Comparison of the local pivotal method and systematic sampling for national forest inventories

Background The local pivotal method (LPM) utilizing auxiliary data in sample selection has recently been proposed as a sampling method for national forest inventories (NFIs). Its performance compared to simple random sampling (SRS) and LPM with geographical coordinates has produced promising results in simulation studies. In this simulation study we compared all these sampling methods to systematic sampling. The LPM samples were selected solely using the coordinates (LPMxy) or, in addition to that, auxiliary remote sensing-based forest variables (RS variables). We utilized field measurement data (NFI-field) and Multi-Source NFI (MS-NFI) maps as target data, and independent MS-NFI maps as auxiliary data. The designs were compared using relative efficiency (RE); a ratio of mean squared errors of the reference sampling design against the studied design. Applying a method in NFI also requires a proven estimator for the variance. Therefore, three different variance estimators were evaluated against the empirical variance of replications: 1) an estimator corresponding to SRS; 2) a Grafström-Schelin estimator repurposed for LPM; and 3) a Matérn estimator applied in the Finnish NFI for systematic sampling design. Results The LPMxy was nearly comparable with the systematic design for the most target variables. The REs of the LPM designs utilizing auxiliary data compared to the systematic design varied between 0.74–1.18, according to the studied target variable. The SRS estimator for variance was expectedly the most biased and conservative estimator. Similarly, the Grafström-Schelin estimator gave overestimates in the case of LPMxy. When the RS variables were utilized as auxiliary data, the Grafström-Schelin estimates tended to underestimate the empirical variance. In systematic sampling the Matérn and Grafström-Schelin estimators performed for practical purposes equally. Conclusions LPM optimized for a specific variable tended to be more efficient than systematic sampling, but all of the considered LPM designs were less efficient than the systematic sampling design for some target variables. The Grafström-Schelin estimator could be used as such with LPMxy or instead of the Matérn estimator in systematic sampling. Further studies of the variance estimators are needed if other auxiliary variables are to be used in LPM.

Feature Variance Regularization: A Simple Way to Improve the Generalizability of Neural Networks

To improve the generalization ability of neural networks, we propose a novel regularization method that regularizes the empirical risk using a penalty on the empirical variance of the features. Intuitively, our approach introduces confusion into feature extraction and prevents the models from learning features that may relate to specific training samples. According to our theoretical analysis, our method encourages models to generate closer feature distributions for the training set and unobservable true data and minimize the expected risk as well, which allows the model to adapt to new samples better. We provide a thorough empirical justification of our approach, and achieves a greater improvement than other regularization methods. The experimental results show the effectiveness of our method on multiple visual tasks, including classification (CIFAR100, ImageNet, fine-grained datasets) and semantic segmentation (Cityscapes).