81,172 research outputs found
A Coordinate System for Gaussian Networks
This paper studies network information theory problems where the external
noise is Gaussian distributed. In particular, the Gaussian broadcast channel
with coherent fading and the Gaussian interference channel are investigated. It
is shown that in these problems, non-Gaussian code ensembles can achieve higher
rates than the Gaussian ones. It is also shown that the strong Shamai-Laroia
conjecture on the Gaussian ISI channel does not hold. In order to analyze
non-Gaussian code ensembles over Gaussian networks, a geometrical tool using
the Hermite polynomials is proposed. This tool provides a coordinate system to
analyze a class of non-Gaussian input distributions that are invariant over
Gaussian networks
On the relationship between Gaussian stochastic blockmodels and label propagation algorithms
The problem of community detection receives great attention in recent years.
Many methods have been proposed to discover communities in networks. In this
paper, we propose a Gaussian stochastic blockmodel that uses Gaussian
distributions to fit weight of edges in networks for non-overlapping community
detection. The maximum likelihood estimation of this model has the same
objective function as general label propagation with node preference. The node
preference of a specific vertex turns out to be a value proportional to the
intra-community eigenvector centrality (the corresponding entry in principal
eigenvector of the adjacency matrix of the subgraph inside that vertex's
community) under maximum likelihood estimation. Additionally, the maximum
likelihood estimation of a constrained version of our model is highly related
to another extension of label propagation algorithm, namely, the label
propagation algorithm under constraint. Experiments show that the proposed
Gaussian stochastic blockmodel performs well on various benchmark networks.Comment: 22 pages, 17 figure
Transferable neural networks for enhanced sampling of protein dynamics
Variational auto-encoder frameworks have demonstrated success in reducing
complex nonlinear dynamics in molecular simulation to a single non-linear
embedding. In this work, we illustrate how this non-linear latent embedding can
be used as a collective variable for enhanced sampling, and present a simple
modification that allows us to rapidly perform sampling in multiple related
systems. We first demonstrate our method is able to describe the effects of
force field changes in capped alanine dipeptide after learning a model using
AMBER99. We further provide a simple extension to variational dynamics encoders
that allows the model to be trained in a more efficient manner on larger
systems by encoding the outputs of a linear transformation using time-structure
based independent component analysis (tICA). Using this technique, we show how
such a model trained for one protein, the WW domain, can efficiently be
transferred to perform enhanced sampling on a related mutant protein, the GTT
mutation. This method shows promise for its ability to rapidly sample related
systems using a single transferable collective variable and is generally
applicable to sets of related simulations, enabling us to probe the effects of
variation in increasingly large systems of biophysical interest.Comment: 20 pages, 10 figure
Distributed Maximum Likelihood for Simultaneous Self-localization and Tracking in Sensor Networks
We show that the sensor self-localization problem can be cast as a static
parameter estimation problem for Hidden Markov Models and we implement fully
decentralized versions of the Recursive Maximum Likelihood and on-line
Expectation-Maximization algorithms to localize the sensor network
simultaneously with target tracking. For linear Gaussian models, our algorithms
can be implemented exactly using a distributed version of the Kalman filter and
a novel message passing algorithm. The latter allows each node to compute the
local derivatives of the likelihood or the sufficient statistics needed for
Expectation-Maximization. In the non-linear case, a solution based on local
linearization in the spirit of the Extended Kalman Filter is proposed. In
numerical examples we demonstrate that the developed algorithms are able to
learn the localization parameters.Comment: shorter version is about to appear in IEEE Transactions of Signal
Processing; 22 pages, 15 figure
A Bayesian Poisson-Gaussian Process Model for Popularity Learning in Edge-Caching Networks
Edge-caching is recognized as an efficient technique for future cellular
networks to improve network capacity and user-perceived quality of experience.
To enhance the performance of caching systems, designing an accurate content
request prediction algorithm plays an important role. In this paper, we develop
a flexible model, a Poisson regressor based on a Gaussian process, for the
content request distribution.
The first important advantage of the proposed model is that it encourages the
already existing or seen contents with similar features to be correlated in the
feature space and therefore it acts as a regularizer for the estimation.
Second, it allows to predict the popularities of newly-added or unseen contents
whose statistical data is not available in advance. In order to learn the model
parameters, which yield the Poisson arrival rates or alternatively the content
\textit{popularities}, we invoke the Bayesian approach which is robust against
over-fitting.
However, the resulting posterior distribution is analytically intractable to
compute. To tackle this, we apply a Markov Chain Monte Carlo (MCMC) method to
approximate this distribution which is also asymptotically exact. Nevertheless,
the MCMC is computationally demanding especially when the number of contents is
large. Thus, we employ the Variational Bayes (VB) method as an alternative low
complexity solution. More specifically, the VB method addresses the
approximation of the posterior distribution through an optimization problem.
Subsequently, we present a fast block-coordinate descent algorithm to solve
this optimization problem. Finally, extensive simulation results both on
synthetic and real-world datasets are provided to show the accuracy of our
prediction algorithm and the cache hit ratio (CHR) gain compared to existing
methods from the literature
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