1,759 research outputs found
Inference in particle tracking experiments by passing messages between images
Methods to extract information from the tracking of mobile objects/particles
have broad interest in biological and physical sciences. Techniques based on
simple criteria of proximity in time-consecutive snapshots are useful to
identify the trajectories of the particles. However, they become problematic as
the motility and/or the density of the particles increases due to uncertainties
on the trajectories that particles followed during the images' acquisition
time. Here, we report an efficient method for learning parameters of the
dynamics of the particles from their positions in time-consecutive images. Our
algorithm belongs to the class of message-passing algorithms, known in computer
science, information theory and statistical physics as Belief Propagation (BP).
The algorithm is distributed, thus allowing parallel implementation suitable
for computations on multiple machines without significant inter-machine
overhead. We test our method on the model example of particle tracking in
turbulent flows, which is particularly challenging due to the strong transport
that those flows produce. Our numerical experiments show that the BP algorithm
compares in quality with exact Markov Chain Monte-Carlo algorithms, yet BP is
far superior in speed. We also suggest and analyze a random-distance model that
provides theoretical justification for BP accuracy. Methods developed here
systematically formulate the problem of particle tracking and provide fast and
reliable tools for its extensive range of applications.Comment: 18 pages, 9 figure
An Iterative Receiver for OFDM With Sparsity-Based Parametric Channel Estimation
In this work we design a receiver that iteratively passes soft information
between the channel estimation and data decoding stages. The receiver
incorporates sparsity-based parametric channel estimation. State-of-the-art
sparsity-based iterative receivers simplify the channel estimation problem by
restricting the multipath delays to a grid. Our receiver does not impose such a
restriction. As a result it does not suffer from the leakage effect, which
destroys sparsity. Communication at near capacity rates in high SNR requires a
large modulation order. Due to the close proximity of modulation symbols in
such systems, the grid-based approximation is of insufficient accuracy. We show
numerically that a state-of-the-art iterative receiver with grid-based sparse
channel estimation exhibits a bit-error-rate floor in the high SNR regime. On
the contrary, our receiver performs very close to the perfect channel state
information bound for all SNR values. We also demonstrate both theoretically
and numerically that parametric channel estimation works well in dense
channels, i.e., when the number of multipath components is large and each
individual component cannot be resolved.Comment: Major revision, accepted for IEEE Transactions on Signal Processin
A Deterministic and Generalized Framework for Unsupervised Learning with Restricted Boltzmann Machines
Restricted Boltzmann machines (RBMs) are energy-based neural-networks which
are commonly used as the building blocks for deep architectures neural
architectures. In this work, we derive a deterministic framework for the
training, evaluation, and use of RBMs based upon the Thouless-Anderson-Palmer
(TAP) mean-field approximation of widely-connected systems with weak
interactions coming from spin-glass theory. While the TAP approach has been
extensively studied for fully-visible binary spin systems, our construction is
generalized to latent-variable models, as well as to arbitrarily distributed
real-valued spin systems with bounded support. In our numerical experiments, we
demonstrate the effective deterministic training of our proposed models and are
able to show interesting features of unsupervised learning which could not be
directly observed with sampling. Additionally, we demonstrate how to utilize
our TAP-based framework for leveraging trained RBMs as joint priors in
denoising problems
Free Energy Approximations for CSMA networks
In this paper we study how to estimate the back-off rates in an idealized
CSMA network consisting of links to achieve a given throughput vector using
free energy approximations. More specifically, we introduce the class of
region-based free energy approximations with clique belief and present a closed
form expression for the back-off rates based on the zero gradient points of the
free energy approximation (in terms of the conflict graph, target throughput
vector and counting numbers). Next we introduce the size clique free
energy approximation as a special case and derive an explicit expression for
the counting numbers, as well as a recursion to compute the back-off rates. We
subsequently show that the size clique approximation coincides with a
Kikuchi free energy approximation and prove that it is exact on chordal
conflict graphs when . As a by-product these results provide us
with an explicit expression of a fixed point of the inverse generalized belief
propagation algorithm for CSMA networks. Using numerical experiments we compare
the accuracy of the novel approximation method with existing methods
Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach
We present a joint message passing approach that combines belief propagation
and the mean field approximation. Our analysis is based on the region-based
free energy approximation method proposed by Yedidia et al. We show that the
message passing fixed-point equations obtained with this combination correspond
to stationary points of a constrained region-based free energy approximation.
Moreover, we present a convergent implementation of these message passing
fixedpoint equations provided that the underlying factor graph fulfills certain
technical conditions. In addition, we show how to include hard constraints in
the part of the factor graph corresponding to belief propagation. Finally, we
demonstrate an application of our method to iterative channel estimation and
decoding in an orthogonal frequency division multiplexing (OFDM) system
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