Uncertainties in a structure is inevitable, which generally lead to variation in dynamic response predictions. For a complex structure, brute force Monte Carlo simulation for response variation analysis is infeasible since one single run may already be computationally costly. Data driven meta-modeling approaches have thus been explored to facilitate efficient emulation and statistical inference. The performance of a meta-model hinges upon both the quality and quantity of training dataset. In actual practice, however, high-fidelity data acquired from high-dimensional finite element simulation or experiment are generally scarce, which poses significant challenge to meta-model establishment. In this research, we take advantage of the multi-level response prediction opportunity in structural dynamic analysis, i.e., acquiring rapidly a large amount of low-fidelity data from reduced-order modeling, and acquiring accurately a small amount of high-fidelity data from full-scale finite element analysis. Specifically, we formulate a composite neural network fusion approach that can fully utilize the multi-level, heterogeneous datasets obtained. It implicitly identifies the correlation of the low- and high-fidelity datasets, which yields improved accuracy when compared with the state-of-the-art. Comprehensive investigations using frequency response variation characterization as case example are carried out to demonstrate the performance.

Model Stealing (MS) attacks allow an adversary with black-box access to a Machine Learning model to replicate its functionality, compromising the confidentiality of the model. Such attacks train a clone model by using the predictions of the target model for different inputs. The effectiveness of such attacks relies heavily on the availability of data necessary to query the target model. Existing attacks either assume partial access to the dataset of the target model or availability of an alternate dataset with semantic similarities.

This paper proposes MAZE -- a data-free model stealing attack using zeroth-order gradient estimation. In contrast to prior works, MAZE does not require any data and instead creates synthetic data using a generative model. Inspired by recent works in data-free Knowledge Distillation (KD), we train the generative model using a disagreement objective to produce inputs that maximize disagreement between the clone and the target model. However, unlike the white-box setting of KD, where the gradient information is available, training a generator for model stealing requires performing black-box optimization, as it involves accessing the target model under attack. MAZE relies on zeroth-order gradient estimation to perform this optimization and enables a highly accurate MS attack.

Our evaluation with four datasets shows that MAZE provides a normalized clone accuracy in the range of 0.91x to 0.99x, and outperforms even the recent attacks that rely on partial data (JBDA, clone accuracy 0.13x to 0.69x) and surrogate data (KnockoffNets, clone accuracy 0.52x to 0.97x). We also study an extension of MAZE in the partial-data setting and develop MAZE-PD, which generates synthetic data closer to the target distribution. MAZE-PD further improves the clone accuracy (0.97x to 1.0x) and reduces the query required for the attack by 2x-24x.

Effective property prediction methods can help accelerate the search for COVID-19 antivirals either through accurate in-silico screens or by effectively guiding on-going at-scale experimental efforts. However, existing prediction tools have limited ability to accommodate scarce or fragmented training data currently available. In this paper, we introduce a novel approach to learn predictors that can generalize or extrapolate beyond the heterogeneous data. Our method builds on and extends recently proposed invariant risk minimization, adaptively forcing the predictor to avoid nuisance variation. We achieve this by continually exercising and manipulating latent representations of molecules to highlight undesirable variation to the predictor. To test the method we use a combination of three data sources: SARS-CoV-2 antiviral screening data, molecular fragments that bind to SARS-CoV-2 main protease and large screening data for SARS-CoV-1. Our predictor outperforms state-of-the-art transfer learning methods by significant margin. We also report the top 20 predictions of our model on Broad drug repurposing hub.

We present the R package mgm for the estimation of k-order mixed graphical models (MGMs) and mixed vector autoregressive (mVAR) models in high-dimensional data. These are a useful extensions of graphical models for only one variable type, since data sets consisting of mixed types of variables (continuous, count, categorical) are ubiquitous. In addition, we allow to relax the stationarity assumption of both models by introducing time-varying versions of MGMs and mVAR models based on a kernel weighting approach. Time-varying models offer a rich description of temporally evolving systems and allow to identify external influences on the model structure such as the impact of interventions. We provide the background of all implemented methods and provide fully reproducible examples that illustrate how to use the package.

