Learning on Bandwidth Constrained Multi-Source Data With MIMO-Inspired DPP MAP Inference

Determinantal Point Process (DPP) is a powerful technique to enhance data diversity by promoting the repulsion of similar elements in the selected samples. Particularly, DPP-based Maximum A Posteriori (MAP) inference is used to identify subsets with the highest diversity. However, a commonly adopted presumption of all data samples being available at one point hinders its applicability to real-world scenarios where data samples are distributed across distinct sources with intermittent and bandwidth-limited connections. This paper proposes a distributed version of DPP inference to enhance multi-source data diversification under limited communication budgets. First, we convert the lower bound of the diversity-maximized distributed sample selection from matrix determinant optimization to a simpler form of the sum of individual terms. Next, a determinant-preserved sparse representation of selected samples is formed by the sink as a surrogate for collected samples and sent back to sources as lightweight messages to eliminate the need for raw data exchange. Our approach is inspired by the channel orthogonalization process of Multiple-Input Multiple-Output (MIMO) systems based on the Channel State Information (CSI). Extensive experiments verify the superiority of our scalable method over the most commonly used data selection methods, including GreeDi, Greedymax, random selection, and stratified sampling by a substantial gain of at least 12% reduction in Relative Diversity Error (RDE). This enhanced diversity translates to a substantial improvement in the performance of various downstream learning tasks, including multi-level classification (2%-4% gain in accuracy), object detection (2% gain in mAP), and multiple-instance learning (1.3% gain in AUC).