Related papers: Bayesian Covariance Modelling of Large Tensor-Vari…
Deep learning offers promising new ways to accurately model aleatoric uncertainty in robotic state estimation systems, particularly when the uncertainty distributions do not conform to traditional assumptions of being fixed and Gaussian. In…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor…
Accurate modelling and quantification of predictive uncertainty is crucial in deep learning since it allows a model to make safer decisions when the data is ambiguous and facilitates the users' understanding of the model's confidence in its…
Recent research has proven neural networks to be a powerful tool for performing hyperspectral imaging (HSI) target identification. However, many deep learning frameworks deliver a single material class prediction and operate on a per-pixel…
We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the…
We develop a Bayesian approach to learning from sequential data by using Gaussian processes (GPs) with so-called signature kernels as covariance functions. This allows to make sequences of different length comparable and to rely on strong…
This paper frames a general prediction system as an observer traveling around a continuous space, measuring values at some locations, and predicting them at others. The observer is completely agnostic about any particular task being solved;…
Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper we refer to this task as "semi-described…
Being able to reliably assess not only the \emph{accuracy} but also the \emph{uncertainty} of models' predictions is an important endeavour in modern machine learning. Even if the model generating the data and labels is known, computing the…
Forecasting future events is a fundamental challenge for temporal knowledge graphs (tKG). As in real life predicting a mean function is most of the time not sufficient, but the question remains how confident can we be about our prediction?…
In many inverse problems, the unknown is composed of multiple components with different regularities, for example, in imaging problems, where the unknown can have both rough and smooth features. We investigate linear Bayesian inverse…
Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection, it would be appealing to…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
Groundwater flow modeling is commonly used to calculate groundwater heads, estimate groundwater flow paths and travel times, and provide insights into solute transport processes within an aquifer. However, the values of input parameters…
We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
Efficient assessment of convolved hidden Markov models is discussed. The bottom-layer is defined as an unobservable categorical first-order Markov chain, while the middle-layer is assumed to be a Gaussian spatial variable conditional on the…
A key element in transfer learning is representation learning; if representations can be developed that expose the relevant factors underlying the data, then new tasks and domains can be learned readily based on mappings of these salient…
A central question in multimodal neuroimaging analysis is to understand the association between two imaging modalities and to identify brain regions where such an association is statistically significant. In this article, we propose a…