Adjustment with Many Regressors Under Covariate-Adaptive Randomizations

Our paper discovers a new trade-off of using regression adjustments (RAs) in causal inference under covariate-adaptive randomizations (CARs). On one hand, RAs can improve the efficiency of causal estimators by incorporating information from covariates that are not used in the randomization. On the other hand, RAs can degrade estimation efficiency due to their estimation errors, which are not asymptotically negligible when the number of regressors is of the same order as the sample size. Ignoring the estimation errors of RAs may result in serious over-rejection of causal inference under the null hypothesis. To address the issue, we develop a unified inference theory for the regression-adjusted average treatment effect (ATE) estimator under CARs. Our theory has two key features: (1) it ensures the exact asymptotic size under the null hypothesis, regardless of whether the number of covariates is fixed or diverges no faster than the sample size; and (2) it guarantees weak efficiency improvement over the ATE estimator without adjustments.Comment: 71 pages, including appendi

Indium Phosphide Bismide

Indium phosphide bismide is a new member to the dilute bismide family. Since the first synthesis by molecular beam epitaxy (MBE) in 2013, it has cut a figure for its abnormal properties comparing with other dilute bismides. Bismuth (Bi) incorporation is always a difficulty for epitaxial growth of dilute. In this chapter, it shows how to regulate MBE growth parameters and their influence on Bi incorporation in InP1−xBix. Structural, electronic and optical properties are systematically reviewed. Thermal annealing to study Bi thermal stability and its effect on physical properties is performed. InP1−xBix shows strong and broad photoluminescence at room temperature, which is a potential candidate for fabricating super-luminescence diodes applied for enhancing spatial resolution in optical coherence tomography. Quaternary phosphide bismide, including InGaPBi and InAlPBi, is briefly introduced in this chapter

Achieving Adversarial Robustness via Sparsity

Network pruning has been known to produce compact models without much accuracy degradation. However, how the pruning process affects a network's robustness and the working mechanism behind remain unresolved. In this work, we theoretically prove that the sparsity of network weights is closely associated with model robustness. Through experiments on a variety of adversarial pruning methods, we find that weights sparsity will not hurt but improve robustness, where both weights inheritance from the lottery ticket and adversarial training improve model robustness in network pruning. Based on these findings, we propose a novel adversarial training method called inverse weights inheritance, which imposes sparse weights distribution on a large network by inheriting weights from a small network, thereby improving the robustness of the large network