2,961 research outputs found
Loop Calculus in Statistical Physics and Information Science
Considering a discrete and finite statistical model of a general position we
introduce an exact expression for the partition function in terms of a finite
series. The leading term in the series is the Bethe-Peierls (Belief
Propagation)-BP contribution, the rest are expressed as loop-contributions on
the factor graph and calculated directly using the BP solution. The series
unveils a small parameter that often makes the BP approximation so successful.
Applications of the loop calculus in statistical physics and information
science are discussed.Comment: 4 pages, submitted to Phys.Rev.Lett. Changes: More general model,
Simpler derivatio
Optimal Quantization for Compressive Sensing under Message Passing Reconstruction
We consider the optimal quantization of compressive sensing measurements
following the work on generalization of relaxed belief propagation (BP) for
arbitrary measurement channels. Relaxed BP is an iterative reconstruction
scheme inspired by message passing algorithms on bipartite graphs. Its
asymptotic error performance can be accurately predicted and tracked through
the state evolution formalism. We utilize these results to design mean-square
optimal scalar quantizers for relaxed BP signal reconstruction and empirically
demonstrate the superior error performance of the resulting quantizers.Comment: 5 pages, 3 figures, submitted to IEEE International Symposium on
Information Theory (ISIT) 2011; minor corrections in v
Statistical Mechanical Approach to Lossy Data Compression:Theory and Practice
The encoder and decoder for lossy data compression of binary memoryless
sources are developed on the basis of a specific-type nonmonotonic perceptron.
Statistical mechanical analysis indicates that the potential ability of the
perceptron-based code saturates the theoretically achievable limit in most
cases although exactly performing the compression is computationally difficult.
To resolve this difficulty, we provide a computationally tractable
approximation algorithm using belief propagation (BP), which is a current
standard algorithm of probabilistic inference. Introducing several
approximations and heuristics, the BP-based algorithm exhibits performance that
is close to the achievable limit in a practical time scale in optimal cases.Comment: 10 pages, 2 figures, REVTEX preprin
- …