Related papers: The Conditional Uncertainty Principle

We use the law of total variance to generate multiple expansions for the posterior predictive variance. These expansions are sums of terms involving conditional expectations and conditional variances and provide a quantification of the…

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…

A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…

The uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The situation is different if one can build a…

We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…

Rule-based classification models described in the language of logic directly predict boolean values, rather than modeling a probability and translating it into a prediction as done in statistical models. The vast majority of existing…

Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…

If uncertainty is modelled by a probability measure, decisions are typically made by choosing the option with the highest expected utility. If an imprecise probability model is used instead, this decision rule can be generalised in several…

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…

To more flexibly balance between exploration and exploitation, a new meta-heuristic method based on Uncertainty Principle concepts is proposed in this paper. UP is is proved effective in multiple branches of science. In the branch of…

Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the…

We develop a new semantics for defeasible inference based on extended probability measures allowed to take infinitesimal values, on the interpretation of defaults as generalized conditional probability constraints and on a preferred-model…

Quantum uncertainty relations are typically analyzed for a pair of incompatible observables, however, the concept per se naturally extends to situations of more than two observables. In this work, we obtain tripartite quantum…

Multimodal foundation models offer a promising framework for robotic perception and planning by processing sensory inputs to generate actionable plans. However, addressing uncertainty in both perception (sensory interpretation) and…

In its most basic form, decision-making can be viewed as a computational process that progressively eliminates alternatives, thereby reducing uncertainty. Such processes are generally costly, meaning that the amount of uncertainty that can…

In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…

Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered…

We provide a unified and strengthened framework for the product form and the sum form variance-based uncertainty relations by constructing a unified uncertainty relation. In the unified framework, we deduce that the uncertainties of the…

In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution…

Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…