1,728 research outputs found
A Simple Derivation of AMP and its State Evolution via First-Order Cancellation
We consider the linear regression problem, where the goal is to recover the
vector from measurements
under known matrix and unknown noise . For
large i.i.d. sub-Gaussian , the approximate message passing
(AMP) algorithm is precisely analyzable through a state-evolution (SE)
formalism, which furthermore shows that AMP is Bayes optimal in certain
regimes. The rigorous SE proof, however, is long and complicated. And, although
the AMP algorithm can be derived as an approximation of loop belief propagation
(LBP), this viewpoint provides little insight into why large i.i.d.
matrices are important for AMP, and why AMP has a state
evolution. In this work, we provide a heuristic derivation of AMP and its state
evolution, based on the idea of "first-order cancellation," that provides
insights missing from the LBP derivation while being much shorter than the
rigorous SE proof
Approximate message passing for nonconvex sparse regularization with stability and asymptotic analysis
We analyse a linear regression problem with nonconvex regularization called
smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis
for Gaussian random data. We propose an approximate message passing (AMP)
algorithm considering nonconvex regularization, namely SCAD-AMP, and
analytically show that the stability condition corresponds to the de
Almeida--Thouless condition in spin glass literature. Through asymptotic
analysis, we show the correspondence between the density evolution of SCAD-AMP
and the replica symmetric solution. Numerical experiments confirm that for a
sufficiently large system size, SCAD-AMP achieves the optimal performance
predicted by the replica method. Through replica analysis, a phase transition
between replica symmetric (RS) and replica symmetry breaking (RSB) region is
found in the parameter space of SCAD. The appearance of the RS region for a
nonconvex penalty is a significant advantage that indicates the region of
smooth landscape of the optimization problem. Furthermore, we analytically show
that the statistical representation performance of the SCAD penalty is better
than that of L1-based methods, and the minimum representation error under RS
assumption is obtained at the edge of the RS/RSB phase. The correspondence
between the convergence of the existing coordinate descent algorithm and RS/RSB
transition is also indicated
Support Recovery with Sparsely Sampled Free Random Matrices
Consider a Bernoulli-Gaussian complex -vector whose components are , with X_i \sim \Cc\Nc(0,\Pc_x) and binary mutually independent
and iid across . This random -sparse vector is multiplied by a square
random matrix \Um, and a randomly chosen subset, of average size , , of the resulting vector components is then observed in additive
Gaussian noise. We extend the scope of conventional noisy compressive sampling
models where \Um is typically %A16 the identity or a matrix with iid
components, to allow \Um satisfying a certain freeness condition. This class
of matrices encompasses Haar matrices and other unitarily invariant matrices.
We use the replica method and the decoupling principle of Guo and Verd\'u, as
well as a number of information theoretic bounds, to study the input-output
mutual information and the support recovery error rate in the limit of . We also extend the scope of the large deviation approach of Rangan,
Fletcher and Goyal and characterize the performance of a class of estimators
encompassing thresholded linear MMSE and relaxation
Energy Efficiency in Communications and Networks
The topic of "Energy Efficiency in Communications and Networks" attracts growing attention due to economical and environmental reasons. The amount of power consumed by information and communication technologies (ICT) is rapidly increasing, as well as the energy bill of service providers. According to a number of studies, ICT alone is responsible for a percentage which varies from 2% to 10% of the world power consumption. Thus, driving rising cost and sustainability concerns about the energy footprint of the IT infrastructure. Energy-efficiency is an aspect that until recently was only considered for battery driven devices. Today we see energy-efficiency becoming a pervasive issue that will need to be considered in all technology areas from device technology to systems management. This book is seeking to provide a compilation of novel research contributions on hardware design, architectures, protocols and algorithms that will improve the energy efficiency of communication devices and networks and lead to a more energy proportional technology infrastructure
NNLO Vertex Corrections in charmless hadronic B decays: Imaginary part
We compute the imaginary part of the 2-loop vertex corrections in the QCD
Factorization framework for hadronic two-body decays as B -> pi pi. This
completes the NNLO calculation of the imaginary part of the topological tree
amplitudes and represents an important step towards a NNLO prediction of direct
CP asymmetries in QCD Factorization. Concerning the technical aspects, we find
that soft and collinear infrared divergences cancel in the hard-scattering
kernels which demonstrates factorization at the 2-loop order. All results are
obtained analytically including the dependence on the charm quark mass. The
numerical impact of the NNLO corrections is found to be significant, in
particular they lead to an enhancement of the strong phase of the
colour-suppressed tree amplitude.Comment: 28 pages, 6 figures. v2: minor changes in Section 4.3, results
unchanged, version accepted for publication in Nuclear Physics
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