RATS: Unsupervised manifold learning using low-distortion alignment of tangent spaces.

With the ubiquity of high-dimensional datasets in various biological fields, identifying low-dimensional topological manifolds within such datasets may reveal principles connecting latent variables to measurable instances in the world. The reliable discovery of such manifold structure in high-dimensional datasets can prove challenging, however, largely due to the introduction of distortion by leading manifold learning methods. The problem is further exacerbated by the lack of consensus on how to evaluate the quality of the recovered manifolds.

Classification logit two-sample testing by neural networks for differentiating near manifold densities.

The recent success of generative adversarial networks and variational learning suggests that training a classification network may work well in addressing the classical two-sample problem, which asks to differentiate two densities given finite samples from each one. Network-based methods have the computational advantage that the algorithm scales to large datasets. This paper considers using the classification logit function, which is provided by a trained classification neural network and evaluated on the testing set split of the two datasets, to compute a two-sample statistic.

A deep network construction that adapts to intrinsic dimensionality beyond the domain.

We study the approximation of two-layer compositions f(x)=g(ϕ(x)) via deep networks with ReLU activation, where ϕ is a geometrically intuitive, dimensionality reducing feature map. We focus on two intuitive and practically relevant choices for ϕ: the projection onto a low-dimensional embedded submanifold and a distance to a collection of low-dimensional sets. We achieve near optimal approximation rates, which depend only on the complexity of the dimensionality reducing map ϕ rather than the ambient dimension.

LDLE: Low Distortion Local Eigenmaps.

We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a data set in lower dimension and registers them to obtain a global embedding. The local views are constructed using the global eigenvectors of the graph Laplacian and are registered using Procrustes analysis. The choice of these eigenvectors may vary across the regions.

Two-sample statistics based on anisotropic kernels.

The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely many multivariate samples. When the distributions are locally low-dimensional, the proposed test can be made more powerful to distinguish certain alternatives by incorporating local covariance matrices and constructing an anisotropic kernel. The kernel matrix is asymmetric; it computes the affinity between [Formula: see text] data points and a set of [Formula: see text] reference points, where [Formula: see text] can be drastically smaller than [Formula: see text].

DeepSurv: personalized treatment recommender system using a Cox proportional hazards deep neural network.

Background: Medical practitioners use survival models to explore and understand the relationships between patients' covariates (e.g. clinical and genetic features) and the effectiveness of various treatment options.

Describing the performance of U.S. hospitals by applying big data analytics.

Public reporting of measures of hospital performance is an important component of quality improvement efforts in many countries. However, it can be challenging to provide an overall characterization of hospital performance because there are many measures of quality. In the United States, the Centers for Medicare and Medicaid Services reports over 100 measures that describe various domains of hospital quality, such as outcomes, the patient experience and whether established processes of care are followed.

Efficient 2D MRI relaxometry using compressed sensing.

Potential applications of 2D relaxation spectrum NMR and MRI to characterize complex water dynamics (e.g., compartmental exchange) in biology and other disciplines have increased in recent years.

Solving 2D Fredholm Integral from Incomplete Measurements Using Compressive Sensing.

We present an algorithm to solve the two-dimensional Fredholm integral of the first kind with tensor product structure from a limited number of measurements, with the goal of using this method to speed up nuclear magnetic resonance spectroscopy. This is done by incorporating compressive sensing-type arguments to fill in missing measurements, using a priori knowledge of the structure of the data. In the first step we recover a compressed data matrix from measurements that form a tight frame, and establish that these measurements satisfy the restricted isometry property.