Abstract

Nonlinear structured latent factor model captures the relationship between ob

served variables and latent variables in a nonlinear way, offering greater flexibility compared

to a linear factor model. Functional data characterizes features of data that vary continuously over time or space and is widely applied across various fields. This paper proposes a

nonlinear structured latent factor model for functional data. We consider correlations for

the latent factor to account for the dependence in functional data at different time points.

The structured identifiability of latent factors is studied to ensure uniqueness, thereby allowing these factors to have a physical interpretation. A Gaussian process (GP) prior is

utilized to estimate the unknown nonlinear link functions. To improve computational efficiency, an efficient algorithm is developed by using the nearest neighbor Gaussian process

(NNGP). The consistency of the latent factors and the unknown parameters, as well as the

posterior consistency of the unknown link functions, was established.

Simulation studies

were conducted to demonstrate the finite-sample performance and the flexibility of the proposed model, and the significant computational time savings achieved by NNGP compared

to GP. The method was applied to analyse the gait data collected in our laboratory for early

detection of neurodegenerative diseases.

Xiaorui Wang and Yimang Zhang contributed equally.

Information

Preprint No.SS-2025-0148
Manuscript IDSS-2025-0148
Complete AuthorsXiaorui Wang, Yimang Zhang, Jian Qing Shi
Corresponding AuthorsJian Qing Shi
Emailsshijq@sustech.edu.cn

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Acknowledgments

The authors would like to thank two anonymous reviewers, an associate editor and

the editor for constructive comments and helpful suggestions. This publication is supported by funds of the National Key R & D Program of China (2023YFA1011400),

National Natural Science Foundation of China (No.12271239), Shenzhen Fundamental Research Program JCYJ20220818100602005 (No.20220111). Wang’s work

is also supported by Postdoctoral Fellowship Program of CPSF under Grant Number GZB20240292 and China Postdoctoral Science Foundation (No. 2024T170376).

Supplementary Materials

The online Supplementary Materials include all the technical proofs.

Supplementary materials are available for download.