Related papers: Comprehensive Description of Uncertainty in Measur…
Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these non-perturbative functions are generated through fits to global data. A problem that several PDF…
Understanding which concepts models can and cannot represent has been fundamental to many tasks: from effective and responsible use of models to detecting out of distribution data. We introduce Gaussian process probes (GPP), a unified and…
Gaussian Mixture Models (GMMs) commonly arise in communication systems, particularly in bilinear joint estimation and detection problems. Although the product of GMMs is still a GMM, as the number of factors increases, the number of…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
Mapping with uncertainty representation is required in many research domains, especially for localization. Although there are many investigations regarding the uncertainty of the pose estimation of an ego-robot with map information, the…
Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of…
In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be…
Reasoning about the pose, i.e. position and orientation of objects is one of the cornerstones of robotic manipulation under uncertainty. In a number of joint research projects our group is developing a robotic perception system that…
We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
Under ideal conditions, the probability density function (PDF) of a random variable, such as a sensor measurement, would be well known and amenable to computation and communication tasks. However, this is often not the case, so the user…
Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…
Quantifying predictive uncertainty is essential for real world machine learning applications, especially in scenarios requiring reliable and interpretable predictions. Many common parametric approaches rely on neural networks to estimate…
Multidimensional data is often associated with uncertainties that are not well-described by normal distributions. In this work, we describe how such distributions can be projected to a low-dimensional space using uncertainty-aware principal…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
Single-channel deep speech enhancement approaches often estimate a single multiplicative mask to extract clean speech without a measure of its accuracy. Instead, in this work, we propose to quantify the uncertainty associated with clean…
Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…
A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the…
This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of…