Federated singular value decomposition for high dimensional data

Federated learning (FL) is emerging as a privacy-aware alternative to classical cloud-based machine learning. In FL, the sensitive data remains in data silos and only aggregated parameters are exchanged. Hospitals and research institutions which are not willing to share their data can join a federated study without breaching confidentiality. In addition to the extreme sensitivity of biomedical data, the high dimensionality poses a challenge in the context of federated genome-wide association studies (GWAS). In this article, we present a federated singular value decomposition (SVD) algorithm, suitable for the privacy-related and computational requirements of GWAS. Notably, the algorithm has a transmission cost independent of the number of samples and is only weakly dependent on the number of features, because the singular vectors associated with the samples are never exchanged and the vectors associated with the features only for a fixed number of iterations. Although motivated by GWAS, the algorithm is generically applicable for both horizontally and vertically partitioned data.Comment: 36 pages, 7 figures, 5 tables, submitted to Data Mining and Knowledge Discover

Designing Wood Supply Scenarios from Forest Inventories with Stratified Predictions

Forest growth and wood supply projections are increasingly used to estimate the future availability of woody biomass and the correlated effects on forests and climate. This research parameterizes an inventory-based business-as-usual wood supply scenario, with a focus on southwest Germany and the period 2002–2012 with a stratified prediction. First, the Classification and Regression Trees algorithm groups the inventory plots into strata with corresponding harvest probabilities. Second, Random Forest algorithms generate individual harvest probabilities for the plots of each stratum. Third, the plots with the highest individual probabilities are selected as harvested until the harvest probability of the stratum is fulfilled. Fourth, the harvested volume of these plots is predicted with a linear regression model trained on harvested plots only. To illustrate the pros and cons of this method, it is compared to a direct harvested volume prediction with linear regression, and a combination of logistic regression and linear regression. Direct harvested volume regression predicts comparable volume figures, but generates these volumes in a way that differs from business-as-usual. The logistic model achieves higher overall classification accuracies, but results in underestimations or overestimations of harvest shares for several subsets of the data. The stratified prediction method balances this shortcoming, and can be of general use for forest growth and timber supply projections from large-scale forest inventories