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When training and test samples follow different input distributions (i.e., the situation called covariate shift), the maximum likelihood estimator is known to lose its consistency. For regaining consistency, the log-likelihood terms need to be weighted according to the importance (i.e., the ratio of test and training input densities). Thus, accurately(More)
A key aspect of semantic image segmentation is to integrate local and global features for the prediction of local segment labels. We present an approach to multi-class segmentation which combines two methods for this integration: a Conditional Random Field (CRF) which couples to local image features and an image classification method which considers global(More)
When only a small number of labeled samples are available, supervised dimensionality reduction methods tend to perform poorly due to overfitting. In such cases, unlabeled samples could be useful in improving the performance. In this paper, we propose a semi-supervised dimensionality reduction method which preserves the global structure of unlabeled samples(More)
In this paper, we present a general class of multivariate priors for group-sparse modeling within the Bayesian framework. We show that special cases of this class correspond to multivariate versions of several classical priors used for sparse modeling. Hence, this general prior formulation is helpful in analyzing the properties of different modeling(More)
The variational Bayesian (VB) approximation is known to be a promising approach to Bayesian estimation, when the rigorous calculation of the Bayes posterior is intractable. The VB approximation has been successfully applied to matrix factorization (MF), offering automatic dimensionality selection for principal component analysis. Generally, finding the VB(More)
The variational Bayesian (VB) approach is one of the best tractable approximations to the Bayesian estimation, and it was demonstrated to perform well in many applications. However, its good performance was not fully understood theoretically. For example, VB sometimes produces a sparse solution, which is regarded as a practical advantage of VB, but such(More)
Bayesian methods of matrix factorization (MF) have been actively explored recently as promising alternatives to classical singular value decomposition. In this paper, we show that, despite the fact that the optimization problem is non-convex, the global optimal solution of variational Bayesian (VB) MF can be computed analytically by solving a quartic(More)
Principal component analysis (PCA) approximates a data matrix with a low-rank one by imposing sparsity on its singular values. Its robust variant can cope with spiky noise by introducing an element-wise sparse term. In this paper, we extend such sparse matrix learning methods, and propose a novel framework called sparse additive matrix factorization (SAMF).(More)
In order to achieve good performance in object classification problems, it is necessary to combine information from various image features. Because the large margin classifiers are constructed based on similarity measures between samples called kernels, finding appropriate feature combinations boils down to designing good kernels among a set of candidates,(More)