When the data are stored in a distributed manner, direct application of traditional statistical inference procedures is often prohibitive due to communication cost and privacy concerns. This paper develops and investigates two Communication-Efficient Accurate Statistical Estimators (CEASE), implemented through iterative algorithms for distributed optimization. In each iteration, node machines carry out computation in
High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and sub-Gaussian-tailed errors. However, neither of them hold in many real highdimensional time-series data. Recently [Sun, Zhou, Fan, 2019, J. Amer. Stat. Assoc., in press] proposed Adaptive Huber Regression (AHR) to address the issue of heavy-tailed errors. They discover that the robustification parameter of the Huber loss should adapt to the sample size, the dimensionality, and the moments of the heavy-tailed errors. We progress in a vertical direction and justify AHR on dependent observations. Specifically, we consider an important dependence structure -Markov dependence. Our results show that the Markov dependence impacts on the adaption of the robustification parameter and the estimation of regression coefficients in the way that the sample size should be discounted by a factor depending on the spectral gap of the underlying Markov chain.
Background: Banana Fusarium wilt is a devastating disease of bananas caused by Fusarium oxysporum f. sp. cubense (Foc) and is a serious threat to the global banana industry. Knowledge of the pathogenic molecular mechanism and interaction between the host and Foc is limited. Results: In this study, we confirmed the changes of gene expression and pathways in the Cavendish banana variety ‘Brazilian’ during early infection with Foc1 and Foc4 by comparative transcriptomics analysis. 1862 and 226 differentially expressed genes (DEGs) were identified in ‘Brazilian’ roots at 48 h after inoculation with Foc1 and Foc4, respectively. After Foc1 infection, lignin and flavonoid synthesis pathways were enriched. Glucosinolates, alkaloid-like compounds and terpenoids were accumulated. Numerous hormonal- and receptor-like kinase (RLK) related genes were differentially expressed. However, after Foc4 infection, the changes in these pathways and gene expression were almost unaffected or weakly affected. Furthermore, the DEGs involved in biological stress-related pathways also significantly differed after infection within two Foc races. The DEGs participating in phenylpropanoid metabolism and cell wall modification were also differentially expressed. By measuring the expression patterns of genes associated with disease defense, we found that five genes that can cause hypersensitive cell death were up-regulated after Foc1 infection. Therefore, the immune responses of the plant may occur at this stage of infection. Conclusion: Results of this study contribute to the elucidation of the interaction between banana plants and Foc and to the development of measures to prevent banana Fusarium wilt.
We consider the problem of variance reduction in randomized controlled trials, through the use of covariates correlated with the outcome but independent of the treatment. We propose a machine learning regression-adjusted treatment effect estimator, which we call MLRATE. MLRATE uses machine learning predictors of the outcome to reduce estimator variance. It employs cross-fitting to avoid overfitting biases, and we prove consistency and asymptotic normality under general conditions. MLRATE is robust to poor predictions from the machine learning step: if the predictions are uncorrelated with the outcomes, the estimator performs asymptotically no worse than the standard difference-in-means estimator, while if predictions are highly correlated with outcomes, the efficiency gains are large. In A/A tests, for a set of 48 outcome metrics commonly monitored in Facebook experiments the estimator has over 70% lower variance than the simple differencein-means estimator, and about 19% lower variance than the common univariate procedure which adjusts only for pre-experiment values of the outcome.Preprint. Under review.
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