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We address the problem of estimating the ratio of two probability density functions, which is often referred to as the importance. The importance values can be used for various succeeding tasks such as covariate shift adaptation or outlier detection. In this paper, we propose a new importance estimation method that has a closed-form solution; the… (More)

We aim at an extension of AdaBoost to U-Boost, in the paradigm to build a stronger classification machine from a set of weak learning machines. A geometric understanding of the Bregman divergence defined by a generic convex function U leads to the U-Boost method in the framework of information geometry extended to the space of the finite measures over a… (More)

Divergence estimators based on direct approximation of density ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution comparison such as outlier detection, transfer learning, and two-sample homogeneity test. However, since density-ratio… (More)

BACKGROUND
Although microarray gene expression analysis has become popular, it remains difficult to interpret the biological changes caused by stimuli or variation of conditions. Clustering of genes and associating each group with biological functions are often used methods. However, such methods only detect partial changes within cell processes. Herein, we… (More)

We address the problem of estimating the ratio of two probability density functions (a.k.a. the importance). The importance values can be used for various succeeding tasks such as non-stationarity adaptation or outlier detection. In this paper, we propose a new importance estimation method that has a closed-form solution; the leave-one-out cross-validation… (More)

Mutual information is useful in various data processing tasks such as feature selection or independent component analysis. In this paper, we propose a new method of approximating mutual information based on maximum likelihood estimation of a density ratio function. Our method, called Maximum Likelihood Mutual Information (MLMI), has several attractive… (More)

A density ratio is defined by the ratio of two probability densities. We study the inference problem of density ratios and apply a semi-parametric density-ratio es-timator to the two-sample homogeneity test. In the proposed test procedure, the f-divergence between two probability densities is estimated using a density-ratio estimator. The f-divergence… (More)

The goal of regression analysis is to describe the stochastic relationship between an input vector x and a scalar output y. This can be achieved by estimating the entire conditional density p(y / x). In this letter, we present a new approach for nonparametric conditional density estimation. We develop a piecewise-linear path-following method for… (More)

Boosting is known as a gradient descent algorithm over loss functions. It is often pointed out that the typical boosting algorithm, Adaboost, is highly affected by outliers. In this letter, loss functions for robust boosting are studied. Based on the concept of robust statistics, we propose a transformation of loss functions that makes boosting algorithms… (More)