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Vertical Federated Learning (FL) is a new paradigm that enables users with non-overlapping attributes of the same data samples to jointly train a model without directly sharing the raw data. Nevertheless, recent works show that it's still not sufficient to prevent privacy leakage from the training process or the trained model. This paper focuses on studying the privacy-preserving tree boosting algorithms under the vertical FL. The existing solutions based on cryptography involve heavy computation and communication overhead and are vulnerable to inference attacks. Although the solution based on Local Differential Privacy (LDP) addresses the above problems, it leads to the low accuracy of the trained model. This paper explores to improve the accuracy of the widely deployed tree boosting algorithms satisfying differential privacy under vertical FL. Specifically, we introduce a framework called OpBoost. Three order-preserving desensitization algorithms satisfying a variant of LDP called distance-based LDP (dLDP) are designed to desensitize the training data. In particular, we optimize the dLDP definition and study efficient sampling distributions to further improve the accuracy and efficiency of the proposed algorithms. The proposed algorithms provide a trade-off between the privacy of pairs with large distance and the utility of desensitized values. Comprehensive evaluations show that OpBoost has a better performance on prediction accuracy of trained models compared with existing LDP approaches on reasonable settings. Our code is open source. 

Abstract Background Plants are naturally associated with root microbiota, which are microbial communities influential to host fitness. Thus, it is important to understand how plants control root microbiota. Epigenetic factors regulate the readouts of genetic information and consequently many essential biological processes. However, it has been elusive whether RNA-directed DNA methylation (RdDM) affects root microbiota assembly. Results By applying 16S rRNA gene sequencing, we investigated root microbiota of Arabidopsis mutants defective in the canonical RdDM pathway, including dcl234 that harbors triple mutation in the Dicer-like proteins DCL3, DCL2, and DCL4, which produce small RNAs for RdDM. Alpha diversity analysis showed reductions in microbe richness from the soil to roots, reflecting the selectivity of plants on root-associated bacteria. The dcl234 triple mutation significantly decreases the levels of Aeromonadaceae and Pseudomonadaceae , while it increases the abundance of many other bacteria families in the root microbiota. However, mutants of the other examined key players in the canonical RdDM pathway showed similar microbiota as Col-0, indicating that the DCL proteins affect root microbiota in an RdDM-independent manner. Subsequently gene analysis by shotgun sequencing of root microbiome indicated a selective pressure on microbial resistance to plant defense in the dcl234 mutant. Consistent with the altered plant-microbe interactions, dcl234 displayed altered characters, including the mRNA and sRNA transcriptomes that jointly highlighted altered cell wall organization and up-regulated defense, the decreased cellulose and callose deposition in root xylem, and the restructured profile of root exudates that supported the alterations in gene expression and cell wall modifications. Conclusion Our findings demonstrate an important role of the DCL proteins in influencing root microbiota through integrated regulation of plant defense, cell wall compositions, and root exudates. Our results also demonstrate that the canonical RdDM is dispensable for Arabidopsis root microbiota. These findings not only establish a connection between root microbiota and plant epigenetic factors but also highlight the complexity of plant regulation of root microbiota.