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Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an…

Inspired by kernel methods that have been used extensively in achieving efficient facial animation retargeting, this paper presents a solution to retargeting facial animation in virtual character's face model based on the kernel projection…

Partial least squares regression (PLSR) has been a popular technique to explore the linear relationship between two datasets. However, most of algorithm implementations of PLSR may only achieve a suboptimal solution through an optimization…

Current deep image super-resolution (SR) approaches aim to restore high-resolution images from down-sampled images or by assuming degradation from simple Gaussian kernels and additive noises. However, these techniques only assume crude…

With massive high-dimensional data now commonplace in research and industry, there is a strong and growing demand for more scalable computational techniques for data analysis and knowledge discovery. Key to turning these data into knowledge…

We consider the problem of conditional independence (CI) testing and adopt a kernel-based approach. Kernel-based CI tests embed variables in reproducing kernel Hilbert spaces, regress their embeddings on the conditioning variables, and test…

We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discrete signed measures and enable…

The performance of reproducing kernel Hilbert space-based methods is known to be sensitive to the choice of the reproducing kernel. Choosing an adequate reproducing kernel can be challenging and computationally demanding, especially in…

This work presents generalized low-rank signal decompositions with the aid of switching techniques and adaptive algorithms, which do not require eigen-decompositions, for space-time adaptive processing. A generalized scheme is proposed to…

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

Estimating the kernel mean in a reproducing kernel Hilbert space is a critical component in many kernel learning algorithms. Given a finite sample, the standard estimate of the target kernel mean is the empirical average. Previous works…

Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher-order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non-Gaussian…

The abundance of training data is not guaranteed in various supervised learning applications. One of these situations is the post-earthquake regional damage assessment of buildings. Querying the damage label of each building requires a…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a…

Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…