Related papers: Conditional expectation using compactification ope…
We propose a scalable and theoretically grounded low-rank conditional expectation model for recursive Monte Carlo optimal stopping problems, in particular American option pricing. Our method reformulates the estimation of continuation…
Computing the expectation of kernel functions is a ubiquitous task in machine learning, with applications from classical support vector machines to exploiting kernel embeddings of distributions in probabilistic modeling, statistical…
The linear conditional expectation (LCE) provides a best linear (or rather, affine) estimate of the conditional expectation and hence plays an important r\^ole in approximate Bayesian inference, especially the Bayes linear approach. This…
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…
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…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
Calibration ensures that probabilistic forecasts meaningfully capture uncertainty by requiring that predicted probabilities align with empirical frequencies. However, many existing calibration methods are specialized for post-hoc…
A non-Euclidean generalization of conditional expectation is introduced and characterized as the minimizer of expected intrinsic squared-distance from a manifold-valued target. The computational tractable formulation expresses the…
In this paper, we illustrate the effectiveness of reproducing kernel Hilbert space techniques in the study of composition operators. For weighted Hardy spaces on the unit disk, we characterize the composition operators whose adjoint is…
We consider the problem of learning convolution operators associated to compact Abelian groups. We study a regularization-based approach and provide corresponding learning guarantees under natural regularity conditions on the convolution…
Given the joint distribution of two random variables $X,Y$ on some second countable locally compact Hausdorff space, we investigate the statistical approximation of the $L^2$-operator defined by $[Pf](x) := \mathbb{E}[ f(Y) \mid X = x ]$…
A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical priors, typically encoded through the PDE operator, into a…
We study prediction-powered conditional inference in the setting where labeled data are scarce, unlabeled covariates are abundant, and a black-box machine-learning predictor is available. The goal is to perform statistical inference on…
We introduce a novel conditional density estimation model termed the conditional density operator (CDO). It naturally captures multivariate, multimodal output densities and shows performance that is competitive with recent neural…
Conditional kernel mean embeddings are nonparametric models that encode conditional expectations in a reproducing kernel Hilbert space. While they provide a flexible and powerful framework for probabilistic inference, their performance is…
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…
In this paper we de ne conditional random elds in reproducing kernel Hilbert spaces and show connections to Gaussian Process classi cation. More speci cally, we prove decomposition results for undirected graphical models and we give…
In spatial statistics and machine learning, the kernel matrix plays a pivotal role in prediction, classification, and maximum likelihood estimation. A thorough examination reveals that for large sample sizes, the kernel matrix becomes…
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…
Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than…