1,572 research outputs found
Hybrid approximate message passing
Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper presents a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with the weak edges representing interactions through aggregates of small, linearizable couplings of variables. AMP approximations based on the Central Limit Theorem can be readily applied to aggregates of many weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (HyGAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition of strong and weak edges, a performance--complexity trade-off can be achieved. Group sparsity and multinomial logistic regression problems are studied as examples of the proposed methodology.The work of S. Rangan was supported in part by the National Science Foundation under Grants 1116589, 1302336, and 1547332, and in part by the industrial affiliates of NYU WIRELESS. The work of A. K. Fletcher was supported in part by the National Science Foundation under Grants 1254204 and 1738286 and in part by the Office of Naval Research under Grant N00014-15-1-2677. The work of V. K. Goyal was supported in part by the National Science Foundation under Grant 1422034. The work of E. Byrne and P. Schniter was supported in part by the National Science Foundation under Grant CCF-1527162. (1116589 - National Science Foundation; 1302336 - National Science Foundation; 1547332 - National Science Foundation; 1254204 - National Science Foundation; 1738286 - National Science Foundation; 1422034 - National Science Foundation; CCF-1527162 - National Science Foundation; NYU WIRELESS; N00014-15-1-2677 - Office of Naval Research
Random Access in C-RAN for User Activity Detection with Limited-Capacity Fronthaul
Cloud-Radio Access Network (C-RAN) is characterized by a hierarchical
structure in which the baseband processing functionalities of remote radio
heads (RRHs) are implemented by means of cloud computing at a Central Unit
(CU). A key limitation of C-RANs is given by the capacity constraints of the
fronthaul links connecting RRHs to the CU. In this letter, the impact of this
architectural constraint is investigated for the fundamental functions of
random access and active User Equipment (UE) identification in the presence of
a potentially massive number of UEs. In particular, the standard C-RAN approach
based on quantize-and-forward and centralized detection is compared to a scheme
based on an alternative CU-RRH functional split that enables local detection.
Both techniques leverage Bayesian sparse detection. Numerical results
illustrate the relative merits of the two schemes as a function of the system
parameters.Comment: 6 pages, 3 figures, under revision in IEEE Signal Processing Letter
Inferring Sparsity: Compressed Sensing using Generalized Restricted Boltzmann Machines
In this work, we consider compressed sensing reconstruction from
measurements of -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 .Comment: IEEE Information Theory Workshop, 201
Approximate Message Passing with Restricted Boltzmann Machine Priors
Approximate Message Passing (AMP) has been shown to be an excellent
statistical approach to signal inference and compressed sensing problem. The
AMP framework provides modularity in the choice of signal prior; here we
propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a
Restricted Boltzmann Machine (RBM) trained on the signal support to push
reconstruction performance beyond that of simple iid priors for signals whose
support can be well represented by a trained binary RBM. We present and analyze
two methods of RBM factorization and demonstrate how these affect signal
reconstruction performance within our proposed algorithm. Finally, using the
MNIST handwritten digit dataset, we show experimentally that using an RBM
allows AMP to approach oracle-support performance
Blind Sensor Calibration using Approximate Message Passing
The ubiquity of approximately sparse data has led a variety of com- munities
to great interest in compressed sensing algorithms. Although these are very
successful and well understood for linear measurements with additive noise,
applying them on real data can be problematic if imperfect sensing devices
introduce deviations from this ideal signal ac- quisition process, caused by
sensor decalibration or failure. We propose a message passing algorithm called
calibration approximate message passing (Cal-AMP) that can treat a variety of
such sensor-induced imperfections. In addition to deriving the general form of
the algorithm, we numerically investigate two particular settings. In the
first, a fraction of the sensors is faulty, giving readings unrelated to the
signal. In the second, sensors are decalibrated and each one introduces a
different multiplicative gain to the measures. Cal-AMP shares the scalability
of approximate message passing, allowing to treat big sized instances of these
problems, and ex- perimentally exhibits a phase transition between domains of
success and failure.Comment: 27 pages, 9 figure
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