Related papers: Erratum to: From Uncertainty Principles to Wegner …
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
Any data annotation for subjective tasks shows potential variations between individuals. This is particularly true for annotations of emotional responses to musical stimuli. While older approaches to music emotion recognition systems…
Rejoinder to ``Least angle regression'' by Efron et al. [math.ST/0406456]
The concept of uncertainty quanta for a general system is introduced and applied to some important problems in physics and mathematics. EPR paradox gives new clue to the further understanding of particle correlation which turns out to be…
The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with…
In Reliability Theory, uncertainty is measured by the Shannon entropy. Recently, in order to analyze the variability of such measure, varentropy has been introduced and studied. In this paper we define a new concept of varentropy for past…
There is an error in the proof (but not the truth) of Theorem 3.2 in the author's 1985 paper "The Double-Wedge Algebra for Quantum Fields on Schwarzschild and Minkowski Spacetimes" in "Communications in Mathematical Physics". The author…
Quantum uncertainty is the cornerstone of quantum mechanics which underlies many counterintuitive nonclassical phenomena. Recent studies remarkably showed that it also fundamentally limits nonclassical correlation, and crucially, a…
Correction to Annals of Probability 29 (2001) 1612--1624 [doi:10.1214/aop/1015345764].
We present some forms of uncertainty principle which involve in a new way localization operators, the concept of $\varepsilon$-concentration and the standard deviation of $L^2$ functions. We show how our results improve the classical…
Using changes of probability measure developed by \mbox{Grama} and Haeusler (Stochastic Process.\ Appl., 2000), we obtain two generalizations of the deviation inequalities of Lanzinger and Stadtm\"{u}ller (Stochastic Process.\ Appl., 2000)…
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for…
The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…
Uncertainty estimation is pivotal in machine learning, especially for classification tasks, as it improves the robustness and reliability of models. We introduce a novel `Epistemic Wrapping' methodology aimed at improving uncertainty…
Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps.…
This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).
This paper uses decision-theoretic principles to obtain new insights into the assessment and updating of probabilities. First, a new foundation of Bayesianism is given. It does not require infinite atomless uncertainties as did Savage s…
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…
The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty…
In this work we aim to obtain computationally-efficient uncertainty estimates with deep networks. For this, we propose a modified knowledge distillation procedure that achieves state-of-the-art uncertainty estimates both for in and…