Determining how certain properties are related to other properties is fundamental to scientific discovery. As data collection rates accelerate, it is becoming increasingly difficult yet ever more important to determine whether one property of data (e.g., cloud density) is related to another (e.g., grass wetness). Only if two properties are related are further investigations into the geometry of the relationship warranted. While existing approaches can test whether two properties are related, they may require unfeasibly large sample sizes in real data scenarios, and do not address how they are related. Our key insight is that one can adaptively restrict the analysis to the "jointly local" observations---that is, one can estimate the scales with the most informative neighbors for determining the existence and geometry of a relationship. "Multiscale Graph Correlation" (MGC) is a framework that extends global procedures to be multiscale; consequently, MGC tests typically require far fewer samples than existing methods for a wide variety of dependence structures and dimensionalities, while maintaining computational efficiency. Moreover, MGC provides a simple and elegant multiscale characterization of the potentially complex latent geometry underlying the relationship. In several real data applications, MGC uniquely detects the presence and reveals the geometry of the relationships.

Generative adversarial networks (GAN) are a powerful subclass of generative models. Despite a very rich research activity leading to numerous interesting GAN algorithms, it is still very hard to assess which algorithm(s) perform better than others. We conduct a neutral, multi-faceted large-scale empirical study on state-of-the art models and evaluation measures. We find that most models can reach similar scores with enough hyperparameter optimization and random restarts. This suggests that improvements can arise from a higher computational budget and tuning more than fundamental algorithmic changes. To overcome some limitations of the current metrics, we also propose several data sets on which precision and recall can be computed. Our experimental results suggest that future GAN research should be based on more systematic and objective evaluation procedures. Finally, we did not find evidence that any of the tested algorithms consistently outperforms the original one.

The central aim in this paper is to address variable selection questions in nonlinear and nonparametric regression. Motivated by statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel, interpretable, and computationally efficient way to summarize the relative importance of predictor variables. Methodologically, we develop the "RelATive cEntrality" (RATE) measure to prioritize candidate genetic variants that are not just marginally important, but whose associations also stem from significant covarying relationships with other variants in the data. We illustrate RATE through Bayesian Gaussian process regression, but the methodological innovations apply to other nonlinear methods. It is known that nonlinear models often exhibit greater predictive accuracy than linear models, particularly for phenotypes generated by complex genetic architectures. With detailed simulations and an Arabidopsis thaliana QTL mapping study, we show that applying RATE enables an explanation for this improved performance.

Magnetic resonance imaging (MRI) has been proposed as a complimentary method to measure bone quality and assess fracture risk. However, manual segmentation of MR images of bone is time-consuming, limiting the use of MRI measurements in the clinical practice. The purpose of this paper is to present an automatic proximal femur segmentation method that is based on deep convolutional neural networks (CNNs). This study had institutional review board approval and written informed consent was obtained from all subjects. A dataset of volumetric structural MR images of the proximal femur from 86 subject were manually-segmented by an expert. We performed experiments by training two different CNN architectures with multiple number of initial feature maps and layers, and tested their segmentation performance against the gold standard of manual segmentations using fourfold cross-validation. Automatic segmentation of the proximal femur achieved a high dice similarity score of 0.94 0.05 with precision 0.95 0.02, and recall 0.94 0.08 using a CNN architecture based on 3D convolution exceeding the performance of 2D CNNs. The high segmentation accuracy provided by CNNs has the potential to help bring the use of structural MRI measurements of bone quality into clinical practice for management of osteoporosis.

In order to reach human performance on complex visual tasks, artificial systems need to incorporate a significant amount of understanding of the world in terms of macroscopic objects, movements, forces, etc. Inspired by work on intuitive physics in infants, we propose an evaluation framework which diagnoses how much a given system understands about physics by testing whether it can tell apart well matched videos of possible versus impossible events. The test requires systems to compute a physical plausibility score over an entire video. It is free of bias and can test a range of specific physical reasoning skills. We then describe the first release of a benchmark dataset aimed at learning intuitive physics in an unsupervised way, using videos constructed with a game engine. We describe two Deep Neural Network baseline systems trained with a future frame prediction objective and tested on the possible versus impossible discrimination task. The analysis of their results compared to human data gives novel insights in the potentials and limitations of next frame prediction architectures.

Estimating multiple sparse Gaussian Graphical Models (sGGMs) jointly for many related tasks (large $K$) under a high-dimensional (large $p$) situation is an important task. Most previous studies for the joint estimation of multiple sGGMs rely on penalized log-likelihood estimators that involve expensive and difficult non-smooth optimizations. We propose a novel approach, FASJEM for \underline{fa}st and \underline{s}calable \underline{j}oint structure-\underline{e}stimation of \underline{m}ultiple sGGMs at a large scale. As the first study of joint sGGM using the Elementary Estimator framework, our work has three major contributions: (1) We solve FASJEM through an entry-wise manner which is parallelizable. (2) We choose a proximal algorithm to optimize FASJEM. This improves the computational efficiency from $O(Kp^3)$ to $O(Kp^2)$ and reduces the memory requirement from $O(Kp^2)$ to $O(K)$. (3) We theoretically prove that FASJEM achieves a consistent estimation with a convergence rate of $O(\log(Kp)/n_{tot})$. On several synthetic and four real-world datasets, FASJEM shows significant improvements over baselines on accuracy, computational complexity, and memory costs.

Lung cancer is the leading cause of cancer-related death worldwide. Early diagnosis of pulmonary nodules in Computed Tomography (CT) chest scans provides an opportunity for designing effective treatment and making financial and care plans. In this paper, we consider the problem of diagnostic classification between benign and malignant lung nodules in CT images, which aims to learn a direct mapping from 3D images to class labels. To achieve this goal, four two-pathway Convolutional Neural Networks (CNN) are proposed, including a basic 3D CNN, a novel multi-output network, a 3D DenseNet, and an augmented 3D DenseNet with multi-outputs. These four networks are evaluated on the public LIDC-IDRI dataset and outperform most existing methods. In particular, the 3D multi-output DenseNet (MoDenseNet) achieves the state-of-the-art classification accuracy on the task of end-to-end lung nodule diagnosis. In addition, the networks pretrained on the LIDC-IDRI dataset can be further extended to handle smaller datasets using transfer learning. This is demonstrated on our dataset with encouraging prediction accuracy in lung nodule classification.

Ensemble methods -- particularly those based on decision trees -- have recently demonstrated superior performance in a variety of machine learning settings. Specifically, Random Forest (RF) was found to outperform >100 other methods in several manuscripts, and gradient boosting trees have been a crucial component of several recent Kaggle competition victories. Building off these successes and recent advances in sparse learning and random matrix theory, we propose a novel ensemble tree method called "Randomer Forest" (RerF). The key intuition behind RerF is that we can use sparse linear combinations at each decision node rather than just one feature (as in RF) or all of them (as in Rotation Forests). RerF significantly outperforms other methods on a standard benchmark suite containing 105 problems with varying dimension, sample size, and number of classes. Moreover, we provide an implementation that scales as or more efficiently than other available packages. Via a combination of basic principles, theory, and extensive numerical experiments, we demonstrate why, when, and how RerF achieves its performance properties.

The positive-unlabeled (PU) classification is a common scenario in real-world applications such as healthcare, text classification, and bioinformatics, in which we only observe a few samples labeled as "positive" together with a large volume of "unlabeled" samples that may contain both positive and negative samples. Building robust classifier for the PU problem is very challenging, especially for complex data where the negative samples overwhelm and mislabeled samples or corrupted features exist. To address these three issues, we propose a robust learning framework that unifies AUC maximization (a robust metric for biased labels), outlier detection (for excluding wrong labels), and feature selection (for excluding corrupted features). The generalization error bounds are provided for the proposed model that give valuable insight into the theoretical performance of the method and lead to useful practical guidance, e.g., to train a model, we find that the included unlabeled samples are sufficient as long as the sample size is comparable to the number of positive samples in the training process. Empirical comparisons and two real-world applications on surgical site infection (SSI) and EEG seizure detection are also conducted to show the effectiveness of the proposed model.

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 .