Direct Density Ratio Estimation with Convolutional Neural Networks with Application in Outlier Detection

Recently, the ratio of probability density functions was demonstrated to be useful in solving various machine learning tasks such as outlier detection, non-stationarity adaptation, feature selection, and clustering. The key idea of this density ratio approach is that the ratio is directly estimated so that difficult density estimation is avoided. So far, parametric and non-parametric direct density ratio estimators with various loss functions have been developed, and the kernel least-squares method was demonstrated to be highly useful both in terms of accuracy and computational efficiency. On the other hand, recent study in pattern recognition exhibited that deep architectures such as a convolutional neural network can significantly outperform kernel methods. In this paper, we propose to use the convolutional neural network in density ratio estimation, and experimentally show that the proposed method tends to outperform the kernel-based method in outlying image detection