On subsampling and inference for multiparameter persistence homology

In topological data analysis, multi-parameter persistence homology is a framework for extracting topological information for point cloud datasets equipped with multiple filtrations. However, existing algorithms become computationally expensive for large datasets, limiting their applicability. In the single-parameter case, subsampling algorithms have been used to reduce the time complexity of computing persistence homology. Convergence properties of the persistence barcodes have also been established in this setting. We extend these results to the multiparameter persistence homology, and develop subsampling algorithms can be used to approximate the fibered barcode in this setting. We conduct experiments on the point cloud dataset ModelNet to demonstrate the efficiency of these algorithms.