This paper introduces the funData R package as an object-oriented implementation of functional data. It implements a unified framework for dense univariate and multivariate functional data on one- and higher dimensional domains as well as for irregular functional data. The aim of this package is to provide a user-friendly, self-contained core toolbox for functional data, including important functionalities for creating, accessing and modifying functional data objects, that can serve as a basis for other packages. The package further contains a full simulation toolbox, which is a useful feature when implementing and testing new methodological developments. Based on the theory of object-oriented data analysis, it is shown why it is natural to implement functional data in an object-oriented manner. The classes and methods provided by funData are illustrated in many examples using two freely available datasets. The MFPCA package, which implements multivariate functional principal component analysis, is presented as an example for an advanced methodological package that uses the funData package as a basis, including a case study with real data. Both packages are publicly available on GitHub and the Comprehensive R Archive Network.

This paper is devoted to the R package JSM which performs joint statistical modeling of survival and longitudinal data. In biomedical studies it has been increasingly common to collect both baseline and longitudinal covariates along with a possibly censored survival time. Instead of analyzing the survival and longitudinal outcomes separately, joint modeling approaches have attracted substantive attention in the recent literature and have been shown to correct biases from separate modeling approaches and enhance information. Most existing approaches adopt a linear mixed effects model for the longitudinal component and the Cox proportional hazards model for the survival component. We extend the Cox model to a more general class of transformation models for the survival process, where the baseline hazard function is completely unspecified leading to semiparametric survival models. We also offer a non-parametric multiplicative random effects model for the longitudinal process in JSM in addition to the linear mixed effects model. In this paper, we present the joint modeling framework that is implemented in JSM, as well as the standard error estimation methods, and illustrate the package with two real data examples: a liver cirrhosis data and a Mayo Clinic primary biliary cirrhosis data.

Harvested produce crops feed Florida Department of Corrections’ (FDC) more than 87,000 inmates; action saves food costs while reducing COVID-19 related supply chain impacts.

(PRWeb April 20, 2020)

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Surveys provide secure, anonymous feedback from staff at all levels of healthcare organizations

(PRWeb May 06, 2020)

Read the full story at https://www.prweb.com/releases/health_worker_data_alliance_monitoring_emotional_physical_and_occupational_health_of_healthcare_workers_during_covid_19/prweb17101008.htm

Niansheng Tang, Xiaodong Yan, Xingqiu Zhao.

Source: The Annals of Statistics, Volume 48, Number 1, 607--627.

Abstract:
This article considers simultaneous variable selection and parameter estimation as well as hypothesis testing in censored survival models where a parametric likelihood is not available. For the problem, we utilize certain growing dimensional general estimating equations and propose a penalized generalized empirical likelihood, where the general estimating equations are constructed based on the semiparametric efficiency bound of estimation with given moment conditions. The proposed penalized generalized empirical likelihood estimators enjoy the oracle properties, and the estimator of any fixed dimensional vector of nonzero parameters achieves the semiparametric efficiency bound asymptotically. Furthermore, we show that the penalized generalized empirical likelihood ratio test statistic has an asymptotic central chi-square distribution. The conditions of local and restricted global optimality of weighted penalized generalized empirical likelihood estimators are also discussed. We present a two-layer iterative algorithm for efficient implementation, and investigate its convergence property. The performance of the proposed methods is demonstrated by extensive simulation studies, and a real data example is provided for illustration.

Stephen M. S. Lee, Puyudi Yang.

Source: The Annals of Statistics, Volume 48, Number 1, 274--299.

Abstract:
Suppose that a confidence region is desired for a subvector $ heta $ of a multidimensional parameter $xi =( heta ,psi )$, based on an M-estimator $hat{xi }_{n}=(hat{ heta }_{n},hat{psi }_{n})$ calculated from a random sample of size $n$. Under nonstandard conditions $hat{xi }_{n}$ often converges at a nonregular rate $r_{n}$, in which case consistent estimation of the distribution of $r_{n}(hat{ heta }_{n}- heta )$, a pivot commonly chosen for confidence region construction, is most conveniently effected by the $m$ out of $n$ bootstrap. The above choice of pivot has three drawbacks: (i) the shape of the region is either subjectively prescribed or controlled by a computationally intensive depth function; (ii) the region is not transformation equivariant; (iii) $hat{xi }_{n}$ may not be uniquely defined. To resolve the above difficulties, we propose a one-dimensional pivot derived from the criterion function, and prove that its distribution can be consistently estimated by the $m$ out of $n$ bootstrap, or by a modified version of the perturbation bootstrap. This leads to a new method for constructing confidence regions which are transformation equivariant and have shapes driven solely by the criterion function. A subsampling procedure is proposed for selecting $m$ in practice. Empirical performance of the new method is illustrated with examples drawn from different nonstandard M-estimation settings. Extension of our theory to row-wise independent triangular arrays is also explored.

