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Spectral methods for data science: A statistical perspective
Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …
Tensor methods in high dimensional data analysis: Opportunities and challenges
Large amount of multidimensional data represented by multiway arrays or tensors are
prevalent in modern applications across various fields such as chemometrics, genomics …
prevalent in modern applications across various fields such as chemometrics, genomics …
Scaling and scalability: Provable nonconvex low-rank tensor estimation from incomplete measurements
Tensors, which provide a powerful and flexible model for representing multi-attribute data
and multi-way interactions, play an indispensable role in modern data science across …
and multi-way interactions, play an indispensable role in modern data science across …
Tensors in High-Dimensional Data Analysis: Methodological Opportunities and Theoretical Challenges
Large amounts of multidimensional data represented by multiway arrays or tensors are
prevalent in modern applications across various fields such as chemometrics, genomics …
prevalent in modern applications across various fields such as chemometrics, genomics …
Exact clustering in tensor block model: Statistical optimality and computational limit
High-order clustering aims to identify heterogeneous substructures in multiway datasets that
arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex …
arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex …
Generalized low-rank plus sparse tensor estimation by fast Riemannian optimization
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor,
where the low-rank tensor often captures the multi-way principal components and the sparse …
where the low-rank tensor often captures the multi-way principal components and the sparse …
Tensor clustering with planted structures: Statistical optimality and computational limits
Tensor clustering with planted structures: Statistical optimality and computational limits
Page 1 The Annals of Statistics 2022, Vol. 50, No. 1, 584–613 https://doi.org/10.1214/21-AOS2123 …
Page 1 The Annals of Statistics 2022, Vol. 50, No. 1, 584–613 https://doi.org/10.1214/21-AOS2123 …
Provable tensor-train format tensor completion by Riemannian optimization
The tensor train (TT) format enjoys appealing advantages in handling structural high-order
tensors. The recent decade has witnessed the wide applications of TT-format tensors from …
tensors. The recent decade has witnessed the wide applications of TT-format tensors from …
High-dimensional low-rank tensor autoregressive time series modeling
Modern technological advances have enabled an unprecedented amount of structured data
with complex temporal dependence, urging the need for new methods to efficiently model …
with complex temporal dependence, urging the need for new methods to efficiently model …
Tensor-on-tensor regression: Riemannian optimization, over-parameterization, statistical-computational gap and their interplay
Tensor-on-tensor regression: Riemannian optimization, over-parameterization, statistical-computational
gap and their interplay Page 1 The Annals of Statistics 2024, Vol. 52, No. 6, 2583–2612 …
gap and their interplay Page 1 The Annals of Statistics 2024, Vol. 52, No. 6, 2583–2612 …