Related papers: Asymptotic mutual information in quadratic estimat…
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…
There has been definite progress recently in proving the variational single-letter formula given by the heuristic replica method for various estimation problems. In particular, the replica formula for the mutual information in the case of…
In this paper, we study community detection when we observe $m$ sparse networks and a high dimensional covariate matrix, all encoding the same community structure among $n$ subjects. In the asymptotic regime where the number of features $p$…
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are characterized by an equivalent Gaussian model with an effective…
We consider the estimation of an n-dimensional vector s from the noisy element-wise measurements of $\mathbf{s}\mathbf{s}^T$, a generic problem that arises in statistics and machine learning. We study a mismatched Bayesian inference…
Regularized system identification is the major advance in system identification in the last decade. Although many promising results have been achieved, it is far from complete and there are still many key problems to be solved. One of them…
A distributed average consensus algorithm robust to a wide range of impulsive channel noise distributions is proposed. This work is the first of its kind in the literature to propose a consensus algorithm which relaxes the requirement of…
The mutual information of a single-layer perceptron with $N$ Gaussian inputs and $P$ deterministic binary outputs is studied by numerical simulations. The relevant parameters of the problem are the ratio between the number of output and…
We show that quantification of the performance of quantum-enhanced measurement schemes based on the concept of quantum Fisher information yields asymptotically equivalent results as the rigorous Bayesian approach, provided generic…
We consider models of Bayesian inference of signals with vectorial components of finite dimensionality. We show that, under a proper perturbation, these models are replica symmetric in the sense that the overlap matrix concentrates. The…
A method to estimate the time-dependent correlation via an empirical bias estimate of the time-delayed mutual information for a time-series is proposed. In particular, the bias of the time-delayed mutual information is shown to often be…
We consider panel data models with group structure. We study the asymptotic behavior of least-squares estimators and information criterion for the number of groups, allowing for the presence of small groups that have an asymptotically…
The emerging problem of joint community detection and group synchronization, with applications in signal processing and machine learning, has been extensively studied in recent years. Previous research has predominantly focused on a…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…
Split-Plot or Repeated Measures Designs with multiple groups occur naturally in sciences. Their analysis is usually based on the classical Repeated Measures ANOVA. Roughly speaking, the latter can be shown to be asymptotically valid for…
We consider a generalization of an important class of high-dimensional inference problems, namely spiked symmetric matrix models, often used as probabilistic models for principal component analysis. Such paradigmatic models have recently…
Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in…
Mutual information is commonly used as a measure of similarity between competing labelings of a given set of objects, for example to quantify performance in classification and community detection tasks. As argued recently, however, the…