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A distribution-free smoothed combination method of biomarkers to improve diagnostic accuracy in multi-category classification

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arXiv 2019年

作者： Maiti, Raju Li, Jialiang Das, Priyam Feng, Lei Hausenloy, Derek Chakraborty, Bibhas Centre for Quantitative Medicine Duke-National University of Singapore Medical School Singapore Department of Statistics and Applied Probability National University of Singapore Singapore Singapore Eye Research Institute Singapore Department of Biostatistics University of Texas MD Anderson Cancer Center United States Department of Psychological Medicine Yong Loo Lin School of Medicine National University of Singapore Singapore Cardiovascular and Metabolic Disorders Program Duke-National University of Singapore Medical School Singapore Department of Biostatistics and Bioinformatics Duke University United States

Results from multiple diagnostic tests are usually combined to improve the overall diagnostic accuracy. For binary classification, maximization of the empirical estimate of the area under the receiver operating characteristic (ROC) curve is widely adopted to produce the optimal linear combination of multiple biomarkers. In the presence of large number of biomarkers, this method proves to be computationally expensive and difficult to implement since it involves maximization of a discontinuous, non-smooth function for which gradient-based methods cannot be used directly. Complexity of this problem increases when the classification problem becomes multi-category. In this article, we develop a linear combination method that maximizes a smooth approximation of the empirical Hypervolume Under Manifolds (HUM) for multi-category outcome. We approximate HUM by replacing the indicator function with the sigmoid function or normal cumulative distribution function (CDF). With the above smooth approximations, efficient gradient-based algorithms can be employed to obtain better solution with less computing time. We show that under some regularity conditions, the proposed method yields consistent estimates of the coefficient parameters. We also derive the asymptotic normality of the coefficient estimates. We conduct extensive simulations to examine our methods. Under different simulation scenarios, the proposed methods are compared with other existing methods and are shown to outperform them in terms of diagnostic accuracy. The proposed method is illustrated using two real medical data sets. Copyright © 2019, The Authors. All rights reserved.

关键词： Biomarkers

Modeling Compositional Regression With Uncorrelated and Correlated Errors: A Bayesian Approach

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Journal of Data Science 2018年第2期16卷 221-249页

作者： Taciana K. O. Shimizu Francisco Louzada Adriano K. Suzuki Ricardo S. Ehlers Inter Program of Graduate Statistics Federal University of São Carlos and University of São Paulo Avenida Trabalhador São-carlense 400 São Carlos São Paulo Brazil Department of Applied Mathematics & Statistics Sciences Institute of Mathematics and Computers ICMC University of São Paulo Avenida Trabalhador São-carlense 400 São Carlos São Paulo Brazil

Compositional data consist of known compositions vectors whose components are positive and defined in the interval (0,1) representing proportions or fractions of a ＂whole＂. The sum of these components must be equal to one. Compositional data is present in different knowledge areas, as in geology, economy, medicine among many others. In this paper, we propose a new statistical tool for volleyball data, i.e., we introduce a Bayesian anal-ysis for compositional regression applying additive log-ratio (ALR) trans- formation and assuming uncorrelated and correlated errors. The Bayesian inference procedure based on Markov Chain Monte Carlo Methods (MCMC). The methodology is applied on an artificial and a real data set of volleyball.

关键词： Compositional data additive log-ratio transformation inference Bayesian correlated errors MCMC

Cosmological tests with the joint lightcurve analysis

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arXiv 2018年

作者： Melia, F. Wei, J.-J. Maier, R.S. Wu, X.-F. Depts. of Physics and Astronomy Applied Math Program University of Arizona AZ85721 United States Purple Mountain Observatory Chinese Academy of Sciences Nanjing210008 China Depts. of Mathematics and Physics Statistics Program University of Arizona AZ85721 United States Purple Mountain Observatory Nanjing210008 China

