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In recent years, machine learning has witnessed extensive adoption across various sectors, yet its application in medical image-based disease detection and diagnosis remains challenging due to distribution shifts in real-world data. In…

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

We describe a mechanism for performing probabilistic reasoning in influence diagrams using interval rather than point valued probabilities. We derive the procedures for node removal (corresponding to conditional expectation) and arc…

We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated…

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…

The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…

We enable aProbLog---a probabilistic logical programming approach---to reason in presence of uncertain probabilities represented as Beta-distributed random variables. We achieve the same performance of state-of-the-art algorithms for highly…

We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…

The objective of this work is to quantify the uncertainty in probability of failure estimates resulting from incomplete knowledge of the probability distributions for the input random variables. We propose a framework that couples the…

We study the problem of data integration from sources that contain probabilistic uncertain information. Data is modeled by possible-worlds with probability distribution, compactly represented in the probabilistic relation model. Integration…

The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown. We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the…

Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating…

Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…

A probabilistic database with attribute-level uncertainty consists of relations where cells of some attributes may hold probability distributions rather than deterministic content. Such databases arise, implicitly or explicitly, in the…

Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or…

The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

A filament is a high density, connected region in a point cloud. There are several methods for estimating filaments but these methods do not provide any measure of uncertainty. We give a definition for the uncertainty of estimated filaments…

This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second order Taylor expansions and polynomial bounding techniques is first…