Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor Regression Meets Gaussian Processes   Low-rank tensor regression, a new model class that learns high-order
correlation from data, has recently received considerable attention. At the
same time, Gaussian processes (GP) are well-studied machine learning models for
structure learning. In this paper, we demonstrate interesting connections
between the two, especially for multi-way data analysis. We show that low-rank
tensor regression is essentially learning a multi-linear kernel in Gaussian
processes, and the low-rank assumption translates to the constrained Bayesian
inference problem. We prove the oracle inequality and derive the average case
learning curve for the equivalent GP model. Our finding implies that low-rank
tensor regression, though empirically successful, is highly dependent on the
eigenvalues of covariance functions as well as variable correlations.

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The categories of this paper are: gr-qc
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The categories of this paper are: econ
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph