arXiv subjects

J. S. Marron

Publications and source records attributed to J. S. Marron.

At least 37 records · Page 2Linked to original sources

arXiv2021

New Perspectives on Centering

Data matrix centering is an ever-present yet under-examined aspect of data analysis. Functional data analysis (FDA) often operates with a default of centering such that the vectors in one dimension have mean zero. We find that centering along the other dimension identifies a novel useful mode of variation beyond those familiar in FDA. We explore ambiguities in both matrix orientation and nomenclature. Differences between centerings and their potential interaction can be easily misunderstood. We propose a unified framework and new terminology for centering operations. We clearly demonstrate the intuition behind and consequences of each centering choice with informative graphics. We also propose a new direction energy hypothesis test as part of a series of diagnostics for determining which choice of centering is best for a data set. We explore the application of these diagnostics in several FDA settings.

stat.ME↗

arXiv2020

Distance weighted discrimination of face images for gender classification

We illustrate the advantages of distance weighted discrimination for classification and feature extraction in a High Dimension Low Sample Size (HDLSS) situation. The HDLSS context is a gender classification problem of face images in which the dimension of the data is several orders of magnitude larger than the sample size. We compare distance weighted discrimination with Fisher's linear discriminant, support vector machines, and principal component analysis by exploring their classification interpretation through insightful visuanimations and by examining the classifiers' discriminant errors. This analysis enables us to make new contributions to the understanding of the drivers of human discrimination between males and females.

stat.AP↗

arXiv2020

diproperm: An R Package for the DiProPerm Test

High-dimensional low sample size (HDLSS) data sets emerge frequently in many biomedical applications. A common task for analyzing HDLSS data is to assign data to the correct class using a classifier. Classifiers which use two labels and a linear combination of features are known as binary linear classifiers. The direction-projection-permutation (DiProPerm) test was developed for testing the difference of two high-dimensional distributions induced by a binary linear classifier. This paper discusses the key components of the DiProPerm test, introduces the diproperm R package, and demonstrates the package on a real-world data set.

stat.CO↗

arXiv2020

Joint and individual analysis of breast cancer histologic images and genomic covariates

A key challenge in modern data analysis is understanding connections between complex and differing modalities of data. For example, two of the main approaches to the study of breast cancer are histopathology (analyzing visual characteristics of tumors) and genetics. While histopathology is the gold standard for diagnostics and there have been many recent breakthroughs in genetics, there is little overlap between these two fields. We aim to bridge this gap by developing methods based on Angle-based Joint and Individual Variation Explained (AJIVE) to directly explore similarities and differences between these two modalities. Our approach exploits Convolutional Neural Networks (CNNs) as a powerful, automatic method for image feature extraction to address some of the challenges presented by statistical analysis of histopathology image data. CNNs raise issues of interpretability that we address by developing novel methods to explore visual modes of variation captured by statistical algorithms (e.g. PCA or AJIVE) applied to CNN features. Our results provide many interpretable connections and contrasts between histopathology and genetics.

q-bio.QM↗

arXiv2019

Theory of high-dimensional outliers

This study concerns the issue of high dimensional outliers which are challenging to distinguish from inliers due to the special structure of high dimensional space. We introduce a new notion of high dimensional outliers that embraces various types and provides deep insights into understanding the behavior of these outliers based on several asymptotic regimes. Our study of geometrical properties of high dimensional outliers reveals an interesting transition phenomenon of outliers from near the surface of a high dimensional sphere to being distant from the sphere. Also, we study the PCA subspace consistency when data contain a limited number of outliers.

math.ST↗

arXiv2019

Variable screening based on Gaussian Centered L-moments

An important challenge in big data is identification of important variables. In this paper, we propose methods of discovering variables with non-standard univariate marginal distributions. The conventional moments-based summary statistics can be well-adopted for that purpose, but their sensitivity to outliers can lead to selection based on a few outliers rather than distributional shape such as bimodality. To address this type of non-robustness, we consider the L-moments. Using these in practice, however, has a limitation because they do not take zero values at the Gaussian distributions to which the shape of a marginal distribution is most naturally compared. As a remedy, we propose Gaussian Centered L-moments which share advantages of the L-moments but have zeros at the Gaussian distributions. The strength of Gaussian Centered L-moments over other conventional moments is shown in theoretical and practical aspects such as their performances in screening important genes in cancer genetics data.

stat.ME↗

arXiv2019

Deep Multi-View Learning via Task-Optimal CCA

Canonical Correlation Analysis (CCA) is widely used for multimodal data analysis and, more recently, for discriminative tasks such as multi-view learning; however, it makes no use of class labels. Recent CCA methods have started to address this weakness but are limited in that they do not simultaneously optimize the CCA projection for discrimination and the CCA projection itself, or they are linear only. We address these deficiencies by simultaneously optimizing a CCA-based and a task objective in an end-to-end manner. Together, these two objectives learn a non-linear CCA projection to a shared latent space that is highly correlated and discriminative. Our method shows a significant improvement over previous state-of-the-art (including deep supervised approaches) for cross-view classification, regularization with a second view, and semi-supervised learning on real data.

