Integrative learning of multiple datasets has the potential to mitigate the challenge of small n and large p that is often encountered in analysis of big biomedical data such as genomics data. Detection of weak yet important signals can be enhanced by jointly selecting features for all datasets. However, the set of important features may not always be the same across all datasets. Although some existing integrative learning methods allow heterogeneous sparsity structure where a subset of datasets can have zero coefficients for some selected features, they tend to yield reduced efficiency, reinstating the problem of losing weak important signals. We propose a new integrative learning approach which can not only aggregate important signals well in homogeneous sparsity structure, but also substantially alleviate the problem of losing weak important signals in heterogeneous sparsity structure. Our approach exploits a priori known graphical structure of features and encourages joint selection of features that are connected in the graph. Integrating such prior information over multiple datasets enhances the power, while also accounting for the heterogeneity across datasets. Theoretical properties of the proposed method are investigated. We also demonstrate the limitations of existing approaches and the superiority of our method using a simulation study and analysis of gene expression data from ADNI.
Differentially private (DP) training preserves the data privacy usually at the cost of slower convergence (and thus lower accuracy), as well as more severe mis-calibration than its non-private counterpart. To analyze the convergence of DP training, we formulate a continuous time analysis through the lens of neural tangent kernel (NTK), which characterizes the per-sample gradient clipping and the noise addition in DP training, for arbitrary network architectures and loss functions. Interestingly, we show that the noise addition only affects the privacy risk but not the convergence or calibration, whereas the per-sample gradient clipping (under both flat and layerwise clipping styles) only affects the convergence and calibration. Furthermore, we observe that while DP models trained with small clipping norm usually achieve the best accurate, but are poorly calibrated and thus unreliable. In sharp contrast, DP models trained with large clipping norm enjoy the same privacy guarantee and similar accuracy, but are significantly more calibrated. Our code can be found at https://github.com/woodyx218/opacus_global_clipping.
Multiple imputation (MI) has been widely applied to missing value problems in biomedical, social and econometric research, in order to avoid improper inference in the downstream data analysis. In the presence of high-dimensional data, imputation models that include feature selection, especially â1 regularized regression (such as Lasso, adaptive Lasso, and Elastic Net), are common choices to prevent the model from underdetermination. However, conducting MI with feature selection is difficult: existing methods are often computationally inefficient and poor in performance. We propose MISNN, a novel and efficient algorithm that incorporates feature selection for MI. Leveraging the approximation power of neural networks, MISNN is a general and flexible framework, compatible with any feature selection method, any neural network architecture, high/low-dimensional data and general missing patterns. Through empirical experiments, MISNN has demonstrated great advantages over state-of-the-art imputation methods (e.g. Bayesian Lasso and matrix completion), in terms of imputation accuracy, statistical consistency and computation speed.
Missing data are ubiquitous in real world applications and, if not adequately handled, may lead to the loss of information and biased findings in downstream analysis. Particularly, high-dimensional incomplete data with a moderate sample size, such as analysis of multi-omics data, present daunting challenges. Imputation is arguably the most popular method for handling missing data, though existing imputation methods have a number of limitations. Single imputation methods such as matrix completion methods do not adequately account for imputation uncertainty and hence would yield improper statistical inference. In contrast, multiple imputation (MI) methods allow for proper inference but existing methods do not perform well in high-dimensional settings. Our work aims to address these significant methodological gaps, leveraging recent advances in neural network Gaussian process (NNGP) from a Bayesian viewpoint. We propose two NNGP-based MI methods, namely MI-NNGP, that can apply multiple imputations for missing values from a joint (posterior predictive) distribution. The MI-NNGP methods are shown to significantly outperform existing state-of-the-art methods on synthetic and real datasets, in terms of imputation error, statistical inference, robustness to missing rates, and computation costs, under three missing data mechanisms, MCAR, MAR, and MNAR. Code is available in the GitHub repository https://github.com/bestadcarry/MI-NNGP.
Missing data are present in most real world problems and need careful handling to preserve the prediction accuracy and statistical consistency in the downstream analysis. As the gold standard of handling missing data, multiple imputation (MI) methods are proposed to account for the imputation uncertainty and provide proper statistical inference. In this work, we propose Multiple Imputation via Generative Adversarial Network (MI-GAN), a deep learning-based (in specific, a GAN-based) multiple imputation method, that can work under missing at random (MAR) mechanism with theoretical support. MI-GAN leverages recent progress in conditional generative adversarial neural works and shows strong performance matching existing state-of-the-art imputation methods on high-dimensional datasets, in terms of imputation error. In particular, MI-GAN significantly outperforms other imputation methods in the sense of statistical inference and computational speed.
