9,795 research outputs found
On Approximate Nonlinear Gaussian Message Passing On Factor Graphs
Factor graphs have recently gained increasing attention as a unified
framework for representing and constructing algorithms for signal processing,
estimation, and control. One capability that does not seem to be well explored
within the factor graph tool kit is the ability to handle deterministic
nonlinear transformations, such as those occurring in nonlinear filtering and
smoothing problems, using tabulated message passing rules. In this
contribution, we provide general forward (filtering) and backward (smoothing)
approximate Gaussian message passing rules for deterministic nonlinear
transformation nodes in arbitrary factor graphs fulfilling a Markov property,
based on numerical quadrature procedures for the forward pass and a
Rauch-Tung-Striebel-type approximation of the backward pass. These message
passing rules can be employed for deriving many algorithms for solving
nonlinear problems using factor graphs, as is illustrated by the proposition of
a nonlinear modified Bryson-Frazier (MBF) smoother based on the presented
message passing rules
Feature selection methods for solving the reference class problem
Probabilistic inference from frequencies, such as "Most Quakers are pacifists; Nixon is a Quaker, so probably Nixon is a pacifist" suffer from the problem that an individual is typically a member of many "reference classes" (such as Quakers, Republicans, Californians, etc) in which the frequency of the target attribute varies. How to choose the best class or combine the information? The article argues that the problem can be solved by the feature selection methods used in contemporary Big Data science: the correct reference class is that determined by the features relevant to the target, and relevance is measured by correlation (that is, a feature is relevant if it makes a difference to the frequency of the target)
MIMO decision feedback equalization from an H∞ perspective
We approach the multiple input multiple output (MIMO) decision feedback equalization (DFE) problem in digital communications from an H∞ estimation point of view. Using the standard (and simplifying) assumption that all previous decisions are correct, we obtain an explicit parameterization of all H∞ optimal DFEs. In particular, we show that, under the above assumption, minimum mean square error (MMSE) DFEs are H∞ optimal. The H∞ approach also suggests a method for dealing with errors in previous decisions
Expectation Propagation for Poisson Data
The Poisson distribution arises naturally when dealing with data involving
counts, and it has found many applications in inverse problems and imaging. In
this work, we develop an approximate Bayesian inference technique based on
expectation propagation for approximating the posterior distribution formed
from the Poisson likelihood function and a Laplace type prior distribution,
e.g., the anisotropic total variation prior. The approach iteratively yields a
Gaussian approximation, and at each iteration, it updates the Gaussian
approximation to one factor of the posterior distribution by moment matching.
We derive explicit update formulas in terms of one-dimensional integrals, and
also discuss stable and efficient quadrature rules for evaluating these
integrals. The method is showcased on two-dimensional PET images.Comment: 25 pages, to be published at Inverse Problem
FPGA-Based Bandwidth Selection for Kernel Density Estimation Using High Level Synthesis Approach
FPGA technology can offer significantly hi\-gher performance at much lower
power consumption than is available from CPUs and GPUs in many computational
problems. Unfortunately, programming for FPGA (using ha\-rdware description
languages, HDL) is a difficult and not-trivial task and is not intuitive for
C/C++/Java programmers. To bring the gap between programming effectiveness and
difficulty the High Level Synthesis (HLS) approach is promoting by main FPGA
vendors. Nowadays, time-intensive calculations are mainly performed on GPU/CPU
architectures, but can also be successfully performed using HLS approach. In
the paper we implement a bandwidth selection algorithm for kernel density
estimation (KDE) using HLS and show techniques which were used to optimize the
final FPGA implementation. We are also going to show that FPGA speedups,
comparing to highly optimized CPU and GPU implementations, are quite
substantial. Moreover, power consumption for FPGA devices is usually much less
than typical power consumption of the present CPUs and GPUs.Comment: 23 pages, 6 figures, extended version of initial pape
Peak effect, vortex-lattice melting-line and order - disorder transition in conventional and high-T superconductors
We investigate the order - disorder transition line from a Bragg glass to an
amorphous vortex glass in the H-T phase diagram of three-dimensional type-II
superconductors with account of both pinning-caused and thermal fluctuations of
the vortex lattice. Our approach is based on the Lindemann criterion and on
results of the collective pinning theory and generalizes previous work of other
authors. It is shown that the shapes of the order - disorder transition line
and the vortex lattice melting curve are determined only by the Ginzburg
number, which characterizes thermal fluctuations, and by a parameter which
describes the strength of the quenched disorder in the flux-line lattice. In
the framework of this unified approach we obtain the H-T phase diagrams for
both conventional and high-Tc superconductors. Several well-known experimental
results concerning the fishtail effect and the phase diagram of high-Tc
superconductors are naturally explained by assuming that a peak effect in the
critical current density versus H signalizes the order - disorder transition
line in superconductors with point defects.Comment: 15 pages including 11 figure
Continuous phase-space representations for finite-dimensional quantum states and their tomography
Continuous phase spaces have become a powerful tool for describing,
analyzing, and tomographically reconstructing quantum states in quantum optics
and beyond. A plethora of these phase-space techniques are known, however a
thorough understanding of their relations was still lacking for
finite-dimensional quantum states. We present a unified approach to continuous
phase-space representations which highlights their relations and tomography.
The infinite-dimensional case from quantum optics is then recovered in the
large-spin limit.Comment: 15 pages, 9 figures, v4: extended tomography analysis, added
references and figure
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