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Effect of global shrinkage parameter of horseshoe prior in compressed sensing
Yasushi Nagano, Koji Hukushima
In sparse signal processing, this study investigates the effect of the global shrinkage parameter of a horseshoe prior, one of the global-local shrinkage prior, on the linear r…
Phase transition in compressed sensing with horseshoe prior
Yasushi Nagano, Koji Hukushima
In Bayesian statistics, horseshoe prior has attracted increasing attention as an approach to the sparse estimation. The estimation accuracy of compressed sensing with the horseshoe…
Statistical-mechanical study of deep Boltzmann machine given weight parameters after training by singular value decomposition
Yuma Ichikawa, Koji Hukushima
Deep learning methods relying on multi-layered networks have been actively studied in a wide range of fields in recent years, and deep Boltzmann machines(DBMs) is one of them. In t…
Absence of Phase Transition in Random Language Model
Kai Nakaishi, Koji Hukushima
The Random Language Model, proposed as a simple model of human languages, is defined by the averaged model of a probabilistic context-free grammar. This grammar expresses the proce…
Large-deviation Properties of Linear-programming Computational Hardness of the Vertex Cover Problem
Satoshi Takabe, Koji Hukushima, Alexander K. Hartmann
The distribution of the computational cost of linear-programming (LP) relaxation for vertex cover problems on Erdos-Renyi random graphs is evaluated by using the rare-event samplin…
Typical Approximation Performance for Maximum Coverage Problem
Satoshi Takabe, Takanori Maehara, Koji Hukushima
This study investigated typical performance of approximation algorithms known as belief propagation, greedy algorithm, and linear-programming relaxation for maximum coverage proble…