Statistics Across Campuses

   Estimating a Change Point in a Sequence of Very High-Dimensional Covariance Matrices Date :  Thursday, 29 April 2021 Time:   10 -11 am Speaker: Dr Qing Yang  ( University of Science and Technology of China ) . Abstract: This paper considers the problem of estimating a change point in the covariance matrix in a sequence of high-dimensional vectors, where the dimension is substantially larger than the sample size. A two-stage approach is proposed to efficiently estimate the location of the change point. The first step consists of a reduction of the dimension to identify elements of the covariance matrices corresponding to significant changes. In a second step we use the components after dimension reduction to determine the position of the change point. Theoretical properties are developed for both steps and numerical studies are conducted to support the new methodology. Zoom Link:  Please contact Yanrong Yang ( yanrong.yang@anu.edu.au ) to obtain...

  How framelets enhance graph neural networks Date:  Friday, 30 April 2021 Time:   9-10am Speaker:   Dr  Yu Guang Wang (Max Planck Institute for Mathematics in the Sciences,  Leipzig, Germany) Abstract:  This work presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node a...

  Projected Estimation for Large-dimensional Matrix Factor Models Date:  Thursday, 8 April 2021 Time:   10am AEST, Canberra.  Speaker: Professor Xinbing Kong  ( Nanjing Audit University ) . Abstract:   In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor analysis for matrix series to that of a lower-dimensional tensor. This method also reduces the magnitudes of the idiosyncratic error components, thereby increasing the signal-to-noise ratio, because the projection matrix linearly filters the idiosyncratic error matrix. We theoretically prove that the projected estimators of the factor loading matrices achieve faster convergence rates than existing estimators under similar conditions. Asymptotic distributions of the projected estimators are also presented. A novel iterative proc...