Related papers: Generalized RBF kernel for incomplete data

This paper deals with the nonparametric density estimation of the regression error term assuming its independence with the covariate. The difference between the feasible estimator which uses the estimated residuals and the unfeasible one…

In this paper, we will show that the recently introduced graphical model: Conditional Random Fields (CRF) provides a template to integrate micro-level information about biological entities into a mathematical model to understand their…

Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on…

Graph kernels have been successfully applied to many graph classification problems. Typically, a kernel is first designed, and then an SVM classifier is trained based on the features defined implicitly by this kernel. This two-stage…

The Gaussian kernel is a very popular kernel function used in many machine learning algorithms, especially in support vector machines (SVMs). It is more often used than polynomial kernels when learning from nonlinear datasets, and is…

Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed…

Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…

Data imputation, the process of filling in missing feature elements for incomplete data sets, plays a crucial role in data-driven learning. A fundamental belief is that data imputation is helpful for learning performance, and it follows…

SVM with an RBF kernel is usually one of the best classification algorithms for most data sets, but it is important to tune the two hyperparameters $C$ and $\gamma$ to the data itself. In general, the selection of the hyperparameters is a…

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 provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…

This paper presents a method for building a preconditioner for a kernel ridge regression problem, where the preconditioner is not only effective in its ability to reduce the condition number substantially, but also efficient in its…

To improve accuracy and speed of regressions and classifications, we present a data-based prediction method, Random Bits Regression (RBR). This method first generates a large number of random binary intermediate/derived features based on…

Consider a setting with multiple units (e.g., individuals, cohorts, geographic locations) and outcomes (e.g., treatments, times, items), where the goal is to learn a multivariate distribution for each unit-outcome entry, such as the…

Support vector data description (SVDD) is a popular technique for detecting anomalies. The SVDD classifier partitions the whole space into an inlier region, which consists of the region near the training data, and an outlier region, which…

Consider the classical supervised learning problem: we are given data $(y_i,{\boldsymbol x}_i)$, $i\le n$, with $y_i$ a response and ${\boldsymbol x}_i\in {\mathcal X}$ a covariates vector, and try to learn a model $f:{\mathcal…

Multivariate associated kernel estimators, which depend on both target point and bandwidth matrix, are appropriate for partially or totally bounded distributions and generalize the classical ones as Gaussian. Previous studies on…

Quantum kernels quantify similarity between data points by measuring the inner product between quantum states, computed through quantum circuit measurements. By embedding data into quantum systems, quantum kernel feature maps, that may be…

Under covariate shift, training (source) data and testing (target) data differ in input space distribution, but share the same conditional label distribution. This poses a challenging machine learning task. Robust Bias-Aware (RBA)…

Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive-to-evaluate. To tackle this challenge, Bayesian optimization, which conducts sequential design via a posterior distribution…