We examine whether a comparison between wCDM and Rh = ct using merged Type Ia SN catalogs produces results consistent with those based on a single homogeneous sample. Using the Betoule et al. [1] joint lightcurve analysis (JLA) of a combined sample of 613 events from SNLS and SDSS-II, we estimate the parameters of the two models and compare them. We find that the improved statistics can alter the model selection in some cases, but not others. In addition, based on the model fits, we find that there appears to be a lingering systematic offset of ∼ 0.04-0.08 mag between the SNLS and SDSS-II sources, in spite of the cross-calibration in the JLA. Treating wCDM, ΛCDM and Rh = ct as separate models, we find in an unbiased pairwise statistical comparison that the Bayes Information Criterion (BIC) favors the Rh = ct Universe with a likelihood of 82.8% versus 17.2% for wCDM, but the ratio of likelihoods is reversed (16.2% versus 83.8%) when wde = −1 (i.e., ΛCDM) and strongly reversed (1.0% versus 99.0%) if in addition k = 0 (i.e., flat ΛCDM). We point out, however, that the value of k is a measure of the net energy (kinetic plus gravitational) in the Universe and is not constrained theoretically, though some models of inflation would drive k → 0 due to an expansion-enforced dilution. Since we here consider only the basic ΛCDM model, the value of k needs to be measured and, therefore, the pre-assumption of flatness introduces a significant bias into the BIC. Copyright © 2018, The Authors. All rights reserved.

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An Early Warning Approach to Monitor COVID-19 Activity with Multiple Digital Traces in Near Real-Time

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arXiv 2020年

作者： Kogan, Nicole E. Clemente, Leonardo Liautaud, Parker Kaashoek, Justin Link, Nicholas B. Nguyen, Andre T. Lu, Fred S. Huybers, Peter Resch, Bernd Havas, Clemens Petutschnig, Andreas Davis, Jessica Chinazzi, Matteo Mustafa, Backtosch Hanage, William P. Vespignani, Alessandro Santillana, Mauricio Computational Health Informatics Program Boston Children’s Hospital BostonMA United States Department of Epidemiology Harvard T.H. Chan School of Public Health BostonMA United States Department of Earth and Planetary Sciences Harvard University CambridgeMA United States School of Engineering and Applied Sciences Harvard University CambridgeMA United States University of Maryland Baltimore County BaltimoreMD United States Booz Allen Hamilton ColumbiaMD United States Department of Statistics Stanford University StanfordCA United States Department of Geoinformatics - Z GIS University of Salzburg Salzburg Austria Center for Geographic Analysis Harvard University CambridgeMA United States Northeastern University BostonMA United States Department of Pediatrics Harvard Medical School BostonMA United States University Medical Center Hamburg-Eppendorf Hamburg Germany

Non-pharmaceutical interventions (NPIs) have been crucial in curbing COVID-19 in the United States (US). Consequently, relaxing NPIs through a phased re-opening of the US amid still-high levels of COVID-19 susceptibility could lead to new epidemic waves. This calls for a COVID-19 early warning system. Here we evaluate multiple digital data streams as early warning indicators of increasing or decreasing state-level US COVID-19 activity between January and June 2020. We estimate the timing of sharp changes in each data stream using a simple Bayesian model that calculates in near real-time the probability of exponential growth or decay. Analysis of COVID-19-related activity on social network microblogs, Internet searches, point-of-care medical software, and a metapopulation mechanistic model, as well as fever anomalies captured by smart thermometer networks, shows exponential growth roughly 2-3 weeks prior to comparable growth in confirmed COVID-19 cases and 3-4 weeks prior to comparable growth in COVID-19 deaths across the US over the last 6 months. We further observe exponential decay in confirmed cases and deaths 5-6 weeks after implementation of NPIs, as measured by anonymized and aggregated human mobility data from mobile phones. Finally, we propose a combined indicator for exponential growth in multiple data streams that may aid in developing an early warning system for future COVID-19 outbreaks. These efforts represent an initial exploratory framework, and both continued study of the predictive power of digital indicators as well as further development of the statistical approach are needed. Copyright © 2020, The Authors. All rights reserved.

