arXiv subjects

Bernard Henri Fleury

Publications and source records attributed to Bernard Henri Fleury.

9 recordsLinked to original sources

arXiv2025

General Pruning Criteria for Fast SBL

Sparse Bayesian learning (SBL) associates to each weight in the underlying linear model a hyperparameter by assuming that each weight is Gaussian distributed with zero mean and precision (inverse variance) equal to its associated hyperparameter. The method estimates the hyperparameters by marginalizing out the weights and performing (marginalized) maximum likelihood (ML) estimation. SBL returns many hyperparameter estimates to diverge to infinity, effectively setting the estimates of the corresponding weights to zero (i.e., pruning the corresponding weights from the model) and thereby yielding a sparse estimate of the weight vector. In this letter, we analyze the marginal likelihood as function of a single hyperparameter while keeping the others fixed, when the Gaussian assumptions on the noise samples and the weight distribution that underlies the derivation of SBL are weakened. We derive sufficient conditions that lead, on the one hand, to finite hyperparameter estimates and, on the other, to infinite ones. Finally, we show that in the Gaussian case, the two conditions are complementary and coincide with the pruning condition of fast SBL (F-SBL), thereby providing additional insights into this algorithm.

stat.ML↗

arXiv2018

Superfast Line Spectral Estimation

A number of recent works have proposed to solve the line spectral estimation problem by applying off-the-grid extensions of sparse estimation techniques. These methods are preferable over classical line spectral estimation algorithms because they inherently estimate the model order. However, they all have computation times which grow at least cubically in the problem size, thus limiting their practical applicability in cases with large dimensions. To alleviate this issue, we propose a low-complexity method for line spectral estimation, which also draws on ideas from sparse estimation. Our method is based on a Bayesian view of the problem. The signal covariance matrix is shown to have Toeplitz structure, allowing superfast Toeplitz inversion to be used. We demonstrate that our method achieves estimation accuracy at least as good as current methods and that it does so while being orders of magnitudes faster.

eess.SP↗

arXiv2017

A Traffic Model for Machine-Type Communications Using Spatial Point Processes

A source traffic model for machine-to-machine communications is presented in this paper. We consider a model in which devices operate in a regular mode until they are triggered into an alarm mode by an alarm event. The positions of devices and events are modeled by means of Poisson point processes, where the generated traffic by a given device depends on its position and event positions. We first consider the case where devices and events are static and devices generate traffic according to a Bernoulli process, where we derive the total rate from the devices at the base station. We then extend the model by defining a two-state Markov chain for each device, which allows for devices to stay in alarm mode for a geometrically distributed holding time. The temporal characteristics of this model are analyzed via the autocovariance function, where the effect of event density and mean holding time are shown.

cs.NI↗

arXiv2017

Variational Bayesian Inference of Line Spectra

In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are continuous-valued, i.e., not restricted to a grid; and the coefficients are governed by a Bernoulli-Gaussian prior model turning model order selection into binary sequence detection. Unlike earlier works which retain only point estimates of the frequencies, we undertake a more complete Bayesian treatment by estimating the posterior probability density functions (pdfs) of the frequencies and computing expectations over them. Thus, we additionally capture and operate with the uncertainty of the frequency estimates. Aiming to maximize the model evidence, variational optimization provides analytic approximations of the posterior pdfs and also gives estimates of the additional parameters. We propose an accurate representation of the pdfs of the frequencies by mixtures of von Mises pdfs, which yields closed-form expectations. We define the algorithm VALSE in which the estimates of the pdfs and parameters are iteratively updated. VALSE is a gridless, convergent method, does not require parameter tuning, can easily include prior knowledge about the frequencies and provides approximate posterior pdfs based on which the uncertainty in line spectral estimation can be quantified. Simulation results show that accounting for the uncertainty of frequency estimates, rather than computing just point estimates, significantly improves the performance. The performance of VALSE is superior to that of state-of-the-art methods and closely approaches the Cramér-Rao bound computed for the true model order.

