Statistical mechanics of relaxation process for Bayesian inference and its application

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We investigated dynamics for CDMA multiuser detection. We applied the statistical neurodynamics, which is based on Gaussian approximation for input distribution, to a detection dynamics of a parallel interference canceller (PIC), and proposed a new detection algorithm based on this theoretical analysis. Recently, we have succeeded in obtaining an exact solution for the PIC detection dynamics without the Gaussian approximation using generating functional analysis (GFA). We applied a dynamical replica theory (DRT) to the CDMA detection dynamics. We also applied these theories to the image, restoration and the error-correcting code.We proposed a numerical approach for a class of non-mean field models and finite-size models with sufficient accuracy, in which principal component analysis (PCA) is employed to analyze configurations sampled through Monte Carlo simulations. We showed that the PCA approach will be effective even with general non-MF finite-size models using examples of two-and three-body mean-field Sourlas codes.The quantum annealing method exploits quantum fluctuations to search the ground state of classical disordered Hamiltonian, which corresponds to maximum a posteriori probability estimation. If the quantum fluctuation is reduced sufficiently slowly and linearly by the time, the residual energy after the quantum annealing falls as the inverse square of the annealing time. We show this feature of the residual energy by numerical calculations for small-sized systems and derive it on the basis of the quantum adiabatic theorem.Additionally, we proposed a new framework for the lossy date compression using a sparsely connected random network, which was originally used on the error-correcting code.