Related papers: On a Relationship between the Correct Probability …
The use of Mutual Information (MI) as a measure to evaluate the efficiency of cryptosystems has an extensive history. However, estimating MI between unknown random variables in a high-dimensional space is challenging. Recent advances in…
Within entanglement theory there are criteria which certify that some quantum states cannot be distilled into pure entanglement. An example is the positive partial transposition criterion. Here we present, for the first time, the analogous…
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good…
We consider the problem of secret key extraction when $n$ honest parties and an eavesdropper share correlated information. We present a family of probability distributions and give the full characterization of its distillation properties.…
Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…
Estimation of the $\phi$-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent…
We studied the mutual information between a stimulus and a large system consisting of stochastic, statistically independent elements that respond to a stimulus. The Mutual Information (MI) of the system saturates exponentially with system…
We derive a tight lower bound on equivocation (conditional entropy), or equivalently a tight upper bound on mutual information between a signal variable and channel outputs. The bound is in terms of the joint distribution of the signals and…
While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the interrelation of two stochastic variables $X$ and $Y$, it fails for multidimensional variables such as Cartesian coordinates.…
By combining a bound on the absolute value of the difference of mutual information between two joint probablity distributions with a fixed variational distance, and a bound on the probability of a maximal deviation in variational distance…
Entropic uncertainty relations are powerful tools, especially in quantum cryptography. They typically bound the amount of uncertainty a third-party adversary may hold on a measurement outcome as a result of the measurement overlap. However,…
As the use of differential privacy (DP) becomes widespread, the development of effective tools for reasoning about the privacy guarantee becomes increasingly critical. In pursuit of this goal, we demonstrate novel relationships between DP…
As digital data transmission continues to scale, concerns about privacy grow increasingly urgent - yet privacy remains a socially constructed and ambiguously defined concept, lacking a universally accepted quantitative measure. This work…
Analysis of a probabilistic system often requires to learn the joint probability distribution of its random variables. The computation of the exact distribution is usually an exhaustive precise analysis on all executions of the system. To…
Estimating mutual information from observed samples is a basic primitive, useful in several machine learning tasks including correlation mining, information bottleneck clustering, learning a Chow-Liu tree, and conditional independence…
Consider two data providers that want to contribute data to a certain learning model. Recent works have shown that the value of the data of one of the providers is dependent on the similarity with the data owned by the other provider. It…
This paper studies an information-theoretic one-shot variable-length secret key agreement problem with public discussion. Let $X$ and $Y$ be jointly distributed random variables, each taking values in some measurable space. Alice and Bob…
The mutual information between two jointly distributed random variables $X$ and $Y$ is a functional of the joint distribution $P_{XY},$ which is sometimes difficult to handle or estimate. A coarser description of the statistical behavior of…
This paper shows that the Hirschfeld-Gebelein-R\'enyi maximal correlation between the message and the ciphertext provides good secrecy guarantees for cryptosystems that use short keys. We first establish a bound on the eavesdropper's…
Recently, the partial information decomposition emerged as a promising framework for identifying the meaningful components of the information contained in a joint distribution. Its adoption and practical application, however, have been…