arXiv subjects

Andre Manoel

Publications and source records attributed to Andre Manoel.

23 records · Page 2Linked to original sources

arXiv2016

Inferring Sparsity: Compressed Sensing using Generalized Restricted Boltzmann Machines

In this work, we consider compressed sensing reconstruction from $M$ measurements of $K$-sparse structured signals which do not possess a writable correlation model. Assuming that a generative statistical model, such as a Boltzmann machine, can be trained in an unsupervised manner on example signals, we demonstrate how this signal model can be used within a Bayesian framework of signal reconstruction. By deriving a message-passing inference for general distribution restricted Boltzmann machines, we are able to integrate these inferred signal models into approximate message passing for compressed sensing reconstruction. Finally, we show for the MNIST dataset that this approach can be very effective, even for $M < K$.

cs.IT↗

arXiv2014

Expectation Propagation

Variational inference is a powerful concept that underlies many iterative approximation algorithms; expectation propagation, mean-field methods and belief propagations were all central themes at the school that can be perceived from this unifying framework. The lectures of Manfred Opper introduce the archetypal example of Expectation Propagation, before establishing the connection with the other approximation methods. Corrections by expansion about the expectation propagation are then explained. Finally some advanced inference topics and applications are explored in the final sections.

stat.ML↗

arXiv2014

Sparse Estimation with the Swept Approximated Message-Passing Algorithm

Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in computational efficiency. However, AMP suffers from serious convergence issues in contexts that do not exactly match its assumptions. We propose a new approach to stabilizing AMP in these contexts by applying AMP updates to individual coefficients rather than in parallel. Our results show that this change to the AMP iteration can provide theoretically expected, but hitherto unobtainable, performance for problems on which the standard AMP iteration diverges. Additionally, we find that the computational costs of this swept coefficient update scheme is not unduly burdensome, allowing it to be applied efficiently to signals of large dimensionality.

cs.IT↗

arXiv2014

Variational Free Energies for Compressed Sensing

We consider the variational free energy approach for compressed sensing. We first show that the naïve mean field approach performs remarkably well when coupled with a noise learning procedure. We also notice that it leads to the same equations as those used for iterative thresholding. We then discuss the Bethe free energy and how it corresponds to the fixed points of the approximate message passing algorithm. In both cases, we test numerically the direct optimization of the free energies as a converging sparse-estimationalgorithm.

cs.IT↗

arXiv2013

Statistical mechanics of reputation systems in autonomous networks

Reputation systems seek to infer which members of a community can be trusted based on ratings they issue about each other. We construct a Bayesian inference model and simulate approximate estimates using belief propagation (BP). The model is then mapped onto computing equilibrium properties of a spin glass in a random field and analyzed by employing the replica symmetric cavity approach. Having the fraction of trustful nodes and environment noise level as control parameters, we evaluate the theoretical performance in terms of estimation error and the robustness of the BP approximation in different scenarios. Regions of degraded performance are then explained by the convergence properties of the BP algorithm and by the emergence of a glassy phase.

cond-mat.dis-nn↗