Learning Rate for Convex Support Tensor Machines

Heng Lian

doi:10.1109/TNNLS.2020.3015477

Learning Rate for Convex Support Tensor Machines

Heng Lian^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

5 Citations (Scopus)

Abstract

Tensors are increasingly encountered in prediction problems. We extend previous results for high-dimensional least-squares convex tensor regression to classification problems with a hinge loss and establish its asymptotic statistical properties. Based on a general convex decomposable penalty, the rate depends on both the intrinsic dimension and the Rademacher complexity of the class of linear functions of tensor predictors.

Original language	English
Article number	9174817
Pages (from-to)	3755-3760
Journal	IEEE Transactions on Neural Networks and Learning Systems
Volume	32
Issue number	8
Online published	24 Aug 2020
DOIs	https://doi.org/10.1109/TNNLS.2020.3015477
Publication status	Published - Aug 2021

Research Keywords

Empirical processes
high-dimensional regression
hinge loss
intrinsic dimension
Rademacher complexity

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10.1109/TNNLS.2020.3015477

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title = "Learning Rate for Convex Support Tensor Machines",

abstract = "Tensors are increasingly encountered in prediction problems. We extend previous results for high-dimensional least-squares convex tensor regression to classification problems with a hinge loss and establish its asymptotic statistical properties. Based on a general convex decomposable penalty, the rate depends on both the intrinsic dimension and the Rademacher complexity of the class of linear functions of tensor predictors.",

keywords = "Empirical processes, high-dimensional regression, hinge loss, intrinsic dimension, Rademacher complexity",

author = "Heng Lian",

year = "2021",

month = aug,

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language = "English",

volume = "32",

pages = "3755--3760",

journal = "IEEE Transactions on Neural Networks and Learning Systems",

issn = "2162-237X",

publisher = "IEEE Computational Intelligence Society",

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T1 - Learning Rate for Convex Support Tensor Machines

AU - Lian, Heng

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N2 - Tensors are increasingly encountered in prediction problems. We extend previous results for high-dimensional least-squares convex tensor regression to classification problems with a hinge loss and establish its asymptotic statistical properties. Based on a general convex decomposable penalty, the rate depends on both the intrinsic dimension and the Rademacher complexity of the class of linear functions of tensor predictors.

AB - Tensors are increasingly encountered in prediction problems. We extend previous results for high-dimensional least-squares convex tensor regression to classification problems with a hinge loss and establish its asymptotic statistical properties. Based on a general convex decomposable penalty, the rate depends on both the intrinsic dimension and the Rademacher complexity of the class of linear functions of tensor predictors.

KW - Empirical processes

KW - high-dimensional regression

KW - hinge loss

KW - intrinsic dimension

KW - Rademacher complexity

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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85111970562&origin=recordpage

U2 - 10.1109/TNNLS.2020.3015477

DO - 10.1109/TNNLS.2020.3015477

M3 - RGC 21 - Publication in refereed journal

SN - 2162-237X

VL - 32

SP - 3755

EP - 3760

JO - IEEE Transactions on Neural Networks and Learning Systems

JF - IEEE Transactions on Neural Networks and Learning Systems

IS - 8

M1 - 9174817

ER -

Learning Rate for Convex Support Tensor Machines

Abstract

Research Keywords

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GRF: Low-rank tensor as a Dimension Reduction Tool in Complex Data Analysis

GRF: Divide and Conquer in High-dimensional Statistical Models

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Learning Rate for Convex Support Tensor Machines

Abstract

Research Keywords

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GRF: Low-rank tensor as a Dimension Reduction Tool in Complex Data Analysis

GRF: Divide and Conquer in High-dimensional Statistical Models

Cite this