High-dimensional change point detection is a fundamental problem in modern statistical learning, particularly when distributional changes are driven by a small and unknown subset of variables. In heterogeneous settings, uniform aggregation across coordinates may suffer from signal dilution, because stable or noisy variables can mask the evidence carried by structurally unstable coordinates. Moreover, many existing procedures primarily focus on temporal localization and provide limited information about the variables responsible for a detected structural break. To address these challenges, we propose WAVE, a weighted adaptive variable selection procedure for interpretable change point detection. WAVE constructs variance-standardized global CUSUM evidence and locally standardized exponentially weighted evidence for each coordinate and then adaptively maps intervalwise coordinate evidence into a continuous weight vector. The learned weights strengthen coordinates with persistent or local evidence of change while downweighting nuisance coordinates with weak evidence. The resulting weighted scan statistic is calibrated by a residual moving block bootstrap that preserves temporal and cross-sectional dependence and re-applies the weighting rule within bootstrap samples to account for data-adaptive aggregation. Detected change points are further equipped with coordinate-level attribution through a multi-criteria fusion rule combining adaptive weights, local standardized effect sizes, and marginal testing evidence. Simulation studies show that WAVE achieves accurate localization and reliable support recovery in both single and multiple change point settings, particularly under sparse and heterogeneous alternatives. An empirical analysis of S&P 100 stock returns in 2020 further demonstrates that WAVE identifies economically meaningful market regime shifts with interpretable coordinate-level attribution.
In this paper, we consider the extremal trace problem for the coupled Laplacian on the sets homeomorphic to the Stiefel manifold defined on the complex Euclidean space. The study is implemented via various mathematical methods, including topological and probabilistic approaches. A detailed, comprehensive classification of the stationary points is given, which itself deserves to be considered as a general method in the framework of the optimization theory. Finally, an application to biologically meaningful integration of heterogeneous datasets, in which the structure of molecular interactions serves as a significant constraint for the mathematical model, is proposed. The main advantage of the elaborated method in comparison with the previously used ones is the absence of any conditions on the structure of the initial heterogeneous datasets. This paper is a continuation of a series of papers by our research group devoted to the development of new mathematical methods for integrating multi-omics data.
