An encoding generative modeling approach to dimension reduction and covariate adjustment in causal inference with observational studies.

In this article, we develop CausalEGM, a deep learning framework for nonlinear dimension reduction and generative modeling of the dependency among covariate features affecting treatment and response. CausalEGM can be used for estimating causal effects in both binary and continuous treatment settings. By learning a bidirectional transformation between the high-dimensional covariate space and a low-dimensional latent space and then modeling the dependencies of different subsets of the latent variables on the treatment and response, CausalEGM can extract the latent covariate features that affect both treatment and response. By conditioning on these features, one can mitigate the confounding effect of the high dimensional covariate on the estimation of the causal relation between treatment and response. In a series of experiments, the proposed method is shown to achieve superior performance over existing methods in both binary and continuous treatment settings. The improvement is substantial when the sample size is large and the covariate is of high dimension. Finally, we established excess risk bounds and consistency results for our method, and discuss how our approach is related to and improves upon other dimension reduction approaches in causal inference.

Riemannian geometry for efficient analysis of protein dynamics data.

An increasingly common viewpoint is that protein dynamics datasets reside in a nonlinear subspace of low conformational energy. Ideal data analysis tools should therefore account for such nonlinear geometry. The Riemannian geometry setting can be suitable for a variety of reasons. First, it comes with a rich mathematical structure to account for a wide range of geometries that can be modeled after an energy landscape. Second, many standard data analysis tools developed for data in Euclidean space can be generalized to Riemannian manifolds. In the context of protein dynamics, a conceptual challenge comes from the lack of guidelines for constructing a smooth Riemannian structure based on an energy landscape. In addition, computational feasibility in computing geodesics and related mappings poses a major challenge. This work considers these challenges. The first part of the paper develops a local approximation technique for computing geodesics and related mappings on Riemannian manifolds in a computationally feasible manner. The second part constructs a smooth manifold and a Riemannian structure that is based on an energy landscape for protein conformations. The resulting Riemannian geometry is tested on several data analysis tasks relevant for protein dynamics data. In particular, the geodesics with given start- and end-points approximately recover corresponding molecular dynamics trajectories for proteins that undergo relatively ordered transitions with medium-sized deformations. The Riemannian protein geometry also gives physically realistic summary statistics and retrieves the underlying dimension even for large-sized deformations within seconds on a laptop.

A novel deep machine learning algorithm with dimensionality and size reduction approaches for feature elimination: thyroid cancer diagnoses with randomly missing data.

Thyroid cancer incidences endure to increase even though a large number of inspection tools have been developed recently. Since there is no standard and certain procedure to follow for the thyroid cancer diagnoses, clinicians require conducting various tests. This scrutiny process yields multi-dimensional big data and lack of a common approach leads to randomly distributed missing (sparse) data, which are both formidable challenges for the machine learning algorithms. This paper aims to develop an accurate and computationally efficient deep learning algorithm to diagnose the thyroid cancer. In this respect, randomly distributed missing data stemmed singularity in learning problems is treated and dimensionality reduction with inner and target similarity approaches are developed to select the most informative input datasets. In addition, size reduction with the hierarchical clustering algorithm is performed to eliminate the considerably similar data samples. Four machine learning algorithms are trained and also tested with the unseen data to validate their generalization and robustness abilities. The results yield 100% training and 83% testing preciseness for the unseen data. Computational time efficiencies of the algorithms are also examined under the equal conditions.

A comprehensive benchmarking of machine learning algorithms and dimensionality reduction methods for drug sensitivity prediction.

A major challenge of precision oncology is the identification and prioritization of suitable treatment options based on molecular biomarkers of the considered tumor. In pursuit of this goal, large cancer cell line panels have successfully been studied to elucidate the relationship between cellular features and treatment response. Due to the high dimensionality of these datasets, machine learning (ML) is commonly used for their analysis. However, choosing a suitable algorithm and set of input features can be challenging. We performed a comprehensive benchmarking of ML methods and dimension reduction (DR) techniques for predicting drug response metrics. Using the Genomics of Drug Sensitivity in Cancer cell line panel, we trained random forests, neural networks, boosting trees and elastic nets for 179 anti-cancer compounds with feature sets derived from nine DR approaches. We compare the results regarding statistical performance, runtime and interpretability. Additionally, we provide strategies for assessing model performance compared with a simple baseline model and measuring the trade-off between models of different complexity. Lastly, we show that complex ML models benefit from using an optimized DR strategy, and that standard models-even when using considerably fewer features-can still be superior in performance.

