Learning from Hidden Signatures in High-Dimensional Models

将开发直接适用于确定与疫苗反应相关的调节细胞机制的方法，作为该项目的一个组成部分。这种机制不能直接观察或测量，但可以获得大量的间接测量，例如抗体滴度驱动效应。为应对从由各种间接测量数据组成的大量数据中提取这些隐藏信号的挑战，开发了新的方法，并立即对新出现的大流行病数据集进行了测试。更广泛地说，从基本但隐藏的特征中进行可靠的、基于数学的推断和预测的技术将被开发出来，并应用于神经科学和高通量文本数据产生的数据集。本课题对基于因子模型建模的低维嵌入的高维数据进行推理和预测的基础研究。在可识别因素回归模型的新类别中，潜在因素是可解释的，将开发新的可扩展方法来估计潜在因素的回归系数。有限样本极小极大估计的最优性，以及估计的渐近极限的推导，特别是其有效渐近方差的推导将是本项目研究的基石。利用降低有效秩协方差矩阵的高维相关特征进行预测，将在通用因子回归模型下进行分析。特别是，深度学习中流行的内插预测器将与其他竞争者进行对比，目的是在数据来自因子回归模型时，提供对无模型预测和基于模型预测的基本理解。稀疏主题模型以及隐藏主题的推断和预测将作为所有特征都是离散的数据的伴侣模型进行研究。新开发的、可扩展的和理论上成立的方法的应用将构成这个项目的重点。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Methods directly applicable to the determination of regulatory cell mechanisms associated with vaccine responses will be developed as an integral part of this project. Such mechanisms are not directly observable or measurable, but a wealth of indirect measurements can be obtained, for instance on antibody titer-driven effects. New methodology, that meets the challenge of extracting these hidden signals from a very large volume of data, consisting of a diverse arrays of indirect measurements, are developed and put to test immediately, for emerging pandemics data sets. More broadly, techniques that allow for reliable, mathematically grounded, inference and prediction from essential, but hidden, signatures will be developed and applied to data sets arising from neuroscience and high-throughput text data. A foundational study of inference and prediction from high-dimensional data with low-dimensional embeddings modeled by factor models are undertaken in this project. Within new classes of identifiable factor regression models in which the latent factors are interpretable, new scalable methods for estimating the regression coefficients of the latent factors will be developed. Optimality of estimation from a finite-sample, minimax perspective, as well as the derivation of the asymptotic limit of the estimates, and especially of their efficient asymptotic variance will be a cornerstone of research under this project. Prediction from high-dimensional dependent features, with reduced-effective-rank covariance matrix, will be analyzed under generic factor regression models. In particular, interpolating predictors, popular in deep-learning, will be contrasted with other contenders, with the aim of offering fundamental understanding of model-free versus model-based prediction, when data arises from a factor regression model. Sparse topic models, together with inference and prediction from the hidden topics, will be studied as companion models for data in which all the features are discrete. Applications of the newly developed, scalable and theoretically founded methods will constitute a focal point of this project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.