Related papers: Probabilistic Data with Continuous Distributions

We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…

Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…

The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the…

In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…

In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…

This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…

Count data take on non-negative integer values and are challenging to properly analyze using standard linear-Gaussian methods such as linear regression and principal components analysis. Generalized linear models enable direct modeling of…

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…

Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…

Language modeling has shifted in recent years from a distribution over strings to prediction models with textual inputs and outputs for general-purpose tasks. This position paper highlights the often overlooked implications of this shift…

Today, many different probabilistic programming languages exist and even more inference mechanisms for these languages. Still, most logic programming based languages use backward reasoning based on SLD resolution for inference. While these…

The emergence of generative AI models has dramatically expanded the availability and use of synthetic data across scientific, industrial, and policy domains. While these developments open new possibilities for data analysis, they also raise…

Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al's ProbLog and Vennekens et al's LPAD, is aimed at combining statistical and logical knowledge representation and inference. A key…

Probabilistic programming has become a standard practice to model stochastic events and learn about the behavior of nature in different scientific contexts, ranging from Genetics and Ecology to Linguistics and Psychology. However, domain…

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…

Query answering over probabilistic data is an important task but is generally intractable. However, a new approach for this problem has recently been proposed, based on structural decompositions of input databases, following, e.g., tree…

Probabilistic programming languages (PPLs) are an expressive means of representing and reasoning about probabilistic models. The computational challenge of probabilistic inference remains the primary roadblock for applying PPLs in practice.…

Diffusion generative models have recently been applied to domains where the available data can be seen as a discretization of an underlying function, such as audio signals or time series. However, these models operate directly on the…

This article provides a mathematically rigorous introduction to denoising diffusion probabilistic models (DDPMs), sometimes also referred to as diffusion probabilistic models or diffusion models, for generative artificial intelligence. We…

This thesis presents a series of theoretical results and practical realisations about the theory of computation in distributive categories. Distributive categories have been proposed as a foundational tool for Computer Science in the last…