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Free energy of Bayesian Convolutional Neural Network with Skip Connection
The upper bound of free energy of Bayesian CNN with skip connection does not depend on the oveparametrization and, the generalization error of Bayesian CNN has similar property.
Bayesian Free Energy of Deep ReLU Neural Network in Overparametrized Cases
In many research fields in artificial intelligence, it has been shown that deep neural networks are useful to estimate unknown functions on high dimensional input spaces.
Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference
Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery.
Recent Advances in Algebraic Geometry and Bayesian Statistics
Two mathematical solutions and three applications to statistics based on algebraic geometry reported in this article are now being used in many practical fields in data science and artificial intelligence.
Mathematical Theory of Bayesian Statistics for Unknown Information Source
We introduce a place of mathematical theory of Bayesian statistics for unknown uncertainty, which clarifies general properties of cross validation, information criteria, and marginal likelihood, even if an unknown data-generating process is unrealizable by a model or even if the posterior distribution cannot be approximated by any normal distribution.
Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures
Multinomial mixtures are widely used in the information engineering field, however, their mathematical properties are not yet clarified because they are singular learning models.
Asymptotic Behavior of Free Energy When Optimal Probability Distribution Is Not Unique
Bayesian inference is a widely used statistical method.
Bayesian Inference
Statistics Theory
Statistics Theory
62F15
Asymptotic Bayesian Generalization Error in Latent Dirichlet Allocation and Stochastic Matrix Factorization
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.
Upper Bound of Bayesian Generalization Error in Non-negative Matrix Factorization
Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis.
Bayesian Cross Validation and WAIC for Predictive Prior Design in Regular Asymptotic Theory
By the formula, three facts are clarified about predictive prior design.