FastRNA: An efficient solution for PCA of single-cell RNA-sequencing data based on a batch-accounting count model.

Almost always, the analysis of single-cell RNA-sequencing (scRNA-seq) data begins with the generation of the low dimensional embedding of the data by principal-component analysis (PCA). Because scRNA-seq data are count data, log transformation is routinely applied to correct skewness prior to PCA, which is often argued to have added bias to data. Alternatively, studies have proposed methods that directly assume a count model and use approximately normally distributed count residuals for PCA. Despite their theoretical advantage of directly modeling count data, these methods are extremely slow for large datasets. In fact, when the data size grows, even the standard log normalization becomes inefficient. Here, we present FastRNA, a highly efficient solution for PCA of scRNA-seq data based on a count model accounting for both batches and cell size factors. Although we assume the same general count model as previous methods, our method uses two orders of magnitude less time and memory than the other count-based methods and an order of magnitude less time and memory than the standard log normalization. This achievement results from our unique algebraic optimization that completely avoids the formation of the large dense residual matrix in memory. In addition, our method enjoys a benefit that the batch effects are eliminated from data prior to PCA. Generating a batch-accounted PC of an atlas-scale dataset with 2 million cells takes less than a minute and 1 GB memory with our method.

Bayesian estimation of covariate assisted principal regression for brain functional connectivity.

This paper presents a Bayesian reformulation of covariate-assisted principal regression for covariance matrix outcomes to identify low-dimensional components in the covariance associated with covariates. By introducing a geometric approach to the covariance matrices and leveraging Euclidean geometry, we estimate dimension reduction parameters and model covariance heterogeneity based on covariates. This method enables joint estimation and uncertainty quantification of relevant model parameters associated with heteroscedasticity. We demonstrate our approach through simulation studies and apply it to analyze associations between covariates and brain functional connectivity using data from the Human Connectome Project.

Functional quantile principal component analysis.

This paper introduces functional quantile principal component analysis (FQPCA), a dimensionality reduction technique that extends the concept of functional principal components analysis (FPCA) to the examination of participant-specific quantiles curves. Our approach borrows strength across participants to estimate patterns in quantiles, and uses participant-level data to estimate loadings on those patterns. As a result, FQPCA is able to capture shifts in the scale and distribution of data that affect participant-level quantile curves, and is also a robust methodology suitable for dealing with outliers, heteroscedastic data or skewed data. The need for such methodology is exemplified by physical activity data collected using wearable devices. Participants often differ in the timing and intensity of physical activity behaviors, and capturing information beyond the participant-level expected value curves produced by FPCA is necessary for a robust quantification of diurnal patterns of activity. We illustrate our methods using accelerometer data from the National Health and Nutrition Examination Survey, and produce participant-level 10%, 50%, and 90% quantile curves over 24 h of activity. The proposed methodology is supported by simulation results, and is available as an R package.

PLSDA-batch: a multivariate framework to correct for batch effects in microbiome data.

Microbial communities are highly dynamic and sensitive to changes in the environment. Thus, microbiome data are highly susceptible to batch effects, defined as sources of unwanted variation that are not related to and obscure any factors of interest. Existing batch effect correction methods have been primarily developed for gene expression data. As such, they do not consider the inherent characteristics of microbiome data, including zero inflation, overdispersion and correlation between variables. We introduce new multivariate and non-parametric batch effect correction methods based on Partial Least Squares Discriminant Analysis (PLSDA). PLSDA-batch first estimates treatment and batch variation with latent components, then subtracts batch-associated components from the data. The resulting batch-effect-corrected data can then be input in any downstream statistical analysis. Two variants are proposed to handle unbalanced batch x treatment designs and to avoid overfitting when estimating the components via variable selection. We compare our approaches with popular methods managing batch effects, namely, removeBatchEffect, ComBat and Surrogate Variable Analysis, in simulated and three case studies using various visual and numerical assessments. We show that our three methods lead to competitive performance in removing batch variation while preserving treatment variation, especially for unbalanced batch $\times $ treatment designs. Our downstream analyses show selections of biologically relevant taxa. This work demonstrates that batch effect correction methods can improve microbiome research outputs. Reproducible code and vignettes are available on GitHub.

Structure-preserved dimension reduction using joint triplets sampling for multi-batch integration of single-cell transcriptomic data.

Dimension reduction (DR) plays an important role in single-cell RNA sequencing (scRNA-seq), such as data interpretation, visualization and other downstream analysis. A desired DR method should be applicable to various application scenarios, including identifying cell types, preserving the inherent structure of data and handling with batch effects. However, most of the existing DR methods fail to accommodate these requirements simultaneously, especially removing batch effects. In this paper, we develop a novel structure-preserved dimension reduction (SPDR) method using intra- and inter-batch triplets sampling. The constructed triplets jointly consider each anchor's mutual nearest neighbors from inter-batch, k-nearest neighbors from intra-batch and randomly selected cells from the whole data, which capture higher order structure information and meanwhile account for batch information of the data. Then we minimize a robust loss function for the chosen triplets to obtain a structure-preserved and batch-corrected low-dimensional representation. Comprehensive evaluations show that SPDR outperforms other competing DR methods, such as INSCT, IVIS, Trimap, Scanorama, scVI and UMAP, in removing batch effects, preserving biological variation, facilitating visualization and improving clustering accuracy. Besides, the two-dimensional (2D) embedding of SPDR presents a clear and authentic expression pattern, and can guide researchers to determine how many cell types should be identified. Furthermore, SPDR is robust to complex data characteristics (such as down-sampling, duplicates and outliers) and varying hyperparameter settings. We believe that SPDR will be a valuable tool for characterizing complex cellular heterogeneity.

Multiple phenotype association tests based on sliced inverse regression.

BACKGROUND: Joint analysis of multiple phenotypes in studies of biological systems such as Genome-Wide Association Studies is critical to revealing the functional interactions between various traits and genetic variants, but growth of data in dimensionality has become a very challenging problem in the widespread use of joint analysis. To handle the excessiveness of variables, we consider the sliced inverse regression (SIR) method. Specifically, we propose a novel SIR-based association test that is robust and powerful in testing the association between multiple predictors and multiple outcomes. RESULTS: We conduct simulation studies in both low- and high-dimensional settings with various numbers of Single-Nucleotide Polymorphisms and consider the correlation structure of traits. Simulation results show that the proposed method outperforms the existing methods. We also successfully apply our method to the genetic association study of ADNI dataset. Both the simulation studies and real data analysis show that the SIR-based association test is valid and achieves a higher efficiency compared with its competitors. CONCLUSION: Several scenarios with low- and high-dimensional responses and genotypes are considered in this paper. Our SIR-based method controls the estimated type I error at the pre-specified level α .

PredictEFC: a fast and efficient multi-label classifier for predicting enzyme family classes.

BACKGROUND: Enzymes play an irreplaceable and important role in maintaining the lives of living organisms. The Enzyme Commission (EC) number of an enzyme indicates its essential functions. Correct identification of the first digit (family class) of the EC number for a given enzyme is a hot topic in the past twenty years. Several previous methods adopted functional domain composition to represent enzymes. However, it would lead to dimension disaster, thereby reducing the efficiency of the methods. On the other hand, most previous methods can only deal with enzymes belonging to one family class. In fact, several enzymes belong to two or more family classes. RESULTS: In this study, a fast and efficient multi-label classifier, named PredictEFC, was designed. To construct this classifier, a novel feature extraction scheme was designed for processing functional domain information of enzymes, which counting the distribution of each functional domain entry across seven family classes in the training dataset. Based on this scheme, each training or test enzyme was encoded into a 7-dimenion vector by fusing its functional domain information and above statistical results. Random k-labelsets (RAKEL) was adopted to build the classifier, where random forest was selected as the base classification algorithm. The two tenfold cross-validation results on the training dataset shown that the accuracy of PredictEFC can reach 0.8493 and 0.8370. The independent test on two datasets indicated the accuracy values of 0.9118 and 0.8777. CONCLUSION: The performance of PredictEFC was slightly lower than the classifier directly using functional domain composition. However, its efficiency was sharply improved. The running time was less than one-tenth of the time of the classifier directly using functional domain composition. In additional, the utility of PredictEFC was superior to the classifiers using traditional dimensionality reduction methods and some previous methods, and this classifier can be transplanted for predicting enzyme family classes of other species. Finally, a web-server available at http://124.221.158.221/ was set up for easy usage.

Analyzing microbial evolution through gene and genome phylogenies.

Microbiome scientists critically need modern tools to explore and analyze microbial evolution. Often this involves studying the evolution of microbial genomes as a whole. However, different genes in a single genome can be subject to different evolutionary pressures, which can result in distinct gene-level evolutionary histories. To address this challenge, we propose to treat estimated gene-level phylogenies as data objects, and present an interactive method for the analysis of a collection of gene phylogenies. We use a local linear approximation of phylogenetic tree space to visualize estimated gene trees as points in low-dimensional Euclidean space, and address important practical limitations of existing related approaches, allowing an intuitive visualization of complex data objects. We demonstrate the utility of our proposed approach through microbial data analyses, including by identifying outlying gene histories in strains of Prevotella, and by contrasting Streptococcus phylogenies estimated using different gene sets. Our method is available as an open-source R package, and assists with estimating, visualizing, and interacting with a collection of bacterial gene phylogenies.

