A situation where training and test samples follow different input distributions is called covariate shift. Under covariate shift, standard learning methods such as maximum likelihood estimation are no longer consistent-weighted variants according to the ratio of test and training input densities are consistent. Therefore, accurately estimating the density ratio, called the importance, is one of the key issues in covariate shift adaptation. A naive approach to this task is to first estimate training and test input densities separately and then estimate the importance by taking the ratio of the estimated densities. However, this naive approach tends to perform poorly since density estimation is a hard task particularly in high dimensional cases. In this paper, we propose a direct importance estimation method that does not involve density estimation. Our method is equipped with a natural cross validation procedure and hence tuning parameters such as the kernel width can be objectively optimized. Furthermore, we give rigorous mathematical proofs for the convergence of the proposed algorithm. Simulations illustrate the usefulness of our approach

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We report on an automated runtime anomaly detection method at the application layer of multi-node computer systems. Although several network management systems are available in the market, none of them have sufficient capabilities to detect faults in multi-tier Web-based systems with redundancy. We model a Web-based system as a weighted graph, where each node represents a "service" and each edge represents a dependency between services. Since the edge weights vary greatly over time, the problem we address is that of anomaly detection from a time sequence of graphs.In our method, we first extract a feature vector from the adjacency matrix that represents the activities of all of the services. The heart of our method is to use the principal eigenvector of the eigenclusters of the graph. Then we derive a probability distribution for an anomaly measure defined for a time-series of directional data derived from the graph sequence. Given a critical probability, the threshold value is adaptively updated using a novel online algorithm.We demonstrate that a fault in a Web application can be automatically detected and the faulty services are identified without using detailed knowledge of the behavior of the system.

Most of the existing analysis methods for tensors (or multiway arrays) only assume that tensors to be completed are of low rank. However, for example, when they are applied to tensor completion problems, their prediction accuracy tends to be significantly worse when only limited entries are observed. In this paper, we propose to use relationships among data as auxiliary information in addition to the low-rank assumption to improve the quality of tensor decomposition. We introduce two regularization approaches using graph Laplacians induced from the relationships, and design iterative algorithms for approximate solutions. Numerical experiments on tensor completion using synthetic and benchmark datasets show that the use of auxiliary information improves completion accuracy over the existing methods based only on the low-rank assumption, especially when observations are sparse.