In frequentist inference, minimizing the Hellinger distance between a kernel density estimate and a parametric family produces estimators that are both robust to outliers and statistically efficienty when the parametric model is correct.…
The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…
A specific implementation of Bayesian model averaging has recently been suggested as a method for the calibration of ensemble temperature forecasts. We point out the similarities between this new approach and an earlier method known as…
In this paper we introduce a kernel-based measure for detecting differences between two conditional distributions. Using the `kernel trick' and nearest-neighbor graphs, we propose a consistent estimate of this measure which can be computed…