Constrained groupwise additive index models.

In environmental epidemiology, there is wide interest in creating and using comprehensive indices that can summarize information from different environmental exposures while retaining strong predictive power on a target health outcome. In this context, the present article proposes a model called the constrained groupwise additive index model (CGAIM) to create easy-to-interpret indices predictive of a response variable, from a potentially large list of variables. The CGAIM considers groups of predictors that naturally belong together to yield meaningful indices. It also allows the addition of linear constraints on both the index weights and the form of their relationship with the response variable to represent prior assumptions or operational requirements. We propose an efficient algorithm to estimate the CGAIM, along with index selection and inference procedures. A simulation study shows that the proposed algorithm has good estimation performances, with low bias and variance and is applicable in complex situations with many correlated predictors. It also demonstrates important sensitivity and specificity in index selection, but non-negligible coverage error on constructed confidence intervals. The CGAIM is then illustrated in the construction of heat indices in a health warning system context. We believe the CGAIM could become useful in a wide variety of situations, such as warning systems establishment, and multipollutant or exposome studies.

RNAI-FRID: novel feature representation method with information enhancement and dimension reduction for RNA-RNA interaction.

Different ribonucleic acids (RNAs) can interact to form regulatory networks that play important role in many life activities. Molecular biology experiments can confirm RNA-RNA interactions to facilitate the exploration of their biological functions, but they are expensive and time-consuming. Machine learning models can predict potential RNA-RNA interactions, which provide candidates for molecular biology experiments to save a lot of time and cost. Using a set of suitable features to represent the sample is crucial for training powerful models, but there is a lack of effective feature representation for RNA-RNA interaction. This study proposes a novel feature representation method with information enhancement and dimension reduction for RNA-RNA interaction (named RNAI-FRID). Diverse base features are first extracted from RNA data to contain more sample information. Then, the extracted base features are used to construct the complex features through an arithmetic-level method. It greatly reduces the feature dimension while keeping the relationship between molecule features. Since the dimension reduction may cause information loss, in the process of complex feature construction, the arithmetic mean strategy is adopted to enhance the sample information further. Finally, three feature ranking methods are integrated for feature selection on constructed complex features. It can adaptively retain important features and remove redundant ones. Extensive experiment results show that RNAI-FRID can provide reliable feature representation for RNA-RNA interaction with higher efficiency and the model trained with generated features obtain better performance than other deep neural network predictors.

High dimensionality reduction by matrix factorization for systems pharmacology.

The extraction of predictive features from the complex high-dimensional multi-omic data is necessary for decoding and overcoming the therapeutic responses in systems pharmacology. Developing computational methods to reduce high-dimensional space of features in in vitro, in vivo and clinical data is essential to discover the evolution and mechanisms of the drug responses and drug resistance. In this paper, we have utilized the matrix factorization (MF) as a modality for high dimensionality reduction in systems pharmacology. In this respect, we have proposed three novel feature selection methods using the mathematical conception of a basis for features. We have applied these techniques as well as three other MF methods to analyze eight different gene expression datasets to investigate and compare their performance for feature selection. Our results show that these methods are capable of reducing the feature spaces and find predictive features in terms of phenotype determination. The three proposed techniques outperform the other methods used and can extract a 2-gene signature predictive of a tyrosine kinase inhibitor treatment response in the Cancer Cell Line Encyclopedia.

Mediation analysis method review of high throughput data.

High-throughput technologies have made high-dimensional settings increasingly common, providing opportunities for the development of high-dimensional mediation methods. We aimed to provide useful guidance for researchers using high-dimensional mediation analysis and ideas for biostatisticians to develop it by summarizing and discussing recent advances in high-dimensional mediation analysis. The method still faces many challenges when extended single and multiple mediation analyses to high-dimensional settings. The development of high-dimensional mediation methods attempts to address these issues, such as screening true mediators, estimating mediation effects by variable selection, reducing the mediation dimension to resolve correlations between variables, and utilizing composite null hypothesis testing to test them. Although these problems regarding high-dimensional mediation have been solved to some extent, some challenges remain. First, the correlation between mediators are rarely considered when the variables are selected for mediation. Second, downscaling without incorporating prior biological knowledge makes the results difficult to interpret. In addition, a method of sensitivity analysis for the strict sequential ignorability assumption in high-dimensional mediation analysis is still lacking. An analyst needs to consider the applicability of each method when utilizing them, while a biostatistician could consider extensions and improvements in the methodology.