Adityanand Guntuboyina, Donovan Lieu, Sabyasachi Chatterjee, Bodhisattva Sen.

Source: The Annals of Statistics, Volume 48, Number 1, 205--229.

Abstract:
We study trend filtering, a relatively recent method for univariate nonparametric regression. For a given integer $rgeq1$, the $r$th order trend filtering estimator is defined as the minimizer of the sum of squared errors when we constrain (or penalize) the sum of the absolute $r$th order discrete derivatives of the fitted function at the design points. For $r=1$, the estimator reduces to total variation regularization which has received much attention in the statistics and image processing literature. In this paper, we study the performance of the trend filtering estimator for every $rgeq1$, both in the constrained and penalized forms. Our main results show that in the strong sparsity setting when the underlying function is a (discrete) spline with few “knots,” the risk (under the global squared error loss) of the trend filtering estimator (with an appropriate choice of the tuning parameter) achieves the parametric $n^{-1}$-rate, up to a logarithmic (multiplicative) factor. Our results therefore provide support for the use of trend filtering, for every $rgeq1$, in the strong sparsity setting.

Kai Tan, Lei Shi, Zhou Yu.

Source: The Annals of Statistics, Volume 48, Number 1, 64--85.

Abstract:
Sliced inverse regression (SIR) is an innovative and effective method for sufficient dimension reduction and data visualization. Recently, an impressive range of penalized SIR methods has been proposed to estimate the central subspace in a sparse fashion. Nonetheless, few of them considered the sparse sufficient dimension reduction from a decision-theoretic point of view. To address this issue, we in this paper establish the minimax rates of convergence for estimating the sparse SIR directions under various commonly used loss functions in the literature of sufficient dimension reduction. We also discover the possible trade-off between statistical guarantee and computational performance for sparse SIR. We finally propose an adaptive estimation scheme for sparse SIR which is computationally tractable and rate optimal. Numerical studies are carried out to confirm the theoretical properties of our proposed methods.

Zhenhua Lin, Fang Yao.

Source: The Annals of Statistics, Volume 47, Number 6, 3533--3577.

Abstract:
In this work we develop a novel and foundational framework for analyzing general Riemannian functional data, in particular a new development of tensor Hilbert spaces along curves on a manifold. Such spaces enable us to derive Karhunen–Loève expansion for Riemannian random processes. This framework also features an approach to compare objects from different tensor Hilbert spaces, which paves the way for asymptotic analysis in Riemannian functional data analysis. Built upon intrinsic geometric concepts such as vector field, Levi-Civita connection and parallel transport on Riemannian manifolds, the developed framework applies to not only Euclidean submanifolds but also manifolds without a natural ambient space. As applications of this framework, we develop intrinsic Riemannian functional principal component analysis (iRFPCA) and intrinsic Riemannian functional linear regression (iRFLR) that are distinct from their traditional and ambient counterparts. We also provide estimation procedures for iRFPCA and iRFLR, and investigate their asymptotic properties within the intrinsic geometry. Numerical performance is illustrated by simulated and real examples.

Zhigang Bao.

Source: The Annals of Statistics, Volume 47, Number 6, 3504--3532.

Abstract:
In this paper, we study a high-dimensional random matrix model from nonparametric statistics called the Kendall rank correlation matrix, which is a natural multivariate extension of the Kendall rank correlation coefficient. We establish the Tracy–Widom law for its largest eigenvalue. It is the first Tracy–Widom law for a nonparametric random matrix model, and also the first Tracy–Widom law for a high-dimensional U-statistic.

Kyoungjae Lee, Jaeyong Lee, Lizhen Lin.

Source: The Annals of Statistics, Volume 47, Number 6, 3413--3437.

Abstract:
In this paper we study the high-dimensional sparse directed acyclic graph (DAG) models under the empirical sparse Cholesky prior. Among our results, strong model selection consistency or graph selection consistency is obtained under more general conditions than those in the existing literature. Compared to Cao, Khare and Ghosh [ Ann. Statist. (2019) 47 319–348], the required conditions are weakened in terms of the dimensionality, sparsity and lower bound of the nonzero elements in the Cholesky factor. Furthermore, our result does not require the irrepresentable condition, which is necessary for Lasso-type methods. We also derive the posterior convergence rates for precision matrices and Cholesky factors with respect to various matrix norms. The obtained posterior convergence rates are the fastest among those of the existing Bayesian approaches. In particular, we prove that our posterior convergence rates for Cholesky factors are the minimax or at least nearly minimax depending on the relative size of true sparseness for the entire dimension. The simulation study confirms that the proposed method outperforms the competing methods.

Ke Zhu.

Source: The Annals of Statistics, Volume 47, Number 6, 3185--3215.

Abstract:
This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute deviations estimator (LADE) for the model. Second, we develop the random weighting (RW) method to estimate its asymptotic covariance matrix, leading to the implementation of the Wald test. Third, we construct a portmanteau test for model checking, and use the RW method to obtain its critical values. As a special weighted LADE, the feasible adaptive LADE (ALADE) is proposed and proved to have the same efficiency as its infeasible counterpart. The importance of our entire methodology based on the feasible ALADE is illustrated by simulation results and the real data analysis on three U.S. economic data sets.

Xin Bing, Marten H. Wegkamp.

Source: The Annals of Statistics, Volume 47, Number 6, 3157--3184.

Abstract:
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the one proposed in Bunea, She and Wegkamp ( Ann. Statist. 39 (2011) 1282–1309) in that it does not require estimation of the unknown variance of the noise, nor does it depend on a delicate choice of a tuning parameter. We develop an iterative, fully data-driven procedure, that adapts to the optimal signal-to-noise ratio. This procedure finds the true rank in a few steps with overwhelming probability. At each step, our estimate increases, while at the same time it does not exceed the true rank. Our finite sample results hold for any sample size and any dimension, even when the number of responses and of covariates grow much faster than the number of observations. We perform an extensive simulation study that confirms our theoretical findings. The new method performs better and is more stable than the procedure of Bunea, She and Wegkamp ( Ann. Statist. 39 (2011) 1282–1309) in both low- and high-dimensional settings.

Heng Lian, Kaifeng Zhao, Shaogao Lv.

Source: The Annals of Statistics, Volume 47, Number 5, 2922--2949.

Abstract:
In this paper, we consider the local asymptotics of the nonparametric function in a partially linear model, within the framework of the divide-and-conquer estimation. Unlike the fixed-dimensional setting in which the parametric part does not affect the nonparametric part, the high-dimensional setting makes the issue more complicated. In particular, when a sparsity-inducing penalty such as lasso is used to make the estimation of the linear part feasible, the bias introduced will propagate to the nonparametric part. We propose a novel approach for estimation of the nonparametric function and establish the local asymptotics of the estimator. The result is useful for massive data with possibly different linear coefficients in each subpopulation but common nonparametric function. Some numerical illustrations are also presented.

Zhiqiang Tan, Cun-Hui Zhang.

Source: The Annals of Statistics, Volume 47, Number 5, 2567--2600.

Abstract:
Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive regression where functional semi-norms are used to induce smoothness of component functions and the empirical $L_{2}$ norm is used to induce sparsity. The functional semi-norms can be of Sobolev or bounded variation types and are allowed to be different amongst individual component functions. We establish oracle inequalities for the predictive performance of such methods under three simple technical conditions: a sub-Gaussian condition on the noise, a compatibility condition on the design and the functional classes under consideration and an entropy condition on the functional classes. For random designs, the sample compatibility condition can be replaced by its population version under an additional condition to ensure suitable convergence of empirical norms. In homogeneous settings where the complexities of the component functions are of the same order, our results provide a spectrum of minimax convergence rates, from the so-called slow rate without requiring the compatibility condition to the fast rate under the hard sparsity or certain $L_{q}$ sparsity to allow many small components in the true regression function. These results significantly broaden and sharpen existing ones in the literature.

Stefan Richter, Rainer Dahlhaus.

Source: The Annals of Statistics, Volume 47, Number 4, 2145--2173.

Abstract:
We propose an adaptive bandwidth selector via cross validation for local M-estimators in locally stationary processes. We prove asymptotic optimality of the procedure under mild conditions on the underlying parameter curves. The results are applicable to a wide range of locally stationary processes such linear and nonlinear processes. A simulation study shows that the method works fairly well also in misspecified situations.

Data about data. In common usage as a generic term, metadata stores data about the structure, context and meaning of raw data, and computers use it to help organize and interpret data, turning it into meaningful information. The WorldWide Web has driven usage of metadata to new levels, as the tags used in HTML and XML are a form of metadata, although the meaning they convey is often limited because the metadata means different things to different people.

A large store of data for analysis. Organizations use data warehouses (and smaller 'data marts') to help them analyze historic transaction data to detect useful patterns and trends. First of all the data is transferred into the data warehouse using a process called extracting, transforming and loading (ETL). Then it is organized and stored in the data warehouse in ways that optimize it for high-performance analysis. The transfer to a separate data warehouse system, which is usually performed as a regular batch job every night or at some other interval, insulates the live transaction systems from any side-effects of the analysis, but at the cost of not having the very latest data included in the analysis.

Boyu Ren, Sergio Bacallado, Stefano Favaro, Tommi Vatanen, Curtis Huttenhower, Lorenzo Trippa.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 494--517.

Abstract:
Detecting associations between microbial compositions and sample characteristics is one of the most important tasks in microbiome studies. Most of the existing methods apply univariate models to single microbial species separately, with adjustments for multiple hypothesis testing. We propose a Bayesian analysis for a generalized mixed effects linear model tailored to this application. The marginal prior on each microbial composition is a Dirichlet process, and dependence across compositions is induced through a linear combination of individual covariates, such as disease biomarkers or the subject’s age, and latent factors. The latent factors capture residual variability and their dimensionality is learned from the data in a fully Bayesian procedure. The proposed model is tested in data analyses and simulation studies with zero-inflated compositions. In these settings and within each sample, a large proportion of counts per microbial species are equal to zero. In our Bayesian model a priori the probability of compositions with absent microbial species is strictly positive. We propose an efficient algorithm to sample from the posterior and visualizations of model parameters which reveal associations between covariates and microbial compositions. We evaluate the proposed method in simulation studies, and then analyze a microbiome dataset for infants with type 1 diabetes which contains a large proportion of zeros in the sample-specific microbial compositions.

Yen-Chi Chen, Adrian Dobra.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 409--432.

Abstract:
Activity spaces are fundamental to the assessment of individuals’ dynamic exposure to social and environmental risk factors associated with multiple spatial contexts that are visited during activities of daily living. In this paper we survey existing approaches for measuring the geometry, size and structure of activity spaces, based on GPS data, and explain their limitations. We propose addressing these shortcomings through a nonparametric approach called density ranking and also through three summary curves: the mass-volume curve, the Betti number curve and the persistence curve. We introduce a novel mixture model for human activity spaces and study its asymptotic properties. We prove that the kernel density estimator, which at the present time, is one of the most widespread methods for measuring activity spaces, is not a stable estimator of their structure. We illustrate the practical value of our methods with a simulation study and with a recently collected GPS dataset that comprises the locations visited by 10 individuals over a six months period.

Kerstin Spitzer, Marta Pelizzola, Andreas Futschik.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 202--220.

Abstract:
Evolve and resequence studies provide a popular approach to simulate evolution in the lab and explore its genetic basis. In this context, Pearson’s chi-square test, Fisher’s exact test as well as the Cochran–Mantel–Haenszel test are commonly used to infer genomic positions affected by selection from temporal changes in allele frequency. However, the null model associated with these tests does not match the null hypothesis of actual interest. Indeed, due to genetic drift and possibly other additional noise components such as pool sequencing, the null variance in the data can be substantially larger than accounted for by these common test statistics. This leads to $p$-values that are systematically too small and, therefore, a huge number of false positive results. Even, if the ranking rather than the actual $p$-values is of interest, a naive application of the mentioned tests will give misleading results, as the amount of overdispersion varies from locus to locus. We therefore propose adjusted statistics that take the overdispersion into account while keeping the formulas simple. This is particularly useful in genome-wide applications, where millions of SNPs can be handled with little computational effort. We then apply the adapted test statistics to real data from Drosophila and investigate how information from intermediate generations can be included when available. We also discuss further applications such as genome-wide association studies based on pool sequencing data and tests for local adaptation.

Arnab Chakraborty, Soumendra Nath Lahiri, Alyson Wilson.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 116--142.

