Browsing by Subject "Dimension reduction"

Now showing 1 - 3 of 3
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    Active learning with generalized sliced inverse regression for high-dimensional reliability analysis
    (Elsevier, 2022-01) Yin, Jianhua; Du, Xiaoping; Mechanical and Energy Engineering, School of Engineering and Technology
    It is computationally expensive to predict reliability using physical models at the design stage if many random input variables exist. This work introduces a dimension reduction technique based on generalized sliced inverse regression (GSIR) to mitigate the curse of dimensionality. The proposed high dimensional reliability method enables active learning to integrate GSIR, Gaussian Process (GP) modeling, and Importance Sampling (IS), resulting in an accurate reliability prediction at a reduced computational cost. The new method consists of three core steps, 1) identification of the importance sampling region, 2) dimension reduction by GSIR to produce a sufficient predictor, and 3) construction of a GP model for the true response with respect to the sufficient predictor in the reduced-dimension space. High accuracy and efficiency are achieved with active learning that is iteratively executed with the above three steps by adding new training points one by one in the region with a high chance of failure.
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    Principal component analysis of hybrid functional and vector data
    (Wiley, 2021) Jang, Jeong Hoon; Biostatistics and Health Data Science, School of Medicine
    We propose a practical principal component analysis (PCA) framework that provides a nonparametric means of simultaneously reducing the dimensions of and modeling functional and vector (multivariate) data. We first introduce a Hilbert space that combines functional and vector objects as a single hybrid object. The framework, termed a PCA of hybrid functional and vector data (HFV-PCA), is then based on the eigen-decomposition of a covariance operator that captures simultaneous variations of functional and vector data in the new space. This approach leads to interpretable principal components that have the same structure as each observation and a single set of scores that serves well as a low-dimensional proxy for hybrid functional and vector data. To support practical application of HFV-PCA, the explicit relationship between the hybrid PC decomposition and the functional and vector PC decompositions is established, leading to a simple and robust estimation scheme where components of HFV-PCA are calculated using the components estimated from the existing functional and classical PCA methods. This estimation strategy allows flexible incorporation of sparse and irregular functional data as well as multivariate functional data. We derive the consistency results and asymptotic convergence rates for the proposed estimators. We demonstrate the efficacy of the method through simulations and analysis of renal imaging data.
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    Robust Inference for Heterogeneous Treatment Effects With Applications to NHANES Data
    (2024-12) Mo, Ran; Wang, Honglang; Li, Fang; Tan, Fei; Peng, Hanxiang
    Estimating the conditional average treatment effect (CATE) using data from the National Health and Nutrition Examination Survey (NHANES) provides valuable insights into the heterogeneous impacts of health interventions across diverse populations, facilitating public health strategies that consider individual differences in health behaviors and conditions. However, estimating CATE with NHANES data face challenges often encountered in observational studies, such as outliers, heavy-tailed error distributions, skewed data, model misspecification, and the curse of dimensionality. To address these challenges, this dissertation presents three consecutive studies that thoroughly explore robust methods for estimating heterogeneous treatment effects. The first study introduces an outlier-resistant estimation method by incorporating M-estimation, replacing the \(L_2\) loss in the traditional inverse propensity weighting (IPW) method with a robust loss function. To assess the robustness of our approach, we investigate its influence function and breakdown point. Additionally, we derive the asymptotic properties of the proposed estimator, enabling valid inference for the proposed outlier-resistant estimator of CATE. The method proposed in the first study relies on a symmetric assumption which is commonly required by standard outlier-resistant methods. To remove this assumption while maintaining unbiasedness, the second study employs the adaptive Huber loss, which dynamically adjusts the robustification parameter based on the sample size to achieve optimal tradeoff between bias and robustness. The robustification parameter is explicitly derived from theoretical results, making it unnecessary to rely on time-consuming data-driven methods for its selection. We also derive concentration and Berry-Esseen inequalities to precisely quantify the convergence rates as well as finite sample performance. In both previous studies, the propensity scores were estimated parametrically, which is sensitive to model misspecification issues. The third study extends the robust estimator from our first project by plugging in a kernel-based nonparametric estimation of the propensity score with sufficient dimension reduction (SDR). Specifically, we adopt a robust minimum average variance estimation (rMAVE) for the central mean space under the potential outcome framework. Together with higher-order kernels, the resulting CATE estimation gains enhanced efficiency. In all three studies, the theoretical results are derived, and confidence intervals are constructed for inference based on these findings. The properties of the proposed estimators are verified through extensive simulations. Additionally, applying these methods to NHANES data validates the estimators' ability to handle diverse and contaminated datasets, further demonstrating their effectiveness in real-world scenarios.