A wide range of machine learning and signal processing applications involve data discrimination through covariance matrices. A broad family of metrics, among which the Frobe-nius, Fisher, Bhattacharyya distances, as well as the Kullback-Leibler or Rényi divergences, are regularly exploited. Not being directly accessible, these metrics are usually assessed through empirical sample covariances. We show here that, for large dimensional data, these approximations lead to dramatically erroneous distance and divergence estimates.In this article, based on advanced random matrix considerations, we provide a novel and versatile consistent estimate for these covariance matrix distances and divergences. While theoretically developed for both large and numerous data, practical simulations demonstrate its large performance gains over the standard approach even for very small dimensions. A particular emphasis is made on the Fisher information metric and a concrete application to covariance-based spectral clustering is investigated.

In this letter, we study the behavior of the maximum likelihood estimator (MLE) in the framework of low noise level (or high signal-to-noise ratio), when the data follow a unimodal elliptical distribution. The MLE appears to be the same as in the Gaussian context, regardless the noise distribution. We also show that the asymptotic distribution of this estimator is unimodal elliptical, where the law is intimately linked to that of the noise distribution. Additionally, this estimator is shown to be not efficient, except in the Gaussian noise case. Finally, we validate our analytic results by some simulations.

In this paper, we propose generalizations of the de Bruijn identity based on extensions of the Shannon entropy, Fisher information and their associated divergences or relative measures. The foundations of these generalizations are the φ-entropies and divergences of the Csiszár (or Salicrú) class considered within a multidimensional context, including the one-dimensional case, and for several types of noisy channels characterized by a more general probability distribution beyond the well-known Gaussian noise. We found that the gradient and/or the Hessian of these entropies or divergences with respect to the noise parameter naturally give rise to generalized versions of the Fisher information or divergence, which are named the φ-Fisher information (divergence). The obtained identities can be viewed as further extensions of the classical de Bruijn identity. Analogously, it is shown that a similar relation holds between the φ-divergence and an extended mean-square error, named φ-mean square error, for the Gaussian channel.

In wireless networks, interferences between transmissions are modelled either in time or frequency domain. In this article, we jointly analyze interferences in the time-frequency domain using a stochastic geometry model assuming the total time-frequency resources to be a two-dimensional plane and transmissions from Internet of Things (IoT) devices time-frequency patterns on this plane. To evaluate the interference, we quantify the overlap between the information packets: provided that the overlap is not too strong, the packets are not necessarily lost due to capture effect. This flexible model can be used for multiple medium access scenarios and is especially adapted to the random time-frequency access schemes used in Low-Power Wide-Area Networks (LPWANs). By characterizing the outage probability and throughput, our approach permits to evaluate the performance of two representative LPWA technologies Sigfox®and LoRaWAN®.

This paper presents a new estimation scheme for optimally deriving clutter parameters with high resolution POLSAR data. The heterogeneous clutter in POLSAR data was described by the Spherically Invariant Random Vectors model. Three parameters were introduced for the high resolution POLSAR data clutter: the span, the normalized texture and the speckle normalized covariance matrix. The asymptotic distribution of the novel span estimator is also investigated. The proposed method is tested with airborne POLSAR images provided by the ONERA RAMSES system.

In connection with the uncertainty principle in quantum mechanics (Heisenberg) or in time-frequency analysis (Heisenberg-Gabor), we study its formulation in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. These results can be considered as generalizations of the Heisenberg inequalities in the sense that they measure the mutual uncertainty of a random variable (or wave function) and its conjugated random variable (or Fourier transformed wave function) through their associated Rényi entropies with conjugated indexes. We consider here the more general case where the entropic indexes are not conjugated, in both cases where the state space is discrete and continuous: we discuss the existence of an uncertainty inequality depending on the location of the entropic indexes α and β in the plane (α, β). Our results explain and extend a recent study by Luis [3], where states with quantum fluctuations below the Gaussian case are discussed at the single point (2, 2).

We study the link between networks of the pooling type and the problem of quantification. Pooling networks consist in parallel processors that are summed after having processed the same information. If the processors are simple threshold model of noisy neurons, the behavior of the network has the behavior of a quantizer. Using the compander approach to quantizers as well as the notion of density of levels, we study these networks and show that they are asymptotically equivalent to quantizers. Furthermore, we show how these devices can be infomax processors

In this paper we revisit the Bialynicki-Birula & Mycielski uncertainty principle (I. Bialynicki-Birula and J. Mycielski, 1975) and the associated cases of equality. This Shannon entropic version of the well-known Heisenberg inequality can be used when dealing with variables that admit no variance. In this paper, we extend this uncertainty principle to Renyi entropies. We recall that in both cases, equality occurs only for Gaussian random variables. However, we show that in the particular n-dimensional Laplace case, the bound is asymptotically attained as n grows. We also show numerically that this effect exists for Cauchy variables whatever the Renyi entropy considered, extending the results of S. Abe and A.K. Rajagopal (2001), These two cases are interesting since they show that this asymptotic behavior cannot be considered as a "Gaussianization" of the variable when the dimension increases, so that the effect is rather "dimensional"