cs.LG↗

arXiv2018

Geometric Insights into Support Vector Machine Behavior using the KKT Conditions

The support vector machine (SVM) is a powerful and widely used classification algorithm. This paper uses the Karush-Kuhn-Tucker conditions to provide rigorous mathematical proof for new insights into the behavior of SVM. These insights provide perhaps unexpected relationships between SVM and two other linear classifiers: the mean difference and the maximal data piling direction. For example, we show that in many cases SVM can be viewed as a cropped version of these classifiers. By carefully exploring these connections we show how SVM tuning behavior is affected by characteristics including: balanced vs. unbalanced classes, low vs. high dimension, separable vs. non-separable data. These results provide further insights into tuning SVM via cross-validation by explaining observed pathological behavior and motivating improved cross-validation methodology. Finally, we also provide new results on the geometry of complete data piling directions in high dimensional space.

stat.ML↗

arXiv2018

Multiple Instance Learning for Heterogeneous Images: Training a CNN for Histopathology

Multiple instance (MI) learning with a convolutional neural network enables end-to-end training in the presence of weak image-level labels. We propose a new method for aggregating predictions from smaller regions of the image into an image-level classification by using the quantile function. The quantile function provides a more complete description of the heterogeneity within each image, improving image-level classification. We also adapt image augmentation to the MI framework by randomly selecting cropped regions on which to apply MI aggregation during each epoch of training. This provides a mechanism to study the importance of MI learning. We validate our method on five different classification tasks for breast tumor histology and provide a visualization method for interpreting local image classifications that could lead to future insights into tumor heterogeneity.

cs.CV↗

arXiv2018

Data Science vs. Statistics: Two Cultures?

Data science is the business of learning from data, which is traditionally the business of statistics. Data science, however, is often understood as a broader, task-driven and computationally-oriented version of statistics. Both the term data science and the broader idea it conveys have origins in statistics and are a reaction to a narrower view of data analysis. Expanding upon the views of a number of statisticians, this paper encourages a big-tent view of data analysis. We examine how evolving approaches to modern data analysis relate to the existing discipline of statistics (e.g. exploratory analysis, machine learning, reproducibility, computation, communication and the role of theory). Finally, we discuss what these trends mean for the future of statistics by highlighting promising directions for communication, education and research.

stat.OT↗

arXiv2018

Estimation of the number of spikes using a generalized spike population model and application to RNA-seq data

Although a generalized spike population model has been actively studied in random matrix theory, its application to real data has been rarely explored. We find that most methods for determining the number of spikes based on the Johnstone's spike population model choose far too many spikes in RNA-seq gene expression data or often fail to determine the number of spikes by indicating that all components are spikes. In this paper, we propose a new algorithm for the estimation of the number of spikes based on a generalized spike population model. Also, we suggest a new noise model for RNA-seq data based on population spectral distribution ideas, which provides a biologically reasonable number of spikes using the proposed algorithm. Furthermore, we propose a graphical tool for assessing the performance of the underlying noise model.

stat.ME↗

arXiv2018

Angle-Based Joint and Individual Variation Explained

Integrative analysis of disparate data blocks measured on a common set of experimental subjects is a major challenge in modern data analysis. This data structure naturally motivates the simultaneous exploration of the joint and individual variation within each data block resulting in new insights. For instance, there is a strong desire to integrate the multiple genomic data sets in The Cancer Genome Atlas to characterize the common and also the unique aspects of cancer genetics and cell biology for each source. In this paper we introduce Angle-Based Joint and Individual Variation Explained capturing both joint and individual variation within each data block. This is a major improvement over earlier approaches to this challenge in terms of a new conceptual understanding, much better adaption to data heterogeneity and a fast linear algebra computation. Important mathematical contributions are the use of score subspaces as the principal descriptors of variation structure and the use of perturbation theory as the guide for variation segmentation. This leads to an exploratory data analysis method which is insensitive to the heterogeneity among data blocks and does not require separate normalization. An application to cancer data reveals different behaviors of each type of signal in characterizing tumor subtypes. An application to a mortality data set reveals interesting historical lessons. Software and data are available at GitHub .

stat.ML↗

arXiv2017

Fast algorithms for large scale generalized distance weighted discrimination

High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the margin. This leads naturally to the development of distance weighted discrimination (DWD), which can be modeled as a second-order cone programming problem and solved by interior-point methods when the scale (in sample size and feature dimension) of the data is moderate. Here, we design a scalable and robust algorithm for solving large scale generalized DWD problems. Numerical experiments on real data sets from the UCI repository demonstrate that our algorithm is highly efficient in solving large scale problems, and sometimes even more efficient than the highly optimized LIBLINEAR and LIBSVM for solving the corresponding SVM problems.

