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

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.

Adverse effect signature extraction and prediction for drugs treating COVID-19

Given the considerable cost of drug discovery, drug repurposing is becoming attractive as it can effectively shorten the development timeline and reduce the development cost. However, most existing drug-repurposing methods omitted the heterogeneous health conditions of different COVID-19 patients. In this study, we evaluated the adverse effect (AE) profiles of 106 COVID-19 drugs. We extracted four AE signatures to characterize the AE distribution of 106 COVID-19 drugs by non-negative matrix factorization (NMF). By integrating the information from four distinct databases (AE, bioassay, chemical structure, and gene expression information), we predicted the AE profiles of 91 drugs with inadequate AE feedback. For each of the drug clusters, discriminant genes accounting for mechanisms of different AE signatures were identified by sparse linear discriminant analysis. Our findings can be divided into three parts. First, drugs abundant with AE-signature 1 (for example, remdesivir) should be taken with caution for patients with poor liver, renal, or cardiac functions, where the functional genes accumulate in the RHO GTPases Activate NADPH Oxidases pathway. Second, drugs featuring AE-signature 2 (for example, hydroxychloroquine) are unsuitable for patients with vascular disorders, with relevant genes enriched in signal transduction pathways. Third, drugs characterized by AE signatures 3 and 4 have relatively mild AEs. Our study showed that NMF and network-based frameworks contribute to more precise drug recommendations.

Multiway sparse distance weighted discrimination

Modern data often take the form of a multiway array. However, most classification methods are designed for vectors, i.e., 1-way arrays. Distance weighted discrimination (DWD) is a popular high-dimensional classification method that has been extended to the multiway context, with dramatic improvements in performance when data have multiway structure. However, the previous implementation of multiway DWD was restricted to classification of matrices, and did not account for sparsity. In this paper, we develop a general framework for multiway classification which is applicable to any number of dimensions and any degree of sparsity. We conducted extensive simulation studies, showing that our model is robust to the degree of sparsity and improves classification accuracy when the data have multiway structure. For our motivating application, magnetic resonance spectroscopy (MRS) was used to measure the abundance of several metabolites across multiple neurological regions and across multiple time points in a mouse model of Friedreich's ataxia, yielding a four-way data array. Our method reveals a robust and interpretable multi-region metabolomic signal that discriminates the groups of interest. We also successfully apply our method to gene expression time course data for multiple sclerosis treatment. An R implementation is available in the package MultiwayClassification at http://github.com/lockEF/MultiwayClassification.

Simultaneous differential network analysis and classification for matrix-variate data with application to brain connectivity

Growing evidence has shown that the brain connectivity network experiences alterations for complex diseases such as Alzheimer's disease (AD). Network comparison, also known as differential network analysis, is thus particularly powerful to reveal the disease pathologies and identify clinical biomarkers for medical diagnoses (classification). Data from neurophysiological measurements are multidimensional and in matrix-form. Naive vectorization method is not sufficient as it ignores the structural information within the matrix. In the article, we adopt the Kronecker product covariance matrices framework to capture both spatial and temporal correlations of the matrix-variate data while the temporal covariance matrix is treated as a nuisance parameter. By recognizing that the strengths of network connections may vary across subjects, we develop an ensemble-learning procedure, which identifies the differential interaction patterns of brain regions between the case group and the control group and conducts medical diagnosis (classification) of the disease simultaneously. Simulation studies are conducted to assess the performance of the proposed method. We apply the proposed procedure to the functional connectivity analysis of an functional magnetic resonance imaging study on AD. The hub nodes and differential interaction patterns identified are consistent with existing experimental studies, and satisfactory out-of-sample classification performance is achieved for medical diagnosis of AD.

Unobserved classes and extra variables in high-dimensional discriminant analysis

In supervised classification problems, the test set may contain data points belonging to classes not observed in the learning phase. Moreover, the same units in the test data may be measured on a set of additional variables recorded at a subsequent stage with respect to when the learning sample was collected. In this situation, the classifier built in the learning phase needs to adapt to handle potential unknown classes and the extra dimensions. We introduce a model-based discriminant approach, Dimension-Adaptive Mixture Discriminant Analysis (D-AMDA), which can detect unobserved classes and adapt to the increasing dimensionality. Model estimation is carried out via a full inductive approach based on an EM algorithm. The method is then embedded in a more general framework for adaptive variable selection and classification suitable for data of large dimensions. A simulation study and an artificial experiment related to classification of adulterated honey samples are used to validate the ability of the proposed framework to deal with complex situations.

Incorporating prior knowledge into regularized regression

MOTIVATION

Associated with genomic features like gene expression, methylation and genotypes, used in statistical modeling of health outcomes, there is a rich set of meta-features like functional annotations, pathway information and knowledge from previous studies, that can be used post hoc to facilitate the interpretation of a model. However, using this meta-feature information a priori rather than post hoc can yield improved prediction performance as well as enhanced model interpretation.

RESULTS

We propose a new penalized regression approach that allows a priori integration of external meta-features. The method extends LASSO regression by incorporating individualized penalty parameters for each regression coefficient. The penalty parameters are, in turn, modeled as a log-linear function of the meta-features and are estimated from the data using an approximate empirical Bayes approach. Optimization of the marginal likelihood on which the empirical Bayes estimation is performed using a fast and stable majorization-minimization procedure. Through simulations, we show that the proposed regression with individualized penalties can outperform the standard LASSO in terms of both parameters estimation and prediction performance when the external data is informative. We further demonstrate our approach with applications to gene expression studies of bone density and breast cancer.

AVAILABILITY AND IMPLEMENTATION

The methods have been implemented in the R package xtune freely available for download from https://cran.r-project.org/web/packages/xtune/index.html.

RAMRSGL: A Robust Adaptive Multinomial Regression Model for Multicancer Classification

In view of the challenges of the group Lasso penalty methods for multicancer microarray data analysis, e.g., dividing genes into groups in advance and biological interpretability, we propose a robust adaptive multinomial regression with sparse group Lasso penalty (RAMRSGL) model. By adopting the overlapping clustering strategy, affinity propagation clustering is employed to obtain each cancer gene subtype, which explores the group structure of each cancer subtype and merges the groups of all subtypes. In addition, the data-driven weights based on noise are added to the sparse group Lasso penalty, combining with the multinomial log-likelihood function to perform multiclassification and adaptive group gene selection simultaneously. The experimental results on acute leukemia data verify the effectiveness of the proposed method.

Sparse Linear Discriminant Analysis using the Prior-Knowledge-Guided Block Covariance Matrix

There are two key challenges when using a linear discriminant analysis in the high-dimensional setting, including singularity of the covariance matrix and difficulty of interpreting the resulting classifier. Although several methods have been proposed to address these problems, they focused only on identifying a parsimonious set of variables maximizing classification accuracy. However, most methods did not consider dependency between variables and efficacy of selected variables appropriately. To address these limitations, here we propose a new approach that directly estimates the sparse discriminant vector without a need of estimating the whole inverse covariance matrix, by formulating a quadratic optimization problem. Furthermore, this approach also allows to integrate external information to guide the structure of covariance matrix. We evaluated the proposed model with simulation studies. We then applied it to the transcriptomic study that aims to identify genomic markers predictive of the response to cancer immunotherapy, where the covariance matrix was constructed based on the prior knowledge available in the pathway database.

High-dimensional integrative copula discriminant analysis for multiomics data

Multiomics or integrative omics data have been increasingly common in biomedical studies, holding a promise in better understanding human health and disease. In this article, we propose an integrative copula discrimination analysis classifier in the context of two-class classification, which relaxes the common Gaussian assumption and gains power by borrowing information from multiple omics data types in discriminant analysis. Numerical studies are conducted to assess the finite sample performance of the new classifier. We apply our model to the Religious Orders Study and Memory and Aging Project (ROSMAP) Study, integrating gene expression and DNA methylation data for better prediction.

Multiclass linear discriminant analysis with ultrahigh-dimensional features

Within the framework of Fisher's discriminant analysis, we propose a multiclass classification method which embeds variable screening for ultrahigh-dimensional predictors. Leveraging interfeature correlations, we show that the proposed linear classifier recovers informative features with probability tending to one and can asymptotically achieve a zero misclassification rate. We evaluate the finite sample performance of the method via extensive simulations and use this method to classify posttransplantation rejection types based on patients' gene expressions.

MODEL-FREE FORWARD SCREENING VIA CUMULATIVE DIVERGENCE

Feature screening plays an important role in the analysis of ultrahigh dimensional data. Due to complicated model structure and high noise level, existing screening methods often suffer from model misspecification and the presence of outliers. To address these issues, we introduce a new metric named cumulative divergence (CD), and develop a CD-based forward screening procedure. This forward screening method is model-free and resistant to the presence of outliers in the response. It also incorporates the joint effects among covariates into the screening process. With a data-driven threshold, the new method can automatically determine the number of features that should be retained after screening. These merits make the CD-based screening very appealing in practice. Under certain regularity conditions, we show that the proposed method possesses sure screening property. The performance of our proposal is illustrated through simulations and a real data example.

Statistical Workflow for Feature Selection in Human Metabolomics Data

High-throughput metabolomics investigations, when conducted in large human cohorts, represent a potentially powerful tool for elucidating the biochemical diversity underlying human health and disease. Large-scale metabolomics data sources, generated using either targeted or nontargeted platforms, are becoming more common. Appropriate statistical analysis of these complex high-dimensional data will be critical for extracting meaningful results from such large-scale human metabolomics studies. Therefore, we consider the statistical analytical approaches that have been employed in prior human metabolomics studies. Based on the lessons learned and collective experience to date in the field, we offer a step-by-step framework for pursuing statistical analyses of cohort-based human metabolomics data, with a focus on feature selection. We discuss the range of options and approaches that may be employed at each stage of data management, analysis, and interpretation and offer guidance on the analytical decisions that need to be considered over the course of implementing a data analysis workflow. Certain pervasive analytical challenges facing the field warrant ongoing focused research. Addressing these challenges, particularly those related to analyzing human metabolomics data, will allow for more standardization of as well as advances in how research in the field is practiced. In turn, such major analytical advances will lead to substantial improvements in the overall contributions of human metabolomics investigations.

DBSDA : Lowering the Bound of Misclassification Rate for Sparse Linear Discriminant Analysis via Model Debiasing

Linear discriminant analysis (LDA) is a well-known technique for linear classification, feature extraction, and dimension reduction. To improve the accuracy of LDA under the high dimension low sample size (HDLSS) settings, shrunken estimators, such as Graphical Lasso, can be used to strike a balance between biases and variances. Although the estimator with induced sparsity obtains a faster convergence rate, however, the introduced bias may also degrade the performance. In this paper, we theoretically analyze how the sparsity and the convergence rate of the precision matrix (also known as inverse covariance matrix) estimator would affect the classification accuracy by proposing an analytic model on the upper bound of an LDA misclassification rate. Guided by the model, we propose a novel classifier, DBSDA , which improves classification accuracy through debiasing. Theoretical analysis shows that DBSDA possesses a reduced upper bound of misclassification rate and better asymptotic properties than sparse LDA (SDA). We conduct experiments on both synthetic datasets and real application datasets to confirm the correctness of our theoretical analysis and demonstrate the superiority of DBSDA over LDA, SDA, and other downstream competitors under HDLSS settings.

Sparse quadratic classification rules via linear dimension reduction

We consider the problem of high-dimensional classification between two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on the original data, with the subsequent application of quadratic discriminant analysis on the reduced space. In contrast to quadratic discriminant analysis, the proposed framework doesn't require the estimation of precision matrices; it scales linearly with the number of measurements, making it especially attractive for the use on high-dimensional datasets. We support the methodology with theoretical guarantees on variable selection consistency, and empirical comparisons with competing approaches. We apply the method to gene expression data of breast cancer patients, and confirm the crucial importance of the ESR1 gene in differentiating estrogen receptor status.

Graph-based sparse linear discriminant analysis for high-dimensional classification

Linear discriminant analysis (LDA) is a well-known classification technique that enjoyed great success in practical applications. Despite its effectiveness for traditional low-dimensional problems, extensions of LDA are necessary in order to classify high-dimensional data. Many variants of LDA have been proposed in the literature. However, most of these methods do not fully incorporate the structure information among predictors when such information is available. In this paper, we introduce a new high-dimensional LDA technique, namely graph-based sparse LDA (GSLDA), that utilizes the graph structure among the features. In particular, we use the regularized regression formulation for penalized LDA techniques, and propose to impose a structure-based sparse penalty on the discriminant vector β . The graph structure can be either given or estimated from the training data. Moreover, we explore the relationship between the within-class feature structure and the overall feature structure. Based on this relationship, we further propose a variant of our proposed GSLDA to utilize effectively unlabeled data, which can be abundant in the semi-supervised learning setting. With the new regularization, we can obtain a sparse estimate of β and more accurate and interpretable classifiers than many existing methods. Both the selection consistency of β estimation and the convergence rate of the classifier are established, and the resulting classifier has an asymptotic Bayes error rate. Finally, we demonstrate the competitive performance of the proposed GSLDA on both simulated and real data studies.

Integrative linear discriminant analysis with guaranteed error rate improvement

Multiple types of data measured on a common set of subjects arise in many areas. Numerous empirical studies have found that integrative analysis of such data can result in better statistical performance in terms of prediction and feature selection. However, the advantages of integrative analysis have mostly been demonstrated empirically. In the context of two-class classification, we propose an integrative linear discriminant analysis method and establish a theoretical guarantee that it achieves a smaller classification error than running linear discriminant analysis on each data type individually. We address the issues of outliers and missing values, frequently encountered in integrative analysis, and illustrate our method through simulations and a neuroimaging study of Alzheimer's disease.