Topics in small area estimation with applications to the National Resources Inventory

A practical application of small area estimation in the National Resources Inventory, a large survey of the non-federal land area in the United States, is described. Several estimation issues raised by this application are discussed as motivation for theoretical investigation of some aspects of small area estimation;The situation in which individual small area sampling variances are directly estimated is studied. This situation is not covered by standard asymptotic results (Prasad and Rao (1990)), which assume that a finite-dimensional parameter characterizes the small area variances. An approximation for the mean square error (MSE) of the empirical best linear unbiased predictor and an estimator of the MSE are developed. Simulation studies show that the theoretical expressions are good approximations for the MSE of the predictors. Also the suggested MSE estimator has smaller overestimation for the MSE than related estimators in the literature when the between-area variance component is small;Small area estimation under a restriction, which forces small area estimates to sum to the direct estimate for a large area, is discussed. A criterion that unifies the derivation of several restricted estimators is proposed. The estimator that is the unique best linear unbiased estimator under the criterion is derived and an approximation for the MSE of the restricted estimator is presented;The bias of the empirical best linear unbiased predictor is assessed for the model in which the sampling errors are not normally distributed. The robustness of the MSE estimator is examined under non-normal error distributions by using simulations. The simulations also demonstrate that imposing a restriction can reduce the bias when the errors are not symmetrically distributed

Downlink Rate Analysis for Virtual-Cell Based Large-Scale Distributed Antenna Systems

Despite substantial rate gains achieved by coordinated transmission from a massive amount of geographically distributed antennas, the resulting computational cost and channel measurement overhead could be unaffordable for a large-scale distributed antenna system (DAS). A scalable signal processing framework is therefore highly desirable, which, as recently demonstrated in \cite{Dai_TWireless}, could be established based on the concept of virtual cell. In a virtual-cell based DAS, each user chooses a few closest base-station (BS) antennas to form its virtual cell, that is, its own serving BS antenna set. In this paper, we focus on a downlink DAS with a large number of users and BS antennas uniformly distributed in a certain area, and aim to study the effect of the virtual cell size on the average user rate. Specifically, by assuming that maximum ratio transmission (MRT) is adopted in each user's virtual cell, the achievable ergodic rate of each user is derived as an explicit function of the large-scale fading coefficients from all the users to their virtual cells, and an upper-bound of the average user rate is established, based on which a rule of thumb is developed for determining the optimal virtual cell size to maximize the average user rate. The analysis is further extended to consider multiple users grouped together and jointly served by their virtual cells using zero-forcing beamforming (ZFBF). In contrast to the no-grouping case where a small virtual cell size is preferred, it is shown that by grouping users with overlapped virtual cells, the average user rate can be significantly improved by increasing the virtual cell size, though at the cost of a higher signal processing complexity

On Dynamic Noise Influence in Differentially Private Learning

Protecting privacy in learning while maintaining the model performance has become increasingly critical in many applications that involve sensitive data. Private Gradient Descent (PGD) is a commonly used private learning framework, which noises gradients based on the Differential Privacy protocol. Recent studies show that \emph{dynamic privacy schedules} of decreasing noise magnitudes can improve loss at the final iteration, and yet theoretical understandings of the effectiveness of such schedules and their connections to optimization algorithms remain limited. In this paper, we provide comprehensive analysis of noise influence in dynamic privacy schedules to answer these critical questions. We first present a dynamic noise schedule minimizing the utility upper bound of PGD, and show how the noise influence from each optimization step collectively impacts utility of the final model. Our study also reveals how impacts from dynamic noise influence change when momentum is used. We empirically show the connection exists for general non-convex losses, and the influence is greatly impacted by the loss curvature

Federated Robustness Propagation: Sharing Adversarial Robustness in Federated Learning

Federated learning (FL) emerges as a popular distributed learning schema that learns a model from a set of participating users without requiring raw data to be shared. One major challenge of FL comes from heterogeneity in users, which may have distributionally different (or non-iid) data and varying computation resources. Just like in centralized learning, FL users also desire model robustness against malicious attackers at test time. Whereas adversarial training (AT) provides a sound solution for centralized learning, extending its usage for FL users has imposed significant challenges, as many users may have very limited training data as well as tight computational budgets, to afford the data-hungry and costly AT. In this paper, we study a novel learning setting that propagates adversarial robustness from high-resource users that can afford AT, to those low-resource users that cannot afford it, during the FL process. We show that existing FL techniques cannot effectively propagate adversarial robustness among non-iid users, and propose a simple yet effective propagation approach that transfers robustness through carefully designed batch-normalization statistics. We demonstrate the rationality and effectiveness of our method through extensive experiments. Especially, the proposed method is shown to grant FL remarkable robustness even when only a small portion of users afford AT during learning. Codes will be published upon acceptance

Temporal-spatial analysis of a foot-and-mouth disease model with spatial diffusion and vaccination

Foot-and-mouth disease is an acute, highly infectious, and economically significant transboundary animal disease. Vaccination is an efficient and cost-effective measure to prevent the transmission of this disease. The primary way that foot-and-mouth disease spreads is through direct contact with infected animals, although it can also spread through contact with contaminated environments. This paper uses a diffuse foot-and-mouth disease model to account for the efficacy of vaccination in managing the disease. First, we transform an age-space structured foot-and-mouth disease into a diffusive epidemic model with nonlocal infection coupling the latent period and the latent diffusive rate. The basic reproduction number, which determines the outbreak of the disease, is then explicitly formulated. Finally, numerical simulations demonstrate that increasing vaccine efficacy has a remarkable effect than increasing vaccine coverage