Related papers: Guessing under source uncertainty
The partial information decomposition (PID) aims to quantify the amount of redundant information that a set of sources provides about a target. Here, we show that this goal can be formulated as a type of information bottleneck (IB) problem,…
Motivated by the advances of quantum Darwinism and recognizing the role played by redundancy in identifying the small subset of quantum states with resilience characteristic of objective classical reality, we explore the implications of…
The information content of a source is defined in terms of the minimum number of bits needed to store the output of the source in a perfectly recoverable way. A similar definition can be given in the case of quantum sources, with qubits…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
In his dissertation, Wadge defined a notion of guessability on subsets of the Baire space and gave two characterizations of guessable sets. A set is guessable iff it is in the second ambiguous class (boldface Delta^0_2), iff it is…
The efficiency of a code is estimated by its redundancy $R$, while the complexity of a code is estimated by its average delay $\bar N$. In this work we construct word-based codes, for which $R \lesssim \bar N^{-5/3}$. Therefore, word-based…
This paper presents a novel theoretical study of the general problem of multiple source adaptation using the notion of Renyi divergence. Our results build on our previous work [12], but significantly broaden the scope of that work in…
As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $\epsilon$-accurate…
How much one has learned from an experiment is quantifiable by the information gain, also known as the Kullback-Leibler divergence. The narrowing of the posterior parameter distribution $P(\theta|D)$ compared with the prior parameter…
This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…
A goal in the forensic interpretation of scientific evidence is to make an inference about the source of a trace of unknown origin. The evidence is composed of the following three elements: (a) the trace of unknown origin, (b) a sample from…
Motivated by earlier results on universal randomized guessing, we consider an individual-sequence approach to the guessing problem: in this setting, the goal is to guess a secret, individual (deterministic) vector $x^n=(x_1,\ldots,x_n)$, by…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
The aim of this work is to provide bounds connecting two probability measures of the same event using R\'enyi $\alpha$-Divergences and Sibson's $\alpha$-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence…
The analysis of decision making under uncertainty is closely related to the analysis of probabilistic inference. Indeed, much of the research into efficient methods for probabilistic inference in expert systems has been motivated by the…
This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles…
According to the probability ranking principle, the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key…
We introduce the study of information leakage through \emph{guesswork}, the minimum expected number of guesses required to guess a random variable. In particular, we define \emph{maximal guesswork leakage} as the multiplicative decrease,…