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  1. Abstract

    Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CANDECOMP/PARAFAC (CP) decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high-order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations.

     
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  2. Dealing with data heterogeneity is a key challenge in the theoretical analysis of federated learning (FL) algorithms. In the literature, gradient divergence is often used as the sole metric for data heterogeneity. However, we observe that the gradient divergence cannot fully characterize the impact of the data heterogeneity in Federated Averaging (FedAvg) even for the quadratic objective functions. This limitation leads to an overestimate of the communication complexity. Motivated by this observation, we propose a new analysis framework based on the difference between the minima of the global objective function and the minima of the local objective functions. Using the new framework, we derive a tighter convergence upper bound for heterogeneous quadratic objective functions. The theoretical results reveal new insights into the impact of the data heterogeneity on the convergence of FedAvg and provide a deeper understanding of the two-stage learning rates. Experimental results using non-IID data partitions validate the theoretical findings. 
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  3. Key Points Geochemical evidence suggests that the Mongolian Plateau (MP) is the main source of dust for Lake Tuofengling (TFL) The East Asian Winter Monsoon (EAWM) is likely the dominant carrier of aeolian dust from the MP to TFL Dust flux and EAWM variability could be driven by a combination of changes in ice volume and Atlantic Ocean circulation 
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  4. International trade research plays an important role to inform trade policy and shed light on wider economic issues. With recent advances in information technology, economic agencies distribute an enormous amount of internationally comparable trading data, providing a gold mine for empirical analysis of international trade. International trading data can be viewed as a dynamic transport network because it emphasizes the amount of goods moving across network edges. Most literature on dynamic network analysis concentrates on parametric modeling of the connectivity network that focuses on link formation or deformation rather than the transport moving across the network. We take a different non-parametric perspective from the pervasive node-and-edge-level modeling: the dynamic transport network is modeled as a time series of relational matrices; variants of the matrix factor model of Wang et al. (2019) are applied to provide a specific interpretation for the dynamic transport network. Under the model, the observed surface network is assumed to be driven by a latent dynamic transport network with lower dimensions. Our method is able to unveil the latent dynamic structure and achieves the goal of dimension reduction. We applied the proposed method to a dataset of monthly trading volumes among 24 countries (and regions) from 1982 to 2015. Our findings shed light on trading hubs, centrality, trends, and patterns of international trade and show matching change points to trading policies. The dataset also provides a fertile ground for future research on international trade.

     
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