no code implementations • 14 Mar 2024 • Naoki Hayashi, Yoshihide Sawada
In this paper, we reveal the Bayesian generalization error in PCBM with a three-layered and linear architecture.
no code implementations • 16 Mar 2023 • Naoki Hayashi, Yoshihide Sawada
However, it has not yet been possible to understand the behavior of the generalization error in CBM since a neural network is a singular statistical model in general.
1 code implementation • 4 Aug 2020 • Naoki Hayashi
The theoretical result shows that the Bayesian generalization error in LDA is expressed in terms of that in matrix factorization and a penalty from the simplex restriction of LDA's parameter region.
1 code implementation • 9 Sep 2018 • Naoki Hayashi
However, the variational approximation error has not been clarified yet, because NMF is not statistically regular and the prior distribution used in variational Bayesian NMF (VBNMF) has zero or divergence points.
no code implementations • 13 Sep 2017 • Naoki Hayashi, Sumio Watanabe
Latent Dirichlet allocation (LDA) is useful in document analysis, image processing, and many information systems; however, its generalization performance has been left unknown because it is a singular learning machine to which regular statistical theory can not be applied.
no code implementations • 13 Dec 2016 • Naoki Hayashi, Sumio Watanabe
Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis.