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1. Multiway clustering via tensor block models

   Wang, Miaoyan ; Zeng, Yuchen ( December 2019 , Advances in Neural Information Processing Systems 32 (NeurIPS))

   We consider the problem of identifying multiway block structure from a large noisy tensor. Such problems arise frequently in applications such as genomics, recommendation system, topic modeling, and sensor network localization. We propose a tensor block model, develop a unified least-square estimation, and obtain the theoretical accuracy guarantees for multiway clustering. The statistical convergence of the estimator is established, and we show that the associated clustering procedure achieves partition consistency. A sparse regularization is further developed for identifying important blocks with elevated means. The proposal handles a broad range of data types, including binary, continuous, and hybrid observations. Through simulation and application to two real datasets, we demonstrate the outperformance of our approach over previous methods. 

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2. Multiway Spherical Clustering via Degree-Corrected Tensor Block Models

   Jiaxin Hu and Miaoyan Wang ( April 2022 , Proceedings of the 25th International Conference on Artificial Intelligence and Statistics (AISTATS) 2022, Valencia, Spain.)

   We consider the problem of multiway clustering in the presence of unknown degree​ ​heterogeneity. Such data problems arise commonly in applications such as recommendation systems, neuroimaging, community detection, and hypergraph partitions​ ​in social networks. The allowance of degree heterogeneity provides great flexibility​ ​in clustering models, but the extra complexity poses significant challenges in both​ ​statistics and computation. Here, we develop a degree-corrected tensor block model​ ​with estimation accuracy guarantees. We present the phase transition of clustering​ ​performance based on the notion of angle separability, and we characterize three​ ​signal-to-noise regimes corresponding to different statistical-computational behaviors.​ ​In particular, we demonstrate that an intrinsic statistical-to-computational gap emerges​ ​only for tensors of order three or greater.​ ​Further, we develop an efficient polynomial time algorithm that provably achieves exact​ ​clustering under mild signal conditions. The​ ​efficacy of our procedure is demonstrated​ ​through both simulations and analyses of​ ​Peru Legislation dataset. 

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3. Multiway spherical clustering via degree-corrected tensor block models.

   Hu, Jiaxin ; Wang, Miaoyan ( April 2022 , The 25th International Conference on Artificial Intelligence and Statistics)

   We consider the problem of multiway clus- tering in the presence of unknown degree heterogeneity. Such data problems arise commonly in applications such as recom- mendation system, neuroimaging, commu- nity detection, and hypergraph partitions in social networks. The allowance of de- gree heterogeneity provides great flexibility in clustering models, but the extra com- plexity poses significant challenges in both statistics and computation. Here, we de- velop a degree-corrected tensor block model with estimation accuracy guarantees. We present the phase transition of clustering performance based on the notion of an- gle separability, and we characterize three signal-to-noise regimes corresponding to dif- ferent statistical-computational behaviors. In particular, we demonstrate that an intrin- sic statistical-to-computational gap emerges only for tensors of order three or greater. Further, we develop an efficient polynomial- time algorithm that provably achieves exact clustering under mild signal conditions. The efficacy of our procedure is demonstrated through both simulations and analyses of Peru Legislation dataset. 

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4. Learning Multiple Networks via Supervised Tensor Decomposition

   Hu, Jiaxin ; Lee, Chanwoo ; Wang, Miaoyan ( December 2020 , NeurIPS 2023, Machine Learning and the Physical Sciences Workshop)

   We consider the problem of tensor decomposition with multiple side information available as interactive features. Such problems are common in neuroimaging, network modeling, and spatial-temporal analysis. We develop a new family of exponential tensor decomposition models and establish the theoretical accuracy guarantees. An efficient alternating optimization algorithm is further developed. Unlike earlier methods, our proposal is able to handle a broad range of data types, including continuous, count, and binary observations. We apply the method to diffusion tensor imaging data from human connectome project and identify the key brain connectivity patterns associated with available features. Our method will help the practitioners efficiently analyze tensor datasets in various areas. Toward this end, all data and code are available at https://CRAN.R-project.org/ package=tensorregress. 

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5. Learning Multiple Networks via Supervised Tensor Decomposition

   Hu, Jiaxin ; Lee, Chanwoo ; Wang, Miaoyan ( December 2020 , Third Workshop on Machine Learning and the Physical Sciences (NeurIPS 2020), Vancouver, Canada.)

   We consider the problem of tensor decomposition with multiple side information available as interactive features. Such problems are common in neuroimaging, network modeling, and spatial-temporal analysis. We develop a new family of exponential tensor decomposition models and establish the theoretical accuracy guarantees. An efficient alternating optimization algorithm is further developed. Unlike earlier methods, our proposal is able to handle a broad range of data types, including continuous, count, and binary observations. We apply the method to diffusion tensor imaging data from human connectome project and identify the key brain connectivity patterns associated with available features. Our method will help the practitioners efficiently analyze tensor datasets in various areas. Toward this end, all data and code are available at https://CRAN.R-project.org/ package=tensorregress. 

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