math.OC↗

arXiv2017

Relative Optimality Conditions and Algorithms for Treespace Fréchet Means

Recent interest in treespaces as well-founded mathematical domains for phylogenetic inference and statistical analysis for populations of anatomical trees has motivated research into efficient and rigorous methods for optimization problems on treespaces. A central problem in this area is computing an average of phylogenetic trees, which is equivalently characterized as the minimizer of the Fréchet function. The Fréchet mean can be used for statistical inference and exploratory data analysis: for example it can be leveraged as a test statistic to compare groups via permutation tests, or to find trends in data over time via kernel smoothing. By analyzing the differential properties of the Fréchet function along geodesics in treespace we obtained a theorem describing a decomposition of the derivative along a geodesic. This decomposition theorem is used to formulate optimality conditions which are used as a logical basis for an algorithm to verify relative optimality at points where the Fréchet function gradient does not exist.

math.OC↗

arXiv2016

Computation of ancestry scores with mixed families and unrelated individuals

The issue of robustness to family relationships in computing genotype ancestry scores such as eigenvector projections has received increased attention in genetic association, as the scores are widely used to control spurious association. We use a motivational example from the North American Cystic Fibrosis (CF) Consortium genetic association study with 3444 individuals and 898 family members to illustrate the challenge of computing ancestry scores when sets of both unrelated individuals and closely-related family members are included. We propose novel methods to obtain ancestry scores and demonstrate that the proposed methods outperform existing methods. The current standard is to compute loadings (left singular vectors) using unrelated individuals and to compute projected scores for remaining family members. However, projected ancestry scores from this approach suffer from shrinkage toward zero. We consider in turn alternate strategies: (i) within-family data orthogonalization, (ii) matrix substitution based on decomposition of a target family-orthogonalized covariance matrix, (iii) covariance-preserving whitening, retaining covariances between unrelated pairs while orthogonalizing family members, and (iv) using family-averaged data to obtain loadings. Except for within-family orthogonalization, our proposed approaches offer similar performance and are superior to the standard approaches. We illustrate the performance via simulation and analysis of the CF dataset.

stat.ME↗

arXiv2016

Non-iterative Joint and Individual Variation Explained

Integrative analysis of disparate data blocks measured on a common set of experimental subjects is one major challenge in modern data analysis. This data structure naturally motivates the simultaneous exploration of the joint and individual variation within each data block resulting in new insights. For instance, there is a strong desire to integrate the multiple genomic data sets in The Cancer Genome Atlas (TCGA) to characterize the common and also the unique aspects of cancer genetics and cell biology for each source. In this paper we introduce Non-iterative Joint and Individual Variation Explained (Non-iterative JIVE), capturing both joint and individual variation within each data block. This is a major improvement over earlier approaches to this challenge in terms of a new conceptual understanding, much better adaption to data heterogeneity and a fast linear algebra computation. Important mathematical contributions are the use of score subspaces as the principal descriptors of variation structure and the use of perturbation theory as the guide for variation segmentation. This leads to a method which is robust against the heterogeneity among data blocks without a need for normalization. An application to TCGA data reveals different behaviors of each type of signal in characterizing tumor subtypes. An application to a mortality data set reveals interesting historical lessons.

stat.ME↗

arXiv2016

"Virus hunting" using radial distance weighted discrimination

Motivated by the challenge of using DNA-seq data to identify viruses in human blood samples, we propose a novel classification algorithm called "Radial Distance Weighted Discrimination" (or Radial DWD). This classifier is designed for binary classification, assuming one class is surrounded by the other class in very diverse radial directions, which is seen to be typical for our virus detection data. This separation of the 2 classes in multiple radial directions naturally motivates the development of Radial DWD. While classical machine learning methods such as the Support Vector Machine and linear Distance Weighted Discrimination can sometimes give reasonable answers for a given data set, their generalizability is severely compromised because of the linear separating boundary. Radial DWD addresses this challenge by using a more appropriate (in this particular case) spherical separating boundary. Simulations show that for appropriate radial contexts, this gives much better generalizability than linear methods, and also much better than conventional kernel based (nonlinear) Support Vector Machines, because the latter methods essentially use much of the information in the data for determining the shape of the separating boundary. The effectiveness of Radial DWD is demonstrated for real virus detection.

stat.AP↗

arXiv2016

A Note on Automatic Data Transformation

Modern data analysis frequently involves variables with highly non-Gaussian marginal distributions. However, commonly used analysis methods are most effective with roughly Gaussian data. This paper introduces an automatic transformation that improves the closeness of distributions to normality. For each variable, a new family of parametrizations of the shifted logarithm transformation is proposed, which is unique in treating the data as real-valued, and in allowing transformation for both left and right skewness within the single family. This also allows an automatic selection of the parameter value (which is crucial for high dimensional data with many variables to transform) by minimizing the Anderson-Darling test statistic of the transformed data. An application to image features extracted from melanoma microscopy slides demonstrate the utility of the proposed transformation in addressing data with excessive skewness, heteroscedasticity and influential observations.

stat.ME↗