Abstract

Functional data is ubiquitous in many domains, such as healthcare, social media, manufacturing process, sensor networks, and so on. The goal of function-on-function regression is to build a mapping from functional predictors to functional response. In this article, we propose a novel function-on-function regression model based on mode-sparsity regularization. The main idea is to represent the regression coefficient function between predictor and response as the double expansion of basis functions, and then use a mode-sparsity regularization to automatically filter out irrelevant basis functions for both predictors and responses. The proposed approach is further extended to the tensor version to accommodate multiple functional predictors. While allowing the dimensionality of the regression weight matrix or tensor to be relatively large, the mode-sparsity regularized model facilitates the multi-way shrinking of basis functions for each mode. The proposed mode-sparsity regularization covers a wide spectrum of sparse models for function-on-function regression. The resulting optimization problem is challenging due to the non-smooth property of the mode-sparsity regularization. We develop an efficient algorithm to solve the problem, which works in an iterative update fashion, and converges to the global optimum. Furthermore, we analyze the generalization performance of the proposed method and derive an upper bound for the consistency between the recovered function and the underlying true function. The effectiveness of the proposed approach is verified on benchmark functional datasets in various domains.

Original languageEnglish (US)
Article number36
JournalACM Transactions on Knowledge Discovery from Data
Volume12
Issue number3
DOIs
StatePublished - Jan 1 2018

Fingerprint

Tensors
Sensor networks

Keywords

  • Function-on-function regression
  • Mode-sparsity regularization

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Function-on-function regression with mode-sparsity regularization. / Yang, Pei; Tan, Qi; He, Jingrui.

In: ACM Transactions on Knowledge Discovery from Data, Vol. 12, No. 3, 36, 01.01.2018.

Research output: Contribution to journalArticle

@article{165dc799fb1f4878a6860c08e6b49089,
title = "Function-on-function regression with mode-sparsity regularization",
abstract = "Functional data is ubiquitous in many domains, such as healthcare, social media, manufacturing process, sensor networks, and so on. The goal of function-on-function regression is to build a mapping from functional predictors to functional response. In this article, we propose a novel function-on-function regression model based on mode-sparsity regularization. The main idea is to represent the regression coefficient function between predictor and response as the double expansion of basis functions, and then use a mode-sparsity regularization to automatically filter out irrelevant basis functions for both predictors and responses. The proposed approach is further extended to the tensor version to accommodate multiple functional predictors. While allowing the dimensionality of the regression weight matrix or tensor to be relatively large, the mode-sparsity regularized model facilitates the multi-way shrinking of basis functions for each mode. The proposed mode-sparsity regularization covers a wide spectrum of sparse models for function-on-function regression. The resulting optimization problem is challenging due to the non-smooth property of the mode-sparsity regularization. We develop an efficient algorithm to solve the problem, which works in an iterative update fashion, and converges to the global optimum. Furthermore, we analyze the generalization performance of the proposed method and derive an upper bound for the consistency between the recovered function and the underlying true function. The effectiveness of the proposed approach is verified on benchmark functional datasets in various domains.",
keywords = "Function-on-function regression, Mode-sparsity regularization",
author = "Pei Yang and Qi Tan and Jingrui He",
year = "2018",
month = "1",
day = "1",
doi = "10.1145/3178113",
language = "English (US)",
volume = "12",
journal = "ACM Transactions on Knowledge Discovery from Data",
issn = "1556-4681",
publisher = "Association for Computing Machinery (ACM)",
number = "3",

}

TY - JOUR

T1 - Function-on-function regression with mode-sparsity regularization

AU - Yang, Pei

AU - Tan, Qi

AU - He, Jingrui

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Functional data is ubiquitous in many domains, such as healthcare, social media, manufacturing process, sensor networks, and so on. The goal of function-on-function regression is to build a mapping from functional predictors to functional response. In this article, we propose a novel function-on-function regression model based on mode-sparsity regularization. The main idea is to represent the regression coefficient function between predictor and response as the double expansion of basis functions, and then use a mode-sparsity regularization to automatically filter out irrelevant basis functions for both predictors and responses. The proposed approach is further extended to the tensor version to accommodate multiple functional predictors. While allowing the dimensionality of the regression weight matrix or tensor to be relatively large, the mode-sparsity regularized model facilitates the multi-way shrinking of basis functions for each mode. The proposed mode-sparsity regularization covers a wide spectrum of sparse models for function-on-function regression. The resulting optimization problem is challenging due to the non-smooth property of the mode-sparsity regularization. We develop an efficient algorithm to solve the problem, which works in an iterative update fashion, and converges to the global optimum. Furthermore, we analyze the generalization performance of the proposed method and derive an upper bound for the consistency between the recovered function and the underlying true function. The effectiveness of the proposed approach is verified on benchmark functional datasets in various domains.

AB - Functional data is ubiquitous in many domains, such as healthcare, social media, manufacturing process, sensor networks, and so on. The goal of function-on-function regression is to build a mapping from functional predictors to functional response. In this article, we propose a novel function-on-function regression model based on mode-sparsity regularization. The main idea is to represent the regression coefficient function between predictor and response as the double expansion of basis functions, and then use a mode-sparsity regularization to automatically filter out irrelevant basis functions for both predictors and responses. The proposed approach is further extended to the tensor version to accommodate multiple functional predictors. While allowing the dimensionality of the regression weight matrix or tensor to be relatively large, the mode-sparsity regularized model facilitates the multi-way shrinking of basis functions for each mode. The proposed mode-sparsity regularization covers a wide spectrum of sparse models for function-on-function regression. The resulting optimization problem is challenging due to the non-smooth property of the mode-sparsity regularization. We develop an efficient algorithm to solve the problem, which works in an iterative update fashion, and converges to the global optimum. Furthermore, we analyze the generalization performance of the proposed method and derive an upper bound for the consistency between the recovered function and the underlying true function. The effectiveness of the proposed approach is verified on benchmark functional datasets in various domains.

KW - Function-on-function regression

KW - Mode-sparsity regularization

UR - http://www.scopus.com/inward/record.url?scp=85047017452&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047017452&partnerID=8YFLogxK

U2 - 10.1145/3178113

DO - 10.1145/3178113

M3 - Article

VL - 12

JO - ACM Transactions on Knowledge Discovery from Data

JF - ACM Transactions on Knowledge Discovery from Data

SN - 1556-4681

IS - 3

M1 - 36

ER -