主講人：李國(guó)棟 香港大學(xué)統(tǒng)計(jì)與精算學(xué)系教授

時(shí)間：2022年11月4日13：00

地點(diǎn)：騰訊會(huì)議 815 7887 2599

舉辦單位：數(shù)理學(xué)院

主講人介紹：李國(guó)棟，本科和碩士畢業(yè)于北大數(shù)學(xué)學(xué)院，2007年于香港大學(xué)統(tǒng)計(jì)精算系獲得統(tǒng)計(jì)學(xué)博士，隨后在南洋理工大學(xué)任助理教授?，F(xiàn)任香港大學(xué)統(tǒng)計(jì)精算系教授。主要研究方向包括時(shí)間序列分析，分位數(shù)回歸，高維統(tǒng)計(jì)數(shù)據(jù)分析和機(jī)器學(xué)習(xí)。李教授目前發(fā)表學(xué)術(shù)論文 40余篇，其中10余篇發(fā)表在統(tǒng)計(jì)學(xué)4大頂級(jí)期刊，以及機(jī)器學(xué)習(xí)的頂級(jí)會(huì)議上。

內(nèi)容介紹：Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater than four or five. However, for the simplest tensor autoregression in handling time series data, its coefficient tensor already has the order of six. This paper revises a newly proposed tensor train (TT) decomposition and then applies it to tensor regression such that a nice statistical interpretation can be obtained. The new tensor regression can well match the data with hierarchical structures, and it even can lead to a better interpretation for the data with factorial structures, which are supposed to be better fitted by models with Tucker decomposition. More importantly, the new tensor regression can be easily applied to the case with higher order tensors since TT decomposition can compress the coefficient tensors much more efficiently. The methodology is also extended to tensor autoregression for time series data, and nonasymptotic properties are derived for the ordinary least squares estimations of both tensor regression and autoregression. A new algorithm is introduced to search for estimators, and its theoretical justification is also discussed. Theoretical and computational properties of the proposed methodology are verified by simulation studies, and the advantages over existing methods are illustrated by two real examples.