Related papers: Correlated Boolean Operators for Uncertainty Logic

This paper introduces two families of probability distributions for Bayesian analysis of hypertoroidal data. The first family consists of symmetric distributions derived from the projection of multivariate normal distributions under…

We employ distribution regression (DR) to estimate the joint distribution of two outcome variables conditional on chosen covariates. While Bivariate Distribution Regression (BDR) is useful in a variety of settings, it is particularly…

Existing results on cooperative control of multi-agent systems with unknown control directions require that the underlying topology is either fixed with a strongly connected graph or switching between different strongly connected graphs.…

For the quantum stochastic processes generated by the Boolean Commutation Relations, we prove the following version of De Finetti Theorem: each of such Boolean process is exchangeable if and only if it is independent and identically…

We show that the ability to create entanglement is necessary for execution of bipartite quantum gates even when they are applied to unentangled states and create no entanglement. Starting with a simple example we demonstrate that to execute…

Decomposing predictive uncertainty into epistemic (model ignorance) and aleatoric (data ambiguity) components is central to reliable decision making, yet most methods estimate both from the same predictive distribution. Recent empirical and…

Whilst an abundance of techniques have recently been proposed to generate counterfactual explanations for the predictions of opaque black-box systems, markedly less attention has been paid to exploring the uncertainty of these generated…

This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for…

We formulate the non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point, and the effects of fluctuations…

We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic…

Parametric copula families have been known to flexibly capture various dependence patterns, e.g., either positive or negative dependence in either the lower or upper tails of bivariate distributions. In this paper, our objective is to…

Copulas are used to construct joint distributions in many areas. In some problems, it is necessary to deal with correlation structures that are more complicated than the commonly known copulas. A finite order multivariate Hermite polynomial…

In this paper we re-examine the traditional problem of connecting the internal fluctuations of a system to its response to external forcings and extend the classical theory in order to be able to encompass also nonlinear processes. With…

This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of $Phi$-divergences. An axiomatic framework for this purpose is provided, after which we…

Backdoors and backbones of Boolean formulas are hidden structural properties. A natural goal, already in part realized, is that solver algorithms seek to obtain substantially better performance by exploiting these structures. However, the…

We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…

Uncertainty in large language model (LLM)-based systems is often studied at the level of a single model output, yet deployed LLM applications are compound systems in which uncertainty is transformed and reused across model internals,…

We are interested in investigating the statistical properties of extreme values for strongly correlated variables. The starting motivation is to understand how the strong-correlation properties of power-law distributed processes affect the…

Empirical evidence has revealed that biological regulatory systems are controlled by high-level coordination between topology and Boolean rules. In this study, we study the joint effects of degree and Boolean functions on the stability of…

Long-term temporal correlations observed in event sequences of natural and social phenomena have been characterized by algebraically decaying autocorrelation functions. Such temporal correlations can be understood not only by heterogeneous…