Sufficient dimension reduction based on an ensemble of minimum average variance estimators

We introduce a class of dimension reduction estimators based on an ensemble of the minimum average variance estimates of functions that characterize the central subspace, such as the characteristic functions, the Box--Cox transformations and wavelet basis. The ensemble estimators exhaustively estimate the central subspace without imposing restrictive conditions on the predictors, and have the same convergence rate as the minimum average variance estimates. They are flexible and easy to implement, and allow repeated use of the available sample, which enhances accuracy. They are applicable to both univariate and multivariate responses in a unified form. We establish the consistency and convergence rate of these estimators, and the consistency of a cross validation criterion for order determination. We compare the ensemble estimators with other estimators in a wide variety of models, and establish their competent performance.Comment: Published in at http://dx.doi.org/10.1214/11-AOS950 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting

Timely accurate traffic forecast is crucial for urban traffic control and guidance. Due to the high nonlinearity and complexity of traffic flow, traditional methods cannot satisfy the requirements of mid-and-long term prediction tasks and often neglect spatial and temporal dependencies. In this paper, we propose a novel deep learning framework, Spatio-Temporal Graph Convolutional Networks (STGCN), to tackle the time series prediction problem in traffic domain. Instead of applying regular convolutional and recurrent units, we formulate the problem on graphs and build the model with complete convolutional structures, which enable much faster training speed with fewer parameters. Experiments show that our model STGCN effectively captures comprehensive spatio-temporal correlations through modeling multi-scale traffic networks and consistently outperforms state-of-the-art baselines on various real-world traffic datasets.Comment: Proceedings of the 27th International Joint Conference on Artificial Intelligenc