Bandit Process Inference for Streaming Functional Data
6 affiliations
- 1School of Mathematics, Shandong University, Jinan 250100, China
- 2School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China
- 3Faculty of Education and Liberal Arts, INTI International University, Nilai 71800, Negeri Sembilan, Malaysia
- 4Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China
- 5School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
- 6School of Software and Microelectronics, Peking University, Beijing 102600, China
Abstract
The functional linear model Y=∫TX(t)β0(t)dt+ε is widely used in various fields, including medical image analysis, economics, and climate science. Reliable statistical inference for β0(t) across the domain t∈T is essential in these applications. While substantial progress has been made in addressing prediction problems in offline settings, hypothesis testing for β0(t), especially in the context of streaming and functional data, continues to present considerable challenges. In the paper, we propose a novel statistical inference framework designed specifically for streaming data based on functional stochastic gradient descent algorithms. Our approach constructs an online sequence of randomly perturbed estimators and incorporates a two-armed bandit process to build an adaptive test statistic for hypothesis testing. Moreover, we establish the limiting distribution of this statistic under both the null and alternative hypotheses, thus ensuring its statistical validity. Simulation studies examine the power and null calibration of the framework, and a real-world application illustrates its use for streaming functional data.
Related
- Exploration strategies for Gaussian process bandit optimization with inference regret guarantees
- Variational Inference for Functional Data Clustering via Dirichlet Process Mixtures with Correlated Errors
- Improved Regret Analysis for Parallel Gaussian Process Bandit Optimization
- When May a Bandit Leave Its Anchor? E-Process-Authorized Thompson Sampling under Non-stationarity
- Sharp Characterization of Bias in Post-Bandit Inference
BibTeX
@article{zhang2026bandit,
title = {{Bandit Process Inference for Streaming Functional Data}},
author = {Ziyu Zhang and Yan Wang and Jingqi Yan and Zhongguo Xu and Rubing Xue and Wei Dong and Zhenzhe Zhang},
journal = {Axioms},
year = {2026},
month = oct,
doi = {10.3390/axioms15100779},
url = {https://www.mdpi.com/2075-1680/15/10/779},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Bandit Process Inference for Streaming Functional Data
AU - Ziyu Zhang
AU - Yan Wang
AU - Jingqi Yan
AU - Zhongguo Xu
AU - Rubing Xue
AU - Wei Dong
AU - Zhenzhe Zhang
PY - 2026
DA - 2026/10/16
JO - Axioms
DO - 10.3390/axioms15100779
UR - https://www.mdpi.com/2075-1680/15/10/779
AB - The functional linear model Y=∫TX(t)β0(t)dt+ε is widely used in various fields, including medical image analysis, economics, and climate science. Reliable statistical inference for β0(t) across the domain t∈T is essential in these applications. While substantial progress has been made in addressing prediction problems in offline settings, hypothesis testing for β0(t), especially in the context of streaming and functional data, continues to present considerable challenges. In the paper, we propose a novel statistical inference framework designed specifically for streaming data based on functional stochastic gradient descent algorithms. Our approach constructs an online sequence of randomly perturbed estimators and incorporates a two-armed bandit process to build an adaptive test statistic for hypothesis testing. Moreover, we establish the limiting distribution of this statistic under both the null and alternative hypotheses, thus ensuring its statistical validity. Simulation studies examine the power and null calibration of the framework, and a real-world application illustrates its use for streaming functional data.
SN - 2075-1680
ER -