关键词： Search engines

Noise induces continuous and noncontinuous transitions in neuronal interspike intervals range

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arXiv 2020年

作者： Protachevicz, P.R. Santos, M.S. Seifert, E.G. Gabrick, E.C. Borges, F.S. Borges, R.R. Trobia, J. Szezech, J.D. Iarosz, K.C. Caldas, I.L. Antonopoulos, C.G. Xu, Y. Viana, R.L. Batista, A.M. Graduate Program in Science-Physics State University of Ponta Grossa Ponta Grossa84030-900 Institute of Physics University of Saõ Paulo Saõ Paulo05508-900 Brazil Department of Physics State University of Ponta Grossa Ponta Grossa84030-900 Center ForMathematics Computation and Cognition Federal University of ABC Sao Bernardo do Campo09606-045 Department of Mathematics Federal University of Technology Paraná Ponta Grossa84016-210 Department of Mathematics and Statistics State University of Ponta Grossa Ponta Grossa84030-900 Faculdade de Telêmaco Borba FATEB Telemaco Borba84266-010 Brazil Department of Mathematical Sciences University of Essex Wivenhoe ParkCO43SQ United Kingdom Department of Applied Mathematics Northwestern Polytechnical University Xi'an710072 Department of Physics Federal University of Paraná Curitiba82590-300 Brazil

Noise appears in the brain due to various sources, such as ionic channel fluctuations and synaptic events. They affect the activities of the brain and influence neuron action potentials. Stochastic differential equations have been used to model firing patterns of neurons subject to noise. In this work, we consider perturbing noise in the adaptive exponential integrate-and-fire (AEIF) neuron. The AEIF is a two-dimensional model that describes different neuronal firing patterns by varying its parameters. Noise is added in the equation related to the membrane potential. We show that a noise current can induce continuous and noncontinuous transitions in neuronal interspike intervals. Moreover, we show that the noncontinuous transition occurs mainly for parameters close to the border between tonic spiking and burst activities of the neuron without noise. Copyright © 2020, The Authors. All rights reserved.

关键词： Neurons

High temperature structure detection in ferromagnets

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arXiv 2018年

作者： Cao, Yuan Neykov, Matey Liu, Han Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Statistics & Data Science Carnegie Mellon University PittsburghPA United States Department of Electrical Engineering and Computer Science Northwestern University EvanstonIL United States

This paper studies structure detection problems in high temperature ferromagnetic (positive interaction only) Ising models. The goal is to distinguish whether the underlying graph is empty, i.e., the model consists of independent Rademacher variables, versus the alternative that the underlying graph contains a subgraph of a certain structure. We give matching upper and lower minimax bounds under which testing this problem is possible/impossible respectively. Our results reveal that a key quantity called graph arboricity drives the testability of the problem. On the computational front, under a conjecture of the computational hardness of sparse principal component analysis, we prove that, unless the signal is strong enough, there are no polynomial time linear tests on the sample covariance matrix which are capable of testing this problem. Copyright © 2018, The Authors. All rights reserved.

关键词： Ferromagnetism

CEMRACS 2017: numerical probabilistic approach to MFG

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arXiv 2018年

作者： Angiuli, Andrea Graves, Christy V. Li, Houzhi Chassagneux, Jean-François Delarue, François Carmona, René Department of Statistics and Applied Probability University of California Santa Barbara Program in Applied and Computational Mathematics Princeton University Laboratoire de Probabilités Modélisation et Statistiques Université Paris Diderot Laboratoire Jean-Alexandre Dieudonné Université de Nice Sophia-Antipolis Operations Research and Financial Engineering Bendheim Center for Finance Princeton University

