arXiv research

The paper extends consistency results for sequential design strategies to vector-valued Gaussian processes.

Study improves self-normalized bounds for vector-valued processes beyond sub-Gaussianity.

Gaussian processes adapted for Riemannian manifolds using gauge-independent kernels.

Multi-output Gaussian processes (MOGP) are probability distributions over vector-valued functions, and have been previously used for multi-output regression and for multi-class classification. A less explored facet of the multi-output Gaussian process is that it can be used as a generative model for vector-valued rando…

The paper introduces novel Gaussian process models for vector-valued signals on manifolds.

This work develops discrete Gaussian models for vector-valued data on triangular meshes.

Optimal transport for vector Gaussian mixtures improves efficiency and structure preservation.

Gaussian processes adapted for non-Euclidean spaces enhance decision-making.

This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process, the mixture model has the advantages of modeling multimodal data and alleviating…

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in all likelihoods as latent functions. Our multi-output Gaussian process uses a c…

Framework for transferring discount curve estimates across fixed-income product classes.

We consider vector valued, unit variance Gaussian processes defined over stratified manifolds and the geometry of their excursion sets. In particular, we develop an explicit formula for the expectation of all the Lipschitz--Killing curvatures of these sets. Whereas our motivation is primarily probabilistic, with statis…

Randomized algorithm solves vector-valued regression problems with low-rank operators.

tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.

We improve bounds for stochastic processes, especially those with heavy tails.

We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different covariance matrices. This model contains as special cases the standard setting …

The paper develops sampling methods for ocean phenomena based on temperature and salinity measurements.

fCBO optimizes interventions in causal graphs using Gaussian processes.

We present the first treatment of the arc length of the Gaussian Process (GP) with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest. Previously, only paths in one dimension have been considered, with no theoretical con…

The paper shows vector-valued risk measures ignore dependence structures.

Study on identifying most preferred policy in bandits with vector-valued rewards.

A recent novel extension of multi-output Gaussian processes handles heterogeneous outputs assuming that each output has its own likelihood function. It uses a vector-valued Gaussian process prior to jointly model all likelihoods' parameters as latent functions drawn from a Gaussian process with a linear model of coregi…

Deep Gaussian processes can have non-degenerate and non-Gaussian limits.

Gaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to re-formulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, re-formulation is not always workable a…

We prove a conjecture about approximating Gaussian Processes on one dimension.

Andreas Maurer in the paper "A vector-contraction inequality for Rademacher complexities" extended the contraction inequality for Rademacher averages to Lipschitz functions with vector-valued domains; He did it replacing the Rademacher variables in the bounding expression by arbitrary idd symmetric and sub-gaussian var…

Study optimizes online learning for vector-valued data regression.

A market model with $d$ assets in discrete time is considered where trades are subject to proportional transaction costs given via bid-ask spreads, while the existence of a numèraire is not assumed. It is shown that robust no arbitrage holds if, and only if, there exists a Pareto solution for some vector-valued utility…

The contraction inequality for Rademacher averages is extended to Lipschitz functions with vector-valued domains, and it is also shown that in the bounding expression the Rademacher variables can be replaced by arbitrary iid symmetric and sub-gaussian variables. Example applications are given for multi-category learnin…

Abstract: Generalizes multisymplectic forms to vector-valued versions.

Algorithm identifies Pareto optimal designs efficiently for noisy, multi-objective functions.

We discuss sharp Sobolev inequalities for vector valued maps.

Development of metrics for structural data-generating mechanisms is fundamental in machine learning and the related fields. In this paper, we give a general framework to construct metrics on random nonlinear dynamical systems, defined with the Perron-Frobenius operators in vector-valued reproducing kernel Hilbert space…

Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBS). Basic properties of the spaces and the associated reproducing kernels are investigated. We also present feature map constructions and several concrete examples of vector-valued RK…

Optimal rates for vector-valued regression on various norms.

SL(n) covariant valuations on Orlicz spaces are represented and characterized.

Boosting framework for vector-valued prediction with geometric stability.

We consider optimization of composite objective functions, i.e., of the form $f(x)=g(h(x))$, where $h$ is a black-box derivative-free expensive-to-evaluate function with vector-valued outputs, and $g$ is a cheap-to-evaluate real-valued function. While these problems can be solved with standard Bayesian optimization, we…

Study confirms learning rates for vector-valued spectral algorithms, proving consistency.

The space of vector-valued forms on any manifold is a graded Lie algebra with respect to the Frolicher-Nijenhuis bracket. In this paper we consider multiplicative vector-valued forms on Lie groupoids and show that they naturally form a graded Lie subalgebra. Along the way, we discuss various examples and different char…

Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and unlabeled data, we derive novel semi-supervised excess risk bounds for general v…

The paper proposes methods to find a shared active subspace for multivariate vector-valued functions.

We present a framework to derive risk bounds for vector-valued learning with a broad class of feature maps and loss functions. Multi-task learning and one-vs-all multi-category learning are treated as examples. We discuss in detail vector-valued functions with one hidden layer, and demonstrate that the conditions under…

Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kernel Hilbert spaces. F…

New imputation strategies improve signature models for irregular time series.

The sequence of moments of a vector-valued random variable can characterize its law. We study the analogous problem for path-valued random variables, that is stochastic processes, by using so-called robust signature moments. This allows us to derive a metric of maximum mean discrepancy type for laws of stochastic proce…

We approximate derivatives of functions on manifolds by embedding them and applying vector-valued operators.

Paper introduces vector-valued variation spaces for multi-output neural networks.