Related papers: The Conditional Uncertainty Principle
Conditional independence plays a foundational role in database theory, probability theory, information theory, and graphical models. In databases, conditional independence appears in database normalization and is known as the (embedded)…
We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…
The theory of belief functions manages uncertainty and also proposes a set of combination rules to aggregate opinions of several sources. Some combination rules mix evidential information where sources are independent; other rules are…
Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…
We derive entropic uncertainty relations for successive generalized measurements by using general descriptions of quantum measurement within two {distinctive operational} scenarios. In the first scenario, by merging {two successive…
All scientific interpretations of statistical outputs depend on background (auxiliary) assumptions that are rarely delineated or explicitly interrogated. These include not only the usual modeling assumptions, but also deeper assumptions…
We introduce an axiomatic approach for characterizing quantum conditional entropy. Our approach relies on two physically motivated axioms: monotonicity under conditional majorization and additivity. We show that these two axioms provide…
A fundamental question in causal inference is whether it is possible to reliably infer manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most…
This paper introduces the notions of independence and conditional independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define independence and…
We present a framework to formally describe probabilistic system behavior and symbolically reason about it. In particular we aim at reasoning about possible failures and fault tolerance. We regard systems which are composed of different…
Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and…
In this paper we introduce a sublinear conditional operator with respect to a family of possibly nondominated probability measures in presence of multiple ordered default times. In this way we generalize the results of [5], where a…
Inferential models have been proposed for valid and efficient prior-free probabilistic inference. As it gradually gained popularity, this theory is subject to further developments for practically challenging problems. This paper considers…
In this thesis, I studied a mathematical development to define and quantify the uncertainty inherent in classical channels. This thesis starts with the introduction and background on how to formally think about uncertainty in the domain of…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher…
As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world…
Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…
Possibilistic conditional independence is investigated: we propose a definition of this notion similar to the one used in probability theory. The links between independence and non-interactivity are investigated, and properties of these…
Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually…