Optimal Linear Discriminant Analysis for High-Dimensional Functional Data

Xue, Kaijie; Yang, Jin; Yao, Fang

doi:10.1080/01621459.2022.2164288

Cited by 10 publications

(1 citation statement)

References 35 publications

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“…Furthermore, as the number of random functions increases, both basis-based and FPCA-based classification algorithms face a significant increase in computational burden. Recently, Xue et al (2023) tackled classification of high-dimensional functional data, in which each observation is potentially associated with a large number of functional processes. They proposed a penalized classifier and established discriminant set inclusion consistency in the sense that the classification responsible functional predictors include those of the underlying optimal classifier.…”

Section: Discussionmentioning

confidence: 99%

Review on functional data classification

Wang,

Huang,

Cao

2023

WIREs Computational Stats

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A fundamental problem in functional data analysis is to classify a functional observation based on training data. The application of functional data classification has gained immense popularity and utility across a wide array of disciplines, encompassing biology, engineering, environmental science, medical science, neurology, social science, and beyond. The phenomenal growth of the application of functional data classification indicates the urgent need for a systematic approach to develop efficient classification methods and scalable algorithmic implementations. Therefore, we here conduct a comprehensive review of classification methods for functional data. The review aims to bridge the gap between the functional data analysis community and the machine learning community, and to intrigue new principles for functional data classification.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification Statistical Models > Classification Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

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Section: Discussionmentioning

confidence: 99%

Review on functional data classification

Wang,

Huang,

Cao

2023

WIREs Computational Stats

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Inference of causal metabolite networks in the presence of invalid instrumental variables with GWAS summary data

Lin

Shen

et al. 2023

Genetic Epidemiology

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We propose structural equation models (SEMs) as a general framework to infer causal networks for metabolites and other complex traits. Traditionally SEMs are used only for individual‐level data under the assumption that all instrumental variables (IVs) are valid. To overcome these limitations, we propose both one‐ and two‐sample approaches for causal network inference based on SEMs that can: (1) perform causal analysis and discover causal relationships among multiple traits; (2) account for the possible presence of some invalid IVs; (3) allow for data analysis using only genome‐wide association studies (GWAS) summary statistics when individual‐level data are not available; (4) consider the possibility of bidirectional relationships between traits. Our method employs a simple stepwise selection to identify invalid IVs, thus avoiding false positives while possibly increasing true discoveries based on two‐stage least squares (2SLS). We use both real GWAS data and simulated data to demonstrate the superior performance of our method over the standard 2SLS/SEMs. For real data analysis, our proposed approach is applied to a human blood metabolite GWAS summary data set to uncover putative causal relationships among the metabolites; we also identify some metabolites (putative) causal to Alzheimer's disease (AD), which, along with the inferred causal metabolite network, suggest some possible pathways of metabolites involved in AD.

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Functional data analysis using deep neural networks

Wang,

Zhang,

Cao

et al. 2024

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Functional data analysis is an evolving field focused on analyzing data that reveals insights into curves, surfaces, or entities within a continuous domain. This type of data is typically distinguished by the inherent dependence and smoothness observed within each data curve. Traditional functional data analysis approaches have predominantly relied on linear models, which, while foundational, often fall short in capturing the intricate, nonlinear relationships within the data. This paper seeks to bridge this gap by reviewing the integration of deep neural networks into functional data analysis. Deep neural networks present a transformative approach to navigating these complexities, excelling particularly in high‐dimensional spaces and demonstrating unparalleled flexibility in managing diverse data constructs. This review aims to advance functional data regression, classification, and representation by integrating deep neural networks with functional data analysis, fostering a harmonious and synergistic union between these two fields. The remarkable ability of deep neural networks to adeptly navigate the intricate functional data highlights a wealth of opportunities for ongoing exploration and research across various interdisciplinary areas.This article is categorized under: Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Learning and Exploratory Methods of the Data Sciences > Deep Learning Statistical Learning and Exploratory Methods of the Data Sciences > Neural Networks

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Optimal Linear Discriminant Analysis for High-Dimensional Functional Data

Cited by 10 publications

References 35 publications

Review on functional data classification

Review on functional data classification

Inference of causal metabolite networks in the presence of invalid instrumental variables with GWAS summary data

Functional data analysis using deep neural networks

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