Bayesian optimization (BO) has been widely used to optimize expensive and gradient-free objective functions across various domains. However, existing BO methods have not addressed the objective where both inputs and outputs are functions, which increasingly arise in complex systems as advanced sensing technologies. To fill this gap, we propose a novel function-on-function Bayesian optimization (FFBO) framework. Specifically, we first introduce a function-on-function Gaussian process (FFGP) model with a separable operator-valued kernel to capture the correlations between function-valued inputs and outputs. Compared to existing Gaussian process models, FFGP is modeled directly in the function space. Based on FFGP, we define a scalar upper confidence bound (UCB) acquisition function using a weighted operator-based scalarization strategy. Then, a scalable functional gradient ascent algorithm (FGA) is developed to efficiently identify the optimal function-valued input. We further analyze the theoretical properties of the proposed method. Extensive experiments on synthetic and real-world data demonstrate the superior performance of FFBO over existing approaches.

Sequential change detection in high-dimensional dynamic networks has attracted growing attention in modern applications. A major challenge is that as network scale increases, limited sensing resources make it difficult to fully observe links at each time point, resulting in partial observability and complicating detection. To tackle this, we propose a Latent Bi-Transit Network (LBTN) that learns unobserved edge formation, latent node states, and the evolution mechanisms of dynamic networks. Based on LBTN, we design a variational Bayesian method to infer sparse node-level changes and employ a likelihood ratio test as the detection statistic. By further formulating the statistic as the reward function of a combinatorial multi-armed bandit (CMAB) problem, we develop a Thompson sampling strategy to adaptively select edges for observation, balancing exploration and exploitation. Comprehensive simulations and real-world experiments show that our method consistently outperforms existing baselines and its variants across diverse scenarios.

The rapid advancement of real-time data monitoring technologies has established functional data analysis as a crucial predictive tool across diverse applications. Despite progress in multivariate functional regression and principal component analysis, significant challenges persist in function-to-function regression and feature selection. These include the inaccurate selection of predictor variables from extensive predictors and flawed parameter estimation, which compromise the precision of function-based data predictions. This paper introduces the SPEVS-CC method, a novel canonical correlation-based feature selection technique specifically designed for function-on-function regression. By effectively decoupling variable selection from model fitting, the SPEVS-CC method enhances both adaptability and interpretability. Validated through rigorous experiments and real-world applications, including in the Shenzhen subway system, semiconductor manufacturing, and ocean climate, SPEVS-CC significantly reduces mean squared error, confirming its robustness and practical utility. This methodological breakthrough harmonizes variable selection with functional regression, providing unmatched interpretability and usability in industrial applications.