Abstract:
Spatial prediction of weather elements like temperature, precipitation, and barometric pressure are generally based on satellite imagery or data collected at ground stations. None of these data provide information at a more granular or “hyperlocal” resolution. On the other hand, crowdsourced weather data, which are captured by sensors installed on mobile devices and gathered by weather-related mobile apps like WeatherSignal and AccuWeather, can serve as potential data sources for analyzing environmental processes at a hyperlocal resolution. However, due to the low quality of the sensors and the nonlaboratory environment, the quality of the observations in crowdsourced data is compromised. This paper describes methods to improve hyperlocal spatial prediction using this varying-quality, noisy crowdsourced information. We introduce a reliability metric, namely Veracity Score (VS), to assess the quality of the crowdsourced observations using a coarser, but high-quality, reference data. A VS-based methodology to analyze noisy spatial data is proposed and evaluated through extensive simulations. The merits of the proposed approach are illustrated through case studies analyzing crowdsourced daily average ambient temperature readings for one day in the contiguous United States.

Bryan D. Martin, Daniela Witten, Amy D. Willis.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 94--115.

Abstract:
Using a sample from a population to estimate the proportion of the population with a certain category label is a broadly important problem. In the context of microbiome studies, this problem arises when researchers wish to use a sample from a population of microbes to estimate the population proportion of a particular taxon, known as the taxon’s relative abundance . In this paper, we propose a beta-binomial model for this task. Like existing models, our model allows for a taxon’s relative abundance to be associated with covariates of interest. However, unlike existing models, our proposal also allows for the overdispersion in the taxon’s counts to be associated with covariates of interest. We exploit this model in order to propose tests not only for differential relative abundance, but also for differential variability. The latter is particularly valuable in light of speculation that dysbiosis , the perturbation from a normal microbiome that can occur in certain disease conditions, may manifest as a loss of stability, or increase in variability, of the counts associated with each taxon. We demonstrate the performance of our proposed model using a simulation study and an application to soil microbial data.

Liberty Vittert, Adrian W. Bowman, Stanislav Katina.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2539--2563.

Abstract:
One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Stereophotogrammetry and laser scanning are two widely available sources of this kind of data. A standardised surface representation is required to provide a meaningful correspondence across different images as a basis for statistical analysis. Point locations with anatomical definitions, referred to as landmarks, have been the traditional approach. Landmarks can also be taken as the starting point for more general surface representations, often using templates which are warped on to an observed surface by matching landmark positions and subsequent local adjustment of the surface. The aim of the present paper is to provide a new approach which places anatomical curves at the heart of the surface representation and its analysis. Curves provide intermediate structures which capture the principal features of the manifold (surface) of interest through its ridges and valleys. As landmarks are often available these are used as anchoring points, but surface curvature information is the principal guide in estimating the curve locations. The surface patches between these curves are relatively flat and can be represented in a standardised manner by appropriate surface transects to give a complete surface model. This new approach does not require the use of a template, reference sample or any external information to guide the method and, when compared with a surface based approach, the estimation of curves is shown to have improved performance. In addition, examples involving applications to mussel shells and human faces show that the analysis of curve information can deliver more targeted and effective insight than the use of full surface information.

Gianluca Mastrantonio, Clara Grazian, Sara Mancinelli, Enrico Bibbona.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2483--2508.

Abstract:
Improved communication systems, shrinking battery sizes and the price drop of tracking devices have led to an increasing availability of trajectory tracking data. These data are often analyzed to understand animal behavior. In this work, we propose a new model for interpreting the animal movent as a mixture of characteristic patterns, that we interpret as different behaviors. The probability that the animal is behaving according to a specific pattern, at each time instant, is nonparametrically estimated using the Logistic-Gaussian process. Owing to a new formalization and the way we specify the coregionalization matrix of the associated multivariate Gaussian process, our model is invariant with respect to the choice of the reference element and of the ordering of the probability vector components. We fit the model under a Bayesian framework, and show that the Markov chain Monte Carlo algorithm we propose is straightforward to implement. We perform a simulation study with the aim of showing the ability of the estimation procedure to retrieve the model parameters. We also test the performance of the information criterion we used to select the number of behaviors. The model is then applied to a real dataset where a wolf has been observed before and after procreation. The results are easy to interpret, and clear differences emerge in the two phases.

John R. Tipton, Mevin B. Hooten, Connor Nolan, Robert K. Booth, Jason McLachlan.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2363--2388.

