Related papers: Gaussian mixture models in Hilbert spaces via kern…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
We describe a new MCMC method optimized for the sampling of probability measures on Hilbert space which have a density with respect to a Gaussian; such measures arise in the Bayesian approach to inverse problems, and in conditioned…
In this paper, we develop an approach to exploiting kernel methods with manifold-valued data. In many computer vision problems, the data can be naturally represented as points on a Riemannian manifold. Due to the non-Euclidean geometry of…
Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…
Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact…
With the emergence of passive and active optical sensors available for geospatial imaging, information fusion across sensors is becoming ever more important. An important aspect of single (or multiple) sensor geospatial image analysis is…
We focus on kernel methods for set-valued inputs and their application to Bayesian set optimization, notably combinatorial optimization. We investigate two classes of set kernels that both rely on Reproducing Kernel Hilbert Space…
This paper introduces a new framework for quantifying predictive uncertainty for both data and models that relies on projecting the data into a Gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
Learning in the reproducing kernel Hilbert space (RKHS) such as the support vector machine has been recognized as a promising technique. It continues to be highly effective and competitive in numerous prediction tasks, particularly in…
This paper presents a general coding method where data in a Hilbert space are represented by finite dimensional coding vectors. The method is based on empirical risk minimization within a certain class of linear operators, which map the set…
This article presents general procedures for constructing, estimating, and testing Hilbert space multi-dimensional (HSM) models, which are based on quantum probability theory. HSM models can be applied to collections of K different…
This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…
Clustering in high-dimensional spaces is a difficult problem which is recurrent in many domains, for example in image analysis. The difficulty is due to the fact that high-dimensional data usually live in different low-dimensional subspaces…
This work studies the convergence and finite sample approximations of entropic regularized Wasserstein distances in the Hilbert space setting. Our first main result is that for Gaussian measures on an infinite-dimensional Hilbert space,…
Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework,…
We propose a novel framework for matching estimators for causal effect from observational data that is based on minimizing the dual norm of estimation error when expressed as an operator. We show that many popular matching estimators can be…
Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional…