Tensor Regression with Applications in Neuroimaging Data Analysis

By Hua Zhou, Lexin Li, Hongtu Zhu. Journal of the American Statistical Association, 2012

629 citations recorded by the source corpus.

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data. Supplementary materials for this article are available online.

Subfields: Computational Mathematics, Numerical Analysis, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/cae78de351d5cbd5bd7fd853cf07034ca2e6659c

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Citations in the corpus

Matrix variate regressions and envelope models (2016, background): “This rank-one formulation and its variants have been studied in recent work for modeling a univariate response with matrix-valued predictors (e.g., Ye et al., 2004; Hung and Wang, 2013; Zhou et al., 2013).”
Tensor Regression Networks (2017, background): “Several prior papers address the power of tensor regression to preserve natural multimodal structure and learn compact predictive models (Guo et al., 2012; Rabusseau and Kadri, 2016; Zhou et al., 2013; Yu and Liu, 2016).”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, background): “5) where “ ̋” denotes the outer product of vectors, leads to a generalized linear model (GLM), called the CP tensor regression [Zhou et al., 2013].”
TensorLy: Tensor Learning in Python (2016, methodology): “…[28]) Tucker decomposition (Higher-Order SVD) (e.g. [17]) Non-Negative Tucker decomposition [16]) Tensor Ridge regression (Tucker and Kruskal) [11, 32, 18] Table 2: Algorithms implemented propose an efﬁcient unfolding of tensors which differs from the traditional one [17] by the ordering of the…”
Learning Multi-Way Relations via Tensor Decomposition With Neural Networks (2018, background): “Several studies on the classification of tensors have been reported (Tao et al. 2007; He et al. 2014; Zhou, Li, and Zhu 2013; Imaizumi and Hayashi 2016).”
On the Convergence of Asynchronous Parallel Iteration with Unbounded Delays (2016, background): “Many applications can be formulated in the form of (1), and they include classic machine learning problems: support vector machine (squared hinge loss and its dual formulation) [6], LASSO [30], and logistic regression (linear or multilinear) [37], and also subspace learning problems: sparse principa”
Foundations for Envelope Models and Methods (2015, background): “Although we focused on vector-valued parameters, the extension in the Supplement for matrix-valued parameters suggests that our general construction can be straightforwardly extend to matrix-valued or even higher-order tensor-valued regressions (see, e.g., Zhou and Li 2014; Zhou, Li, and Zhu 2013).”