Abstract:
Multivariate compositional count data arise in many applications including ecology, microbiology, genetics and paleoclimate. A frequent question in the analysis of multivariate compositional count data is what underlying values of a covariate(s) give rise to the observed composition. Learning the relationship between covariates and the compositional count allows for inverse prediction of unobserved covariates given compositional count observations. Gaussian processes provide a flexible framework for modeling functional responses with respect to a covariate without assuming a functional form. Many scientific disciplines use Gaussian process approximations to improve prediction and make inference on latent processes and parameters. When prediction is desired on unobserved covariates given realizations of the response variable, this is called inverse prediction. Because inverse prediction is often mathematically and computationally challenging, predicting unobserved covariates often requires fitting models that are different from the hypothesized generative model. We present a novel computational framework that allows for efficient inverse prediction using a Gaussian process approximation to generative models. Our framework enables scientific learning about how the latent processes co-vary with respect to covariates while simultaneously providing predictions of missing covariates. The proposed framework is capable of efficiently exploring the high dimensional, multi-modal latent spaces that arise in the inverse problem. To demonstrate flexibility, we apply our method in a generalized linear model framework to predict latent climate states given multivariate count data. Based on cross-validation, our model has predictive skill competitive with current methods while simultaneously providing formal, statistical inference on the underlying community dynamics of the biological system previously not available.

Ningshan Zhang, Kyle Schmaus, Patrick O. Perry.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2260--2288.

Abstract:
We consider a particular instance of a common problem in recommender systems, using a database of book reviews to inform user-targeted recommendations. In our dataset, books are categorized into genres and subgenres. To exploit this nested taxonomy, we use a hierarchical model that enables information pooling across across similar items at many levels within the genre hierarchy. The main challenge in deploying this model is computational. The data sizes are large and fitting the model at scale using off-the-shelf maximum likelihood procedures is prohibitive. To get around this computational bottleneck, we extend a moment-based fitting procedure proposed for fitting single-level hierarchical models to the general case of arbitrarily deep hierarchies. This extension is an order of magnitude faster than standard maximum likelihood procedures. The fitting method can be deployed beyond recommender systems to general contexts with deeply nested hierarchical generalized linear mixed models.

Ian L. Dryden, Kwang-Rae Kim, Charles A. Laughton, Huiling Le.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2213--2234.

Abstract:
Molecular dynamics simulations produce huge datasets of temporal sequences of molecules. It is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such as principal components analysis (PCA) can be problematic as the data may lie far from in a flat manifold. Principal nested spheres gives a fundamentally different decomposition of data from the usual Euclidean subspace based PCA [ Biometrika 99 (2012) 551–568]. Subspaces of successively lower dimension are fitted to the data in a backwards manner with the aim of retaining signal and dispensing with noise at each stage. We adapt the methodology to 3D subshape spaces and provide some practical fitting algorithms. The methodology is applied to cluster analysis of peptides, where different states of the molecules can be identified. Also, the temporal transitions between cluster states are explored.

Jose Ameijeiras-Alonso, Akli Benali, Rosa M. Crujeiras, Alberto Rodríguez-Casal, José M. C. Pereira.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2120--2139.

Abstract:
Understanding the role of vegetation fires in the Earth system is an important environmental problem. Although fire occurrence is influenced by natural factors, human activity related to land use and management has altered the temporal patterns of fire in several regions of the world. Hence, for a better insight into fires regimes it is of special interest to analyze where human activity has altered fire seasonality. For doing so, multimodality tests are a useful tool for determining the number of annual fire peaks. The periodicity of fires and their complex distributional features motivate the use of nonparametric circular statistics. The unsatisfactory performance of previous circular nonparametric proposals for testing multimodality justifies the introduction of a new approach, considering an adapted version of the excess mass statistic, jointly with a bootstrap calibration algorithm. A systematic application of the test on the Russia–Kazakhstan area is presented in order to determine how many fire peaks can be identified in this region. A False Discovery Rate correction, accounting for the spatial dependence of the data, is also required.

Hannah Worthington, Rachel McCrea, Ruth King, Richard Griffiths.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2043--2064.

