Monte Carlo Study of Complex Information Processing Models

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Our aim in this project is to develop numerical tools for analyzing large-scale phase space of probabilistic models which are commonly discussed in statistical-mechanics and information processing, and to clarify their statistical properties by using the tools. Particularly, an extended ensemble Monte Carlo (MC) method has been employed actively as a useful probabilistic algorithm. Main achievements are as follows :1. Development of MC methods and analysis tools : We have proposed a new MC algorithm called "population annealing", which is regarded as a modified way of the simulated annealing to an algorithm for finite-temperature sampling. In addition, we have developed a way to evaluate free-energy difference and have applied multivariate analysis such as principal component analysis (PCA) to large-scale simulation data. A latter example is a PCA study of Sourlas codes, in which a proper stable solution is automatically separated from many metastable solutions in simulation data2. Dev … More elopment in information theory : Survey propagation is a recently developed probabilistic algorithm in the field of information processing. While the method has been already applied to many models, its performance and validity are still poorly understood. We have developed a way for determining a model parameter which is unknown a priori in the survey propagation by using MC method and have found that it works in a random multi-body interaction model.3. Spin glass physics : By large-scale MC simulations, we have found peculiar properties of low-temperature spin glass states which are, for example, fragility under weak perturbation and the existence of chiral glass phase. In addition, we discover extended scaling formulae which express to leading order of thermodynamic observables over a wide range. The extended scaling, illustrated by data on the 3d bimodal Ising spin glass, leads to consistency for the estimates of critical parameters obtained from scaling analyses for different observables. Less