Search Results for author: Naoki Hayashi

Found 6 papers, 2 papers with code

Upper Bound of Bayesian Generalization Error in Partial Concept Bottleneck Model (CBM): Partial CBM outperforms naive CBM

no code implementations14 Mar 2024 Naoki Hayashi, Yoshihide Sawada

In this paper, we reveal the Bayesian generalization error in PCBM with a three-layered and linear architecture.

Bayesian Generalization Error in Linear Neural Networks with Concept Bottleneck Structure and Multitask Formulation

no code implementations16 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.

The Exact Asymptotic Form of Bayesian Generalization Error in Latent Dirichlet Allocation

1 code implementation4 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.

Bayesian Inference Clustering

Variational Approximation Error in Bayesian Non-negative Matrix Factorization

1 code implementation9 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.

Variational Inference

Asymptotic Bayesian Generalization Error in Latent Dirichlet Allocation and Stochastic Matrix Factorization

no code implementations13 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.

Bayesian Inference Topic Models

Upper Bound of Bayesian Generalization Error in Non-negative Matrix Factorization

no code implementations13 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.

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