Related papers: A Data-Adaptive Prior for Bayesian Learning of Ker…
Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown…
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…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise…
Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…
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 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…
We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly…
A key property of neural networks driving their success is their ability to learn features from data. Understanding feature learning from a theoretical viewpoint is an emerging field with many open questions. In this work we capture…
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…
Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependence and the attractive feature of being resolution-invariant.…
Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…
Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform…
Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…
Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…
This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. Following the manifold hypothesis and adopting a generative modelling…
This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…
Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…
Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and…
Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…