Related papers: On a Relationship between the Correct Probability …
This paper discloses a simple algorithm for encrypting text messages, based on the NP-completeness of the subset sum problem, such that the similarity between encryptions is roughly proportional to the semantic similarity between their…
Previously, Barlow and Attneave hypothesised a link between biological vision and information maximisation. Following Shannon, information was defined using the probability of natural images. Several physiological and psychophysical…
We address the practical problems of estimating the information relations that characterize large networks. Building on methods developed for analysis of the neural code, we show that reliable estimates of mutual information can be obtained…
This paper is concerned with several security notions for information theoretically secure encryptions defined by the variational (statistical) distance. To ensure the perfect secrecy (PS), the mutual information is often used to evaluate…
L\'evy's Upward Theorem says that the conditional expectation of an integrable random variable converges with probability one to its true value with increasing information. In this paper, we use methods from effective probability theory to…
We consider the problem of estimating mutual information between dependent data, an important problem in many science and engineering applications. We propose a data-driven, non-parametric estimator of mutual information in this paper. The…
We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…
We study the connection between mixing properties for bipartite graphs and materialization of the mutual information in one-shot settings. We show that mixing properties of a graph imply impossibility to extract the mutual information…
The presence of mutual information in the research of deep learning has grown significantly. It has been proven that mutual information can be a good objective function to build a robust deep learning model. Most of the researches utilize…
We study private two-terminal hypothesis testing with simple hypotheses where the privacy goal is to ensure that participating in the testing protocol reveals little additional information about the other user's observation when a user is…
We derive complementarity relations for arbitrary quantum states of multiparty systems, of arbitrary number of parties and dimensions, between the purity of a part of the system and several correlation quantities, including entanglement and…
The mutual information between a set of stimuli and the elicited neural responses is compared to the corresponding decoded information. The decoding procedure is presented as an artificial distortion of the joint probabilities between…
Consider a random sample $X_1 , X_2 , ..., X_n$ drawn independently and identically distributed from some known sampling distribution $P_X$. Let $X_{(1)} \le X_{(2)} \le ... \le X_{(n)}$ represent the order statistics of the sample. The…
Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…
For discrete random variables X_1,..., X_n we construct an n by n matrix. In the (i,j) entry we put the mutual information I(X_i;X_j) between X_i and X_j. In particular, in the (i,i) entry we put the entropy H(X_i)=I(X_i;X_i) of X_i. This…
For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}.…
We consider the problem of decomposing the total mutual information conveyed by a pair of predictor random variables about a target random variable into redundant, unique and synergistic contributions. We focus on the relationship between…
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 a previous paper certain measurable criteria have been derived, that are sufficient to demonstrate the existence of Einstein-Podolsky-Rosen (EPR) correlations for measurements with continuous variable outcomes. Here it is shown how such…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…