Broadcasted Nonparametric Tensor Regression

Zhou, Yue; Wong, Raymond Chi-Wing; He, Kebin

doi:10.48550/arxiv.2008.12927

Cited by 3 publications

(5 citation statements)

References 44 publications

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“…Thus, some works use basis functions to approximate the true functions using weighting factors. In other words, the true function which needs to be estimated can be represented by basis functions, such as finite multidimensional Fourier series (Wahls et al, 2014), polynomial splines (Hao et al, 2021), and B-splines (Zhou et al, 2020b). Specifically,…”

Section: Tensor Additive Modelsmentioning

confidence: 99%

“…1561/2200000087 et al (2021) and Zhou et al (2020b) both assumed the coefficient tensor to be low CP rank, while low rank tensor train approximation is employed in Wahls et al (2014). In addition, the sparsity constraints are enforced over the latent factors to select the important correlated subregions for the response, such as the group sparsity constraint (Hao et al, 2021), and the elastic-net penalty (Zhou et al, 2020b). The alternating minimization method is used to update the latent factors.…”

Section: Tensor Additive Modelsmentioning

confidence: 99%

“…7.2. Later, some nonlinear models such as kernelized HOPLS (Zhao et al, 2013b), online tensor Gaussian process regression models , penalized N -way PLS (Eliseyev and Aksenova, 2016), online adaptive group-wise sparse N -way PLS (Moly et al, 2020) and broadcasted nonparametric tensor regression (Zhou et al, 2020b), are also used to decode ECoG signals. It is worth noting that most of the ECOG signal decoding works mentioned above are based on experimental cases of primates, while Moly et al (2020) decodes the ECoG recordings of a tetraplegic patient.…”

Section: Neural Decodingmentioning

confidence: 99%

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Tensor Regression

Liu

Zhu

Zhang

et al. 2021

FNT in Machine Learning

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The presence of multidirectional correlations in emerging multidimensional data poses a challenge to traditional regression modeling methods. Traditional modeling methods based on matrix or vector, for example, not only overlook the data's multidimensional information and lower model performance, but also add additional computations and storage requirements. Driven by the recent advances in applied mathematics, tensor regression has been widely used and proven effective in many fields, such as sociology, climatology, geography, economics, computer vision, chemometrics, and neuroscience. Tensor regression can explore multidirectional relatedness, reduce the number of model parameters and improve model robustness and efficiency. It is timely and valuable to summarize the developments of tensor regression in recent years and discuss promising future directions, which will help accelerate the research process of tensor regression, broaden the research direction, and provide tutorials for researchers interested in high dimensional regression tasks.

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Section: Tensor Additive Modelsmentioning

confidence: 99%

Section: Tensor Additive Modelsmentioning

confidence: 99%

Section: Neural Decodingmentioning

confidence: 99%

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Tensor Regression

Liu

Zhu

Zhang

et al. 2021

FNT in Machine Learning

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“…Indeed, most existing methods to solve the optimization over a low-CP-rank space are iterative algorithms (e.g. Guo et al, 2011;Tan et al, 2012;Zhou et al, 2013;Lock, 2018;Zhang et al, 2018;Hao et al, 2019;Zhou et al, 2020). Let θ t represent the output value of θ at the t-th iteration of the algorithm.…”

Section: Characterization Of Degeneracymentioning

confidence: 99%

CP Degeneracy in Tensor Regression

Zhou,

Wong,

2020

Preprint

Self Cite

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Tensor linear regression is an important and useful tool for analyzing tensor data. To deal with high dimensionality, CANDECOMP/PARAFAC (CP) low-rank constraints are often imposed on the coefficient tensor parameter in the (penalized) M -estimation. However, we show that the corresponding optimization may not be attainable, and when this happens, the estimator is not well-defined. This is closely related to a phenomenon, called CP degeneracy, in low-rank tensor approximation problems. In this article, we provide useful results of CP degeneracy in tensor regression problems. In addition, we provide a general penalized strategy as a solution to overcome CP degeneracy. The asymptotic properties of the resulting estimation are also studied. Numerical experiments are conducted to illustrate our findings.

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“…Early tensor predictor regression solutions focus on parametric and usually linear or generalized linear type models (Zhou et al 2013). More recently, Hao et al (2019), Zhou et al (2020) extended tensor predictor regression to nonparametric models through basis expansion. Relatedly, Rabusseau & Kadri (2016), , Sun & Li (2017) studied tensor response regression under different low-dimensional structures, but all assumed linear association models and often assumed the normality distribution.…”

Section: Introductionmentioning

confidence: 99%

Mean Dimension Reduction And Testing For Nonparametric Tensor Response Regression

Lee,

Zhang,

2026

STAT SINICA

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In this article, we propose a flexible model-free approach to the regression analysis of a tensor response and a vector predictor. Without specifying the specific form of the regression mean function, we consider two closely related statistical problems: (i) estimation of the dimension reduction subspace that captures all the variations in the regression mean function, and (ii) hypothesis testing of whether the conditional expectation of a linear dimension reduction of the response given the predictor is invariant to the changes in the predictor. We propose a new nonparametric metric called tensor martingale difference divergence, and study its statistical properties. Built on this new metric, we develop computationally efficient estimation and asymptotically valid testing procedures. We demonstrate the efficacy of our method through both simulations and two real data applications for macroeconomics and e-commerce.

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Broadcasted Nonparametric Tensor Regression

Cited by 3 publications

References 44 publications

Tensor Regression

Tensor Regression

CP Degeneracy in Tensor Regression

Mean Dimension Reduction And Testing For Nonparametric Tensor Response Regression

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