cs.IT↗

arXiv2016

Turbo-Equalization Using Partial Gaussian Approximation

This paper deals with turbo-equalization for coded data transmission over intersymbol interference (ISI) channels. We propose a message-passing algorithm that uses the expectation-propagation rule to convert messages passed from the demodulator-decoder to the equalizer and computes messages returned by the equalizer by using a partial Gaussian approximation (PGA). Results from Monte Carlo simulations show that this approach leads to a significant performance improvement compared to state-of-the-art turbo-equalizers and allows for trading performance with complexity. We exploit the specific structure of the ISI channel model to significantly reduce the complexity of the PGA compared to that considered in the initial paper proposing the method.

cs.IT↗

arXiv2014

Sparse Estimation using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper proposes a GSM model - the Bessel K model - that induces concave penalty functions for the estimation of complex sparse signals. The properties of the Bessel K model are analyzed when it is applied to Type I and Type II estimation. This analysis reveals that, by tuning the parameters of the mixing pdf different penalty functions are invoked depending on the estimation type used, the value of the noise variance, and whether real or complex signals are estimated. Using the Bessel K model, we derive a sparse estimator based on a modification of the expectation-maximization algorithm formulated for Type II estimation. The estimator includes as a special instance the algorithms proposed by Tipping and Faul [1] and by Babacan et al. [2]. Numerical results show the superiority of the proposed estimator over these state-of-the-art estimators in terms of convergence speed, sparseness, reconstruction error, and robustness in low and medium signal-to-noise ratio regimes.

stat.ML↗

arXiv2012

Message-Passing Algorithms for Channel Estimation and Decoding Using Approximate Inference

We design iterative receiver schemes for a generic wireless communication system by treating channel estimation and information decoding as an inference problem in graphical models. We introduce a recently proposed inference framework that combines belief propagation (BP) and the mean field (MF) approximation and includes these algorithms as special cases. We also show that the expectation propagation and expectation maximization algorithms can be embedded in the BP-MF framework with slight modifications. By applying the considered inference algorithms to our probabilistic model, we derive four different message-passing receiver schemes. Our numerical evaluation demonstrates that the receiver based on the BP-MF framework and its variant based on BP-EM yield the best compromise between performance, computational complexity and numerical stability among all candidate algorithms.

cs.IT↗

arXiv2012

Distributed Iterative Processing for Interference Channels with Receiver Cooperation

We propose a framework for the derivation and evaluation of distributed iterative algorithms for receiver cooperation in interference-limited wireless systems. Our approach views the processing within and collaboration between receivers as the solution to an inference problem in the probabilistic model of the whole system. The probabilistic model is formulated to explicitly incorporate the receivers' ability to share information of a predefined type. We employ a recently proposed unified message-passing tool to infer the variables of interest in the factor graph representation of the probabilistic model. The exchange of information between receivers arises in the form of passing messages along some specific edges of the factor graph; the rate of updating and passing these messages determines the communication overhead associated with cooperation. Simulation results illustrate the high performance of the proposed algorithm even with a low number of message exchanges between receivers.

cs.IT↗

arXiv2012

Application of Bayesian Hierarchical Prior Modeling to Sparse Channel Estimation

Existing methods for sparse channel estimation typically provide an estimate computed as the solution maximizing an objective function defined as the sum of the log-likelihood function and a penalization term proportional to the l1-norm of the parameter of interest. However, other penalization terms have proven to have strong sparsity-inducing properties. In this work, we design pilot-assisted channel estimators for OFDM wireless receivers within the framework of sparse Bayesian learning by defining hierarchical Bayesian prior models that lead to sparsity-inducing penalization terms. The estimators result as an application of the variational message-passing algorithm on the factor graph representing the signal model extended with the hierarchical prior models. Numerical results demonstrate the superior performance of our channel estimators as compared to traditional and state-of-the-art sparse methods.

stat.ML↗