Related papers: Kernel-based guarantees for nonlinear parametric m…

Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…

For Bayesian optimization (BO) on high-dimensional data with complex structure, neural network-based kernels for Gaussian processes (GPs) have been used to learn flexible surrogate functions by the high representation power of deep…

The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…

In this work, we broadly connect kernel-based filtering (e.g. approaches such as the bilateral filters and nonlocal means, but also many more) with general variational formulations of Bayesian regularized least squares, and the related…

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…

Structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or…

Many recent theoretical works on \emph{meta-learning} aim to achieve guarantees in leveraging similar representational structures from related tasks towards simplifying a target task. The main aim of theoretical guarantees on the subject is…

Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in…

In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered…

Some applied researchers hesitate to use nonparametric methods, worrying that they will lose power in small samples or overfit the data when simpler models are sufficient. We argue that at least some of these concerns are unfounded when…

We propose a set of kernel-based tools to evaluate the designs and tune the hyperparameters of conditional sequence models, with a focus on problems in computational biology. The backbone of our tools is a new measure of discrepancy between…

By removing irrelevant and redundant features, feature selection aims to find a good representation of the original features. With the prevalence of unlabeled data, unsupervised feature selection has been proven effective in alleviating the…

We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…

Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location-scale mixture of Gaussian kernels is the golden standard, both having nice…

Normative and task-driven theories offer powerful top-down explanations for biological systems, yet the goals of quantitatively arbitrating between competing theories, and utilizing them as inductive biases to improve data-driven fits of…

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…