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. To analyze the approximation and estimation error of the logit function to differentiate near-manifold densities, we introduce a new result of near-manifold integral approximation by neural networks. We then show that the logit function provably differentiates two sub-exponential densities given that the network is sufficiently parametrized, and for on or near manifold densities, the needed network complexity is reduced to only scale with the intrinsic dimensionality. In experiments, the network logit test demonstrates better performance than previous network-based tests using classification accuracy, and also compares favorably to certain kernel maximum mean discrepancy tests on synthetic datasets and hand-written digit datasets.

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. Since ϕ encapsulates all nonlinear features that are material to the function f, this suggests that deep nets are faithful to an intrinsic dimension governed by f rather than the complexity of the domain of f. In particular, the prevalent assumption of approximating functions on low-dimensional manifolds can be significantly relaxed using functions of type f(x)=g(ϕ(x)) with ϕ representing an orthogonal projection onto the same manifold.

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. In contrast to existing techniques, LDLE can embed closed and non-orientable manifolds into their intrinsic dimension by tearing them apart. It also provides gluing instruction on the boundary of the torn embedding to help identify the topology of the original manifold. Our experimental results will show that LDLE largely preserved distances up to a constant scale while other techniques produced higher distortion. We also demonstrate that LDLE produces high quality embeddings even when the data is noisy or sparse.

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]. While the proposed statistic can be viewed as a special class of Reproducing Kernel Hilbert Space MMD, the consistency of the test is proved, under mild assumptions of the kernel, as long as [Formula: see text], and a finite-sample lower bound of the testing power is obtained. Applications to flow cytometry and diffusion MRI datasets are demonstrated, which motivate the proposed approach to compare distributions.

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. Standard survival models like the linear Cox proportional hazards model require extensive feature engineering or prior medical knowledge to model treatment interaction at an individual level. While nonlinear survival methods, such as neural networks and survival forests, can inherently model these high-level interaction terms, they have yet to be shown as effective treatment recommender systems. METHODS: We introduce DeepSurv, a Cox proportional hazards deep neural network and state-of-the-art survival method for modeling interactions between a patient's covariates and treatment effectiveness in order to provide personalized treatment recommendations. RESULTS: We perform a number of experiments training DeepSurv on simulated and real survival data. We demonstrate that DeepSurv performs as well as or better than other state-of-the-art survival models and validate that DeepSurv successfully models increasingly complex relationships between a patient's covariates and their risk of failure. We then show how DeepSurv models the relationship between a patient's features and effectiveness of different treatment options to show how DeepSurv can be used to provide individual treatment recommendations. Finally, we train DeepSurv on real clinical studies to demonstrate how it's personalized treatment recommendations would increase the survival time of a set of patients. CONCLUSIONS: The predictive and modeling capabilities of DeepSurv will enable medical researchers to use deep neural networks as a tool in their exploration, understanding, and prediction of the effects of a patient's characteristics on their risk of failure.

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. Although individual quality measures provide important insight, it is challenging to understand hospital performance as characterized by multiple quality measures. Accordingly, we developed a novel approach for characterizing hospital performance that highlights the similarities and differences between hospitals and identifies common patterns of hospital performance. Specifically, we built a semi-supervised machine learning algorithm and applied it to the publicly-available quality measures for 1,614 U.S. hospitals to graphically and quantitatively characterize hospital performance. In the resulting visualization, the varying density of hospitals demonstrates that there are key clusters of hospitals that share specific performance profiles, while there are other performance profiles that are rare. Several popular hospital rating systems aggregate some of the quality measures included in our study to produce a composite score; however, hospitals that were top-ranked by such systems were scattered across our visualization, indicating that these top-ranked hospitals actually excel in many different ways. Our application of a novel graph analytics method to data describing U.S. hospitals revealed nuanced differences in performance that are obscured in existing hospital rating systems.

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. However, the large amount of data and long MR acquisition times required for conventional 2D MR relaxometry limits its applicability for in vivo preclinical and clinical MRI. We present a new MR pipeline for 2D relaxometry that incorporates compressed sensing (CS) as a means to vastly reduce the amount of 2D relaxation data needed for material and tissue characterization without compromising data quality. Unlike the conventional CS reconstruction in the Fourier space (k-space), the proposed CS algorithm is directly applied onto the Laplace space (the joint 2D relaxation data) without compressing k-space to reduce the amount of data required for 2D relaxation spectra. This framework is validated using synthetic data, with NMR data acquired in a well-characterized urea/water phantom, and on fixed porcine spinal cord tissue. The quality of the CS-reconstructed spectra was comparable to that of the conventional 2D relaxation spectra, as assessed using global correlation, local contrast between peaks, peak amplitude and relaxation parameters, etc. This result brings this important type of contrast closer to being realized in preclinical, clinical, and other applications.

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. Recovery can be done from as few as 10% of the total measurements. In the second and third steps, we solve the zeroth-order regularization minimization problem using the Venkataramanan-Song-Hürlimann algorithm. We demonstrate the performance of this algorithm on simulated data and show that our approach is a realistic approach to speeding up the data acquisition.