Estimation of place-based vulnerability scores for HIV viral non-suppression: an application leveraging data from a cohort of people with histories of using drugs.

The relationships between place (e.g., neighborhood) and HIV are commonly investigated. As measurements of place are multivariate, most studies apply some dimension reduction, resulting in one variable (or a small number of variables), which is then used to characterize place. Typical dimension reduction methods seek to capture the most variance of the raw items, resulting in a type of summary variable we call "disadvantage score". We propose to add a different type of summary variable, the "vulnerability score," to the toolbox of the researchers doing place and HIV research. The vulnerability score measures how place, as known through the raw measurements, is predictive of an outcome. It captures variation in place characteristics that matters most for the particular outcome. We demonstrate the estimation and utility of place-based vulnerability scores for HIV viral non-suppression, using data with complicated clustering from a cohort of people with histories of injecting drugs.

Multi-layer Bundling as a New Approach for Determining Multi-scale Correlations Within a High-Dimensional Dataset.

The growing complexity of biological data has spurred the development of innovative computational techniques to extract meaningful information and uncover hidden patterns within vast datasets. Biological networks, such as gene regulatory networks and protein-protein interaction networks, hold critical insights into biological features' connections and functions. Integrating and analyzing high-dimensional data, particularly in gene expression studies, stands prominent among the challenges in deciphering these networks. Clustering methods play a crucial role in addressing these challenges, with spectral clustering emerging as a potent unsupervised technique considering intrinsic geometric structures. However, spectral clustering's user-defined cluster number can lead to inconsistent and sometimes orthogonal clustering regimes. We propose the Multi-layer Bundling (MLB) method to address this limitation, combining multiple prominent clustering regimes to offer a comprehensive data view. We call the outcome clusters "bundles". This approach refines clustering outcomes, unravels hierarchical organization, and identifies bridge elements mediating communication between network components. By layering clustering results, MLB provides a global-to-local view of biological feature clusters enabling insights into intricate biological systems. Furthermore, the method enhances bundle network predictions by integrating the bundle co-cluster matrix with the affinity matrix. The versatility of MLB extends beyond biological networks, making it applicable to various domains where understanding complex relationships and patterns is needed.

An enriched approach to combining high-dimensional genomic and low-dimensional phenotypic data.

We describe an approach for combining and analyzing high-dimensional genomic and low-dimensional phenotypic data. The approach leverages a scheme of weights applied to the variables instead of observations and, hence, permits incorporation of the information provided by the low dimensional data source. It can also be incorporated into commonly used downstream techniques, such as random forest or penalized regression. Finally, the simulated lupus studies involving genetic and clinical data are used to illustrate the overall idea and show that the proposed enriched penalized method can select significant genetic variables while keeping several important clinical variables in the final model.

Dimension reduction and outlier detection of 3-D shapes derived from multi-organ CT images.

BACKGROUND: Unsupervised clustering and outlier detection are important in medical research to understand the distributional composition of a collective of patients. A number of clustering methods exist, also for high-dimensional data after dimension reduction. Clustering and outlier detection may, however, become less robust or contradictory if multiple high-dimensional data sets per patient exist. Such a scenario is given when the focus is on 3-D data of multiple organs per patient, and a high-dimensional feature matrix per organ is extracted. METHODS: We use principal component analysis (PCA), t-distributed stochastic neighbor embedding (t-SNE) and multiple co-inertia analysis (MCIA) combined with bagplots to study the distribution of multi-organ 3-D data taken by computed tomography scans. After point-set registration of multiple organs from two public data sets, multiple hundred shape features are extracted per organ. While PCA and t-SNE can only be applied to each organ individually, MCIA can project the data of all organs into the same low-dimensional space. RESULTS: MCIA is the only approach, here, with which data of all organs can be projected into the same low-dimensional space. We studied how frequently (i.e., by how many organs) a patient was classified to belong to the inner or outer 50% of the population, or as an outlier. Outliers could only be detected with MCIA and PCA. MCIA and t-SNE were more robust in judging the distributional location of a patient in contrast to PCA. CONCLUSIONS: MCIA is more appropriate and robust in judging the distributional location of a patient in the case of multiple high-dimensional data sets per patient. It is still recommendable to apply PCA or t-SNE in parallel to MCIA to study the location of individual organs.