Higher-order tensor data are prevailing in a wide range of fields including high-resolution videos, multimodality imaging such as MRI and fMRI scans, commercial networks, engineering such as signal processing, and elsewhere. Tucker decomposition may be the most general low-rank approximation method among versatile decompositions of higher-order tensors owning to its strong compression ability, whilst statistical properties of the induced Tucker tensor factor model (TuTFaM) remains a big challenge and yet critical before it provides justification for applications in machine learning and beyond. Existing theoretical developments mainly focus on the field of time series with the assumption of strong auto-correlation among temporally ordered observations, which is ineffective for independent and weakly dependent tensor observations.
Under quite mild assumptions, this article kicks off matricization of raw weakly correlated tensor observations within the TuTFaM setting, and proposes two sets of PCA based estimation procedures, moPCA and its refinement IPmoPCA, the latter of which is enhanced in rate of convergence. We develop their asymptotic behaviors, including mainly convergence rates and asymptotic distributions of estimators of loading matrices, latent tensor factors and signal parts.
The theoretical results can reduce to those in low-order tensor factor models in existing literature. The proposed approaches outperform existing auto-covariance based methods for tensor time series in terms of effects of estimation and tensor reconstruction, in both simulation experiments and two real data examples.
個人簡介:
張旭，東北師範大學博士，香港大學及香港理工大學博士後。現為華南師範大學特聘副研究員，碩士生導師。主要研究方向是網絡數據、張量數據的統計建模與推斷。現有論文發表于Statistica Sinica, Journal of Multivariate Analysis等雜志。
報告時間：2023.05.04（周四），19：30—20：30
騰訊會議号：304-394-970
舉辦學院：統計與數據科學學院、bat365在线唯一官网登录