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[2602.20651] Sparse Bayesian Deep Functional Learning with Structured Region Selection
Summary
The paper presents a Sparse Bayesian Functional Deep Neural Network (sBayFDNN) that addresses the limitations of conventional functional models and deep learning by enabling interpretable region selection in complex data analysis.
Why It Matters
This research is significant as it bridges the gap between linear functional models and deep learning approaches, providing a statistically rigorous method for analyzing complex, structured data. The sBayFDNN enhances interpretability and accuracy in applications like ECG monitoring and neuroimaging, which are critical in healthcare and industrial diagnostics.
Key Takeaways
- sBayFDNN captures complex nonlinear relationships in functional data.
- The model provides interpretable region selection with quantified uncertainty.
- Theoretical guarantees ensure reliability and statistical rigor.
- Empirical studies demonstrate the model's effectiveness over existing methods.
- sBayFDNN is applicable in various fields including healthcare and industrial diagnostics.
Computer Science > Machine Learning arXiv:2602.20651 (cs) [Submitted on 24 Feb 2026] Title:Sparse Bayesian Deep Functional Learning with Structured Region Selection Authors:Xiaoxian Zhu, Yingmeng Li, Shuangge Ma, Mengyun Wu View a PDF of the paper titled Sparse Bayesian Deep Functional Learning with Structured Region Selection, by Xiaoxian Zhu and 3 other authors View PDF HTML (experimental) Abstract:In modern applications such as ECG monitoring, neuroimaging, wearable sensing, and industrial equipment diagnostics, complex and continuously structured data are ubiquitous, presenting both challenges and opportunities for functional data analysis. However, existing methods face a critical trade-off: conventional functional models are limited by linearity, whereas deep learning approaches lack interpretable region selection for sparse effects. To bridge these gaps, we propose a sparse Bayesian functional deep neural network (sBayFDNN). It learns adaptive functional embeddings through a deep Bayesian architecture to capture complex nonlinear relationships, while a structured prior enables interpretable, region-wise selection of influential domains with quantified uncertainty. Theoretically, we establish rigorous approximation error bounds, posterior consistency, and region selection consistency. These results provide the first theoretical guarantees for a Bayesian deep functional model, ensuring its reliability and statistical rigor. Empirically, comprehensive simulations and r...
