202,180 research outputs found
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
Deeply Learning the Messages in Message Passing Inference
Deep structured output learning shows great promise in tasks like semantic
image segmentation. We proffer a new, efficient deep structured model learning
scheme, in which we show how deep Convolutional Neural Networks (CNNs) can be
used to estimate the messages in message passing inference for structured
prediction with Conditional Random Fields (CRFs). With such CNN message
estimators, we obviate the need to learn or evaluate potential functions for
message calculation. This confers significant efficiency for learning, since
otherwise when performing structured learning for a CRF with CNN potentials it
is necessary to undertake expensive inference for every stochastic gradient
iteration. The network output dimension for message estimation is the same as
the number of classes, in contrast to the network output for general CNN
potential functions in CRFs, which is exponential in the order of the
potentials. Hence CNN message learning has fewer network parameters and is more
scalable for cases that a large number of classes are involved. We apply our
method to semantic image segmentation on the PASCAL VOC 2012 dataset. We
achieve an intersection-over-union score of 73.4 on its test set, which is the
best reported result for methods using the VOC training images alone. This
impressive performance demonstrates the effectiveness and usefulness of our CNN
message learning method.Comment: 11 pages. Appearing in Proc. The Twenty-ninth Annual Conference on
Neural Information Processing Systems (NIPS), 2015, Montreal, Canad
Decentralized Generalized Approximate Message-Passing for Tree-Structured Networks
Decentralized generalized approximate message-passing (GAMP) is proposed for
compressed sensing from distributed generalized linear measurements in a
tree-structured network. Consensus propagation is used to realize average
consensus required in GAMP via local communications between adjacent nodes.
Decentralized GAMP is applicable to all tree-structured networks that do not
necessarily have central nodes connected to all other nodes. State evolution is
used to analyze the asymptotic dynamics of decentralized GAMP for zero-mean
independent and identically distributed Gaussian sensing matrices. The state
evolution recursion for decentralized GAMP is proved to have the same fixed
points as that for centralized GAMP when homogeneous measurements with an
identical dimension in all nodes are considered. Furthermore, existing
long-memory proof strategy is used to prove that the state evolution recursion
for decentralized GAMP with the Bayes-optimal denoisers converges to a fixed
point. These results imply that the state evolution recursion for decentralized
GAMP with the Bayes-optimal denoisers converges to the Bayes-optimal fixed
point for the homogeneous measurements when the fixed point is unique.
Numerical results for decentralized GAMP are presented in the cases of linear
measurements and clipping. As examples of tree-structured networks, a
one-dimensional chain and a tree with no central nodes are considered.Comment: submitted to IEEE Trans. Inf. Theor
Graph Convolutional Matrix Completion
We consider matrix completion for recommender systems from the point of view
of link prediction on graphs. Interaction data such as movie ratings can be
represented by a bipartite user-item graph with labeled edges denoting observed
ratings. Building on recent progress in deep learning on graph-structured data,
we propose a graph auto-encoder framework based on differentiable message
passing on the bipartite interaction graph. Our model shows competitive
performance on standard collaborative filtering benchmarks. In settings where
complimentary feature information or structured data such as a social network
is available, our framework outperforms recent state-of-the-art methods.Comment: 9 pages, 3 figures, updated with additional experimental evaluatio
Multilayer wave functions: A recursive coupling of local excitations
Finding a succinct representation to describe the ground state of a
disordered interacting system could be very helpful in understanding the
interplay between the interactions that is manifested in a quantum phase
transition. In this work we use some elementary states to construct recursively
an ansatz of multilayer wave functions, where in each step the higher-level
wave function is represented by a superposition of the locally "excited states"
obtained from the lower-level wave function. This allows us to write the
Hamiltonian expectation in terms of some local functions of the variational
parameters, and employ an efficient message-passing algorithm to find the
optimal parameters. We obtain good estimations of the ground-state energy and
the phase transition point for the transverse Ising model with a few layers of
mean-field and symmetric tree states. The work is the first step towards the
application of local and distributed message-passing algorithms in the study of
structured variational problems in finite dimensions.Comment: 23 pages, including 3 appendices and 6 figures. A shortened version
published in EP
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