Pierre-Olivier Amblard

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Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks can be used to assess Granger causality graphs of stochastic processes. We show that directed information theory(More)
This report reviews the conceptual and theoretical links between Granger causality and directed information theory. We begin with a short historical tour of Granger causality, concentrating on its closeness to information theory. The definitions of Granger causality based on prediction are recalled, and the importance of the observation set is discussed. We(More)
In passive monitoring using sensor networks, low energy supplies drastically constrain sensors in terms of calculation and communication abilities. Designing processing algorithms at the sensor level that take into account these constraints is an important problem in this context. Here we study the estimation of correlation functions between sensors using(More)
We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, i.e., in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling scheme that enables perfect recovery of bandlimited signals. For large graphs, i.e., in cases where the graph's spectrum(More)
In this letter, we investigated the connection between information and estimation measures for mismatched Gaussian models. In addition to the input prior mismatch, we take into account the noise mismatch and establish a new relation between relative entropy and excess mean square error. The derived formula shows that the input prior mismatch may be canceled(More)
In two recent studies, Dudok de Wit et al. (2005) and Kretzschmar et al. (2006) have shown that the solar Ultra-Violet spectrum between 25 and 195 nm can be reconstructed from the observation of a set of 6 to 10 carefully chosen spectral lines. The best set of lines, however, is application dependent. In this study, we demonstrate that a good candidate for(More)
The work developed in the paper concerns the multivariate fractional Brownian motion (mfBm) viewed through the lens of the wavelet transform. After recalling some basic properties on the mfBm, we calculate the correlation structure of its wavelet transform. We particularly study the asymptotic behavior of the correlation, showing that if the analyzing(More)
We consider the problem of sampling k-bandlimited graph signals, i.e., linear combinations of the first k graph Fourier modes. We know that a set of k nodes embedding all k-bandlimited signals always exists, thereby enabling their perfect reconstruction after sampling. Unfortunately, to exhibit such a set, one needs to partially diagonalize the graph(More)