This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the potential application of these equations to optimization problems over a large population, say for instance mean field games (MFG) and optimal mean field control problems. Theory for this kind of problems has met with great success since the early works on mean field games by Lasry and Lions, see [27], and by Huang, Caines, and Malhamé, see [24]. Generally speaking, the purpose is to understand the continuum limit of optimizers or of equilibria (say in Nash sense) as the number of underlying players tends to infinity. When approached from the probabilistic viewpoint, solutions to these control problems (or games) can be described by coupled mean field FBSDEs, meaning that the coefficients depend upon the own marginal laws of the solution. In this note, we detail two methods for solving such FBSDEs which we implement and apply to five benchmark problems. The first method uses a tree structure to represent the pathwise laws of the solution, whereas the second method uses a grid discretization to represent the time marginal laws of the solutions. Both are based on a Picard scheme;importantly, we combine each of them with a generic continuation method that permits to extend the time horizon (or equivalently the coupling strength between the two equations) for which the Picard iteration converges. Copyright © 2018, The Authors. All rights reserved.

关键词： Numerical methods

Using spatial characteristics to aid automation of SOM segmentation of functional image data 12

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Using spatial characteristics to aid automation of SOM segme...

12th International Workshop on Self-Organizing Maps and Learning Vector Quantization, Clustering and Data Visualization, WSOM 2017

作者： Grossman, Robert Merényi, Erzsébet O’Driscoll, Patrick Department of Neurosurgery Houston Methodist Neurological Institute HoustonTX77030 United States Department of Statistics and Electrical and Computer Engineering Rice University HoustonTX77005 United States Applied Physics Program Department of Statistics Rice University HoustonTX77005 United States

ISBN: (纸本)9781509066384

We propose a new similarity measure, Combined Connectivity and Spatial Adjacency (CCSA), to be used in hierarchical agglomerative clustering (HAC) for automated segmentation of Self-Organizing Maps (SOMs, Kohonen [1]). The CCSA measure is specifically designed to assist segmentation of large, complex, functional image data by exploiting general spatial characteristics of such data. The proposed CCSA measure is constructed from two strong indicators of cluster structure: the degree of localization of data points in physical space and the degree of connectivity of SOM prototypes (as defined by Tasdemir and Merényi [2]). The new measure is expected to enhance cluster capture in large functional image data cubes such as hyperspectral imagery or fMRI brain images, where many relevant clusters exist with widely varying statistical properties and in complex relationships both in feature space and in physical (image) space. We demonstrate the effectiveness of our approach using the CCSA measure on progressively complex synthetic spatial data and on real fMRI brain data. © 2017 IEEE.

关键词： Self organizing maps

Manifold learning for organizing unstructured sets of process observations

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arXiv 2018年

作者： Dietrich, Felix Kooshkbaghi, Mahdi Bollt, Erik M. Kevrekidis, Ioannis G. Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Department of Electrical and Computer Engineering Clarkson Center for Complex Systems Science Clarkson University PotsdamNY13699-5815 United States

Data mining is routinely used to organize ensembles of short temporal observations so as to reconstruct useful, low-dimensional realizations of an underlying dynamical system. In this paper, we use manifold learning to organize unstructured ensembles of observations ("trials") of a system's response surface. We have no control over where every trial starts;and during each trial operating conditions are varied by turning "agnostic" knobs, which change system parameters in a systematic but unknown way. As one (or more) knobs "turn" we record (possibly partial) observations of the system response. We demonstrate how such partial and disorganized observation ensembles can be integrated into coherent response surfaces whose dimension and parametrization can be systematically recovered in a data-driven fashion. The approach can be justified through the Whitney and Takens embedding theorems, allowing reconstruction of manifolds/attractors through different types of observations. We demonstrate our approach by organizing unstructured observations of response surfaces, including the reconstruction of a cusp bifurcation surface for Hydrogen combustion in a Continuous Stirred Tank Reactor. Finally, we demonstrate how this observation-based reconstruction naturally leads to informative transport maps between input parameter space and output/state variable *** codes 37M20 Copyright © 2018, The Authors. All rights reserved.

关键词： Dynamical systems