34 research outputs found
Statistical mechanical assessment of a reconstruction limit of compressed sensing: Toward theoretical analysis of correlated signals
We provide a scheme for exploring the reconstruction limit of compressed
sensing by minimizing the general cost function under the random measurement
constraints for generic correlated signal sources. Our scheme is based on the
statistical mechanical replica method for dealing with random systems. As a
simple but non-trivial example, we apply the scheme to a sparse autoregressive
model, where the first differences in the input signals of the correlated time
series are sparse, and evaluate the critical compression rate for a perfect
reconstruction. The results are in good agreement with a numerical experiment
for a signal reconstruction.Comment: 6 pages, 3 figure
Statistical mechanical analysis of the Kronecker channel model for MIMO wireless communication
The Kronecker channel model of wireless communication is analyzed using
statistical mechanics methods. In the model, spatial proximities among
transmission/reception antennas are taken into account as certain correlation
matrices, which generally yield non-trivial dependence among symbols to be
estimated. This prevents accurate assessment of the communication performance
by naively using a previously developed analytical scheme based on a matrix
integration formula. In order to resolve this difficulty, we develop a
formalism that can formally handle the correlations in Kronecker models based
on the known scheme. Unfortunately, direct application of the developed scheme
is, in general, practically difficult. However, the formalism is still useful,
indicating that the effect of the correlations generally increase after the
fourth order with respect to correlation strength. Therefore, the known
analytical scheme offers a good approximation in performance evaluation when
the correlation strength is sufficiently small. For a class of specific
correlation, we show that the performance analysis can be mapped to the problem
of one-dimensional spin systems in random fields, which can be investigated
without approximation by the belief propagation algorithm
Generalization of generative model for neuronal ensemble inference method
Various brain functions that are necessary to maintain life activities
materialize through the interaction of countless neurons. Therefore, it is
important to analyze the structure of functional neuronal network. To elucidate
the mechanism of brain function, many studies are being actively conducted on
the structure of functional neuronal ensemble and hub, including all areas of
neuroscience. In addition, recent study suggests that the existence of
functional neuronal ensembles and hubs contributes to the efficiency of
information processing. For these reasons, there is a demand for methods to
infer functional neuronal ensembles from neuronal activity data, and methods
based on Bayesian inference have been proposed. However, there is a problem in
modeling the activity in Bayesian inference. The features of each neuron's
activity have non-stationarity depending on physiological experimental
conditions. As a result, the assumption of stationarity in Bayesian inference
model impedes inference, which leads to destabilization of inference results
and degradation of inference accuracy. In this study, we extend the range of
the variable for expressing the neuronal state, and generalize the likelihood
of the model for extended variables. By comparing with the previous study, our
model can express the neuronal state in larger space. This generalization
without restriction of the binary input enables us to perform soft clustering
and apply the method to non-stationary neuroactivity data. In addition, for the
effectiveness of the method, we apply the developed method to multiple
synthetic fluorescence data generated from the electrical potential data in
leaky integrated-and-fire model.Comment: 24 pages, 6 figure