Fumiyasu Komaki

Shrinkage priors for bayesian prediction

We investigate shrinkage priors for constructing Bayesian predictive distributions. It is shown that there exist shrinkage predictive distributions asymptotically dominating Bayesian predictive distributions based on the Jeffreys prior or other vague priors if the model manifold satisfies some differential geometric conditions. Kullback-Leibler divergence from the true distribution to a predictive distribution is adopted as a loss function. Conformal transformations of model manifolds corresponding to vague priors are introduced. We show several examples where shrinkage predictive distributions dominate Bayesian predictive distributions based on vague priors.

Simultaneous prediction of independent Poisson observables

Simultaneous predictive distributions for independent Poisson observables are investigated. A class of improper prior distributions for Poisson means is introduced. The Bayesian predictive distributions based on priors from the introduced class are shown to be admissible under the Kullback-Leibler loss. A Bayesian predictive distribution based on a prior in this class dominates the Bayesian predictive distribution based on the Jeffreys prior.

Information criteria for support vector machines

This paper presents kernel regularization information criterion (KRIC), which is a new criterion for tuning regularization parameters in kernel logistic regression (KLR) and support vector machines (SVMs). The main idea of the KRIC is based on the regularization information criterion (RIC). We derive an eigenvalue equation to calculate the KRIC and solve the problem. The computational cost for parameter tuning by the KRIC is reduced drastically by using the Nystroumlm approximation. The test error rate of SVMs or KLR with the regularization parameter tuned by the KRIC is comparable with the one by the cross validation or evaluation of the evidence. The computational cost of the KRIC is significantly lower than the one of the other criteria

Asymptotic Properties of Bayesian Predictive Densities When the Distributions of Data and Target Variables are Different

Bayesian predictive densities when the observed data

An Extension of Least Angle Regression Based on the Information Geometry of Dually Flat Spaces

x

Bayesian Predictive Distribution with Right Invariant Priors

and the target variable

A superharmonic prior for the autoregressive process of the second-order

y

Asymptotically minimax Bayesian predictive densities for multinomial models

to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is evaluated by the Kullback--Leibler divergence. The parametric models are formulated as Riemannian manifolds. In the conventional setting in which

Singular value shrinkage priors for Bayesian prediction

x

An Estimating Method for Parametric Spectral Densities of Gaussian Time Series

and