Interpretable discriminant analysis for functional data supported on random nonlinear domains with an application to Alzheimer's disease.

IF 3.1 1区 数学 Q1 STATISTICS & PROBABILITY
Eardi Lila, Wenbo Zhang, Swati Rane Levendovszky
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引用次数: 0

Abstract

We introduce a novel framework for the classification of functional data supported on nonlinear, and possibly random, manifold domains. The motivating application is the identification of subjects with Alzheimer's disease from their cortical surface geometry and associated cortical thickness map. The proposed model is based upon a reformulation of the classification problem as a regularized multivariate functional linear regression model. This allows us to adopt a direct approach to the estimation of the most discriminant direction while controlling for its complexity with appropriate differential regularization. Our approach does not require prior estimation of the covariance structure of the functional predictors, which is computationally prohibitive in our application setting. We provide a theoretical analysis of the out-of-sample prediction error of the proposed model and explore the finite sample performance in a simulation setting. We apply the proposed method to a pooled dataset from Alzheimer's Disease Neuroimaging Initiative and Parkinson's Progression Markers Initiative. Through this application, we identify discriminant directions that capture both cortical geometric and thickness predictive features of Alzheimer's disease that are consistent with the existing neuroscience literature.

对随机非线性域支持的功能数据进行可解释的判别分析,并应用于阿尔茨海默病。
我们引入了一个新框架,用于对非线性流形域(可能是随机流形域)上的功能数据进行分类。应用的动机是通过皮质表面几何图形和相关皮质厚度图识别阿尔茨海默氏症患者。所提出的模型是基于将分类问题重新表述为正则化多元函数线性回归模型。这使我们能够采用直接方法来估计最具区分度的方向,同时通过适当的微分正则化来控制其复杂性。我们的方法不需要对函数预测因子的协方差结构进行先验估计,而在我们的应用设置中,这种先验估计在计算上是难以实现的。我们对所提模型的样本外预测误差进行了理论分析,并在模拟环境中探索了有限样本性能。我们将提出的方法应用于阿尔茨海默病神经影像倡议和帕金森病进展标记倡议的集合数据集。通过这一应用,我们确定了同时捕捉阿尔茨海默病皮质几何和厚度预测特征的判别方向,这与现有的神经科学文献是一致的。
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来源期刊
CiteScore
8.80
自引率
0.00%
发文量
83
审稿时长
>12 weeks
期刊介绍: Series B (Statistical Methodology) aims to publish high quality papers on the methodological aspects of statistics and data science more broadly. The objective of papers should be to contribute to the understanding of statistical methodology and/or to develop and improve statistical methods; any mathematical theory should be directed towards these aims. The kinds of contribution considered include descriptions of new methods of collecting or analysing data, with the underlying theory, an indication of the scope of application and preferably a real example. Also considered are comparisons, critical evaluations and new applications of existing methods, contributions to probability theory which have a clear practical bearing (including the formulation and analysis of stochastic models), statistical computation or simulation where original methodology is involved and original contributions to the foundations of statistical science. Reviews of methodological techniques are also considered. A paper, even if correct and well presented, is likely to be rejected if it only presents straightforward special cases of previously published work, if it is of mathematical interest only, if it is too long in relation to the importance of the new material that it contains or if it is dominated by computations or simulations of a routine nature.
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