Related papers: Pointwise Relations between Information and Estima…
We investigate the correlations of initially separable probability distributions in a globally pure bipartite system with two degrees of freedom for classical and quantum systems. A classical version of the quantum linear mutual information…
We consider the characterization of the asymptotic behavior of the average minimum mean-squared error (MMSE) and the average mutual information in scalar and vector fading coherent channels, where the receiver knows the exact fading channel…
Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…
Information estimates such as the ``direct method'' of Strong et al. (1998) sidestep the difficult problem of estimating the joint distribution of response and stimulus by instead estimating the difference between the marginal and…
An important notion of common information between two random variables is due to Wyner. In this paper, we derive a lower bound on Wyner's common information for continuous random variables. The new bound improves on the only other general…
In recent years, there has been an upswing of interest in estimating information from data emerging in a lot of areas beyond communications. This paper aims at estimating the information between two random phenomena by using consolidated…
Several proofs of the monotonicity of the non-Gaussianness (divergence with respect to a Gaussian random variable with identical second order statistics) of the sum of n independent and identically distributed (i.i.d.) random variables were…
In this paper, we derive new closed-form expressions for the gradient of the mutual information with respect to arbitrary parameters of the two-user multiple access channel (MAC). The derived relations generalize the fundamental relation…
The pointwise mutual information profile, or simply profile, is the distribution of pointwise mutual information for a given pair of random variables. One of its important properties is that its expected value is precisely the mutual…
Noise Contrastive Estimation (NCE) is a popular approach for learning probability density functions parameterized up to a constant of proportionality. The main idea is to design a classification problem for distinguishing training data from…
Using random Gaussian vectors and an information-uncertainty relation, we give a proof that the coherent information is an achievable rate for entanglement transmission through a noisy quantum channel. The codes are random subspaces…
A recent result of the authors shows a so-called I-MMSE-like relationship that, for the two-user Gaussian interference channel, an I-MMSE relationship holds in the limit, as n $\to \infty$, between the interference and the interfered-with…
In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to…
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…
Inferring the causal direction and causal effect between two discrete random variables X and Y from a finite sample is often a crucial problem and a challenging task. However, if we have access to observational and interventional data, it…
The measurement outcomes of two incompatible observables on a particle can be precisely predicted when it is maximally entangled with a quantum memory, as quantified recently [Nature Phys. 6, 659 (2010)]. We explore the behavior of the…
We provide a model to study memory effects in quantum Gaussian channels with additive classical noise over an arbitrary number of uses. The correlation among different uses is introduced by contiguous two-mode interactions. Numerical…
Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…
This paper examines how an event from one random variable provides pointwise mutual information about an event from another variable via probability mass exclusions. We start by introducing probability mass diagrams, which provide a visual…
Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not reciprocal. This lack of reciprocity is often treated as a defect…