The minibatching technique has been extensively adopted to facilitate stochastic first-order methods because of their computational efficiency in parallel computing for large-scale machine learning and data mining. However, the optimal minibatch size determination for accelerated stochastic gradient methods is not completely understood. Actually, there appears trade-off between the iteration complexity and the total computational complexity; that is, the number of iterations (minibatch queries) can be decreased by increasing the minibatch size, but too large minibatch size would result in an unnecessarily large total computational cost. In this study, we give a sharp characterization of the minimax optimal minibatch size to achieve the optimal iteration complexity by providing a reachable lower bound for minimizing finite sum of convex functions and, surprisingly, show that the optimal method with the minimax optimal minibatch size can achieve both of the optimal iteration complexity and the optimal total computational complexity simultaneously. Finally, this feature is verified experimentally.

This paper proposes a very-short-term, i.e., less than 1-hour, local weather forecast method. In general, a short-term weather forecast within 3 hours is difficult due to lack of surface weather data and limitations of computation resources. However, such a short-term prediction is getting more and more anticipated in several industrial situations such as transportation, retailing business, agriculture, and energy management as well as our daily life. To keep up with this huge demands, services based on very-short-term weather forecast began to be provided. Data sources for such kind of forecast are private company-owned surface sensor networks in addition to nation-owned surface sensors. Some surface weather sensors of private companies are more densely distributed than nation-owned sensors. We call these surface weather sensor network as dense weather stations. Among them, for example, POTEKA sensors are located in roughly every 2 to 3 km and provide observed data every minute through mobile network. Those dense sensors are spreading its locations over the world. However, a data mining technique for such a device has not been well developed. In this paper, we propose a deep learning architecture specifically developed for the short-term weather forecasting based on the dense weather station device. Our proposal consists of two folds: point prediction model and tensor prediction model. The point prediction model is useful for forecasting exactly on the location of the dense weather station. The tensor prediction model interpolate the prediction of the point prediction model to cover whole range of locations around the interested area. It is shown that our model outperforms the existing state-of-the-art methods such as XGBoost and support vector machines using a large real observed data.

Methods for directly estimating the ratio of two probability density functions without going through density estimation have been actively explored recently since they can be used for various data processing tasks such as non-stationarity adaptation, outlier detection, conditional density estimation, feature selection, and independent component analysis. However, even the state-of-the-art density ratio estimation methods still perform rather poorly in high-dimensional problems. In this paper, we propose a new density ratio estimation method which incorporates dimensionality reduction into a density ratio estimation procedure. Our key idea is to identify a low-dimensional subspace in which the two densities corresponding to the denominator and the numerator in the density ratio are significantly different. Then the density ratio is estimated only within this low-dimensional subspace. Through numerical examples, we illustrate the effectiveness of the proposed method.