Abstract:
Capture-recapture studies often involve collecting data on numerous capture occasions over a relatively short period of time. For many study species this process is repeated, for example, annually, resulting in capture information spanning multiple sampling periods. To account for the different temporal scales, the robust design class of models have traditionally been applied providing a framework in which to analyse all of the available capture data in a single likelihood expression. However, these models typically require strong constraints, either the assumption of closure within a sampling period (the closed robust design) or conditioning on the number of individuals captured within a sampling period (the open robust design). For real datasets these assumptions may not be appropriate. We develop a general modelling structure that requires neither assumption by explicitly modelling the movement of individuals into the population both within and between the sampling periods, which in turn permits the estimation of abundance within a single consistent framework. The flexibility of the novel model structure is further demonstrated by including the computationally challenging case of multi-state data where there is individual time-varying discrete covariate information. We derive an efficient likelihood expression for the new multi-state multi-period stopover model using the hidden Markov model framework. We demonstrate the significant improvement in parameter estimation using our new modelling approach in terms of both the multi-period and multi-state components through both a simulation study and a real dataset relating to the protected species of great crested newts, Triturus cristatus .

Ye Zhang, Zhigang Yao, Patrik Forssén, Torgny Fornstedt.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2011--2042.

Abstract:
The means to obtain the rate constants of a chemical reaction is a fundamental open problem in both science and the industry. Traditional techniques for finding rate constants require either chemical modifications of the reactants or indirect measurements. The rate constant map method is a modern technique to study binding equilibrium and kinetics in chemical reactions. Finding a rate constant map from biosensor data is an ill-posed inverse problem that is usually solved by regularization. In this work, rather than finding a deterministic regularized rate constant map that does not provide uncertainty quantification of the solution, we develop an adaptive variational Bayesian approach to estimate the distribution of the rate constant map, from which some intrinsic properties of a chemical reaction can be explored, including information about rate constants. Our new approach is more realistic than the existing approaches used for biosensors and allows us to estimate the dynamics of the interactions, which are usually hidden in a deterministic approximate solution. We verify the performance of the new proposed method by numerical simulations, and compare it with the Markov chain Monte Carlo algorithm. The results illustrate that the variational method can reliably capture the posterior distribution in a computationally efficient way. Finally, the developed method is also tested on the real biosensor data (parathyroid hormone), where we provide two novel analysis tools—the thresholding contour map and the high order moment map—to estimate the number of interactions as well as their rate constants.

Youyi Zhang, Jeffrey S. Morris, Shivali Narang Aerry, Arvind U. K. Rao, Veerabhadran Baladandayuthapani.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1957--1988.

Abstract:
Technological innovations have produced large multi-modal datasets that include imaging and multi-platform genomics data. Integrative analyses of such data have the potential to reveal important biological and clinical insights into complex diseases like cancer. In this paper, we present Bayesian approaches for integrative analysis of radiological imaging and multi-platform genomic data, where-in our goals are to simultaneously identify genomic and radiomic, that is, radiology-based imaging markers, along with the latent associations between these two modalities, and to detect the overall prognostic relevance of the combined markers. For this task, we propose Radio-iBAG: Radiomics-based Integrative Bayesian Analysis of Multiplatform Genomic Data , a multi-scale Bayesian hierarchical model that involves several innovative strategies: it incorporates integrative analysis of multi-platform genomic data sets to capture fundamental biological relationships; explores the associations between radiomic markers accompanying genomic information with clinical outcomes; and detects genomic and radiomic markers associated with clinical prognosis. We also introduce the use of sparse Principal Component Analysis (sPCA) to extract a sparse set of approximately orthogonal meta-features each containing information from a set of related individual radiomic features, reducing dimensionality and combining like features. Our methods are motivated by and applied to The Cancer Genome Atlas glioblastoma multiforme data set, where-in we integrate magnetic resonance imaging-based biomarkers along with genomic, epigenomic and transcriptomic data. Our model identifies important magnetic resonance imaging features and the associated genomic platforms that are related with patient survival times.

Yiyi Liu, Joshua L. Warren, Hongyu Zhao.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1733--1752.

Abstract:
Understanding the heterogeneity of cells is an important biological question. The development of single-cell RNA-sequencing (scRNA-seq) technology provides high resolution data for such inquiry. A key challenge in scRNA-seq analysis is the high variability of measured RNA expression levels and frequent dropouts (missing values) due to limited input RNA compared to bulk RNA-seq measurement. Existing clustering methods do not perform well for these noisy and zero-inflated scRNA-seq data. In this manuscript we propose a Bayesian hierarchical model, called BasClu, to appropriately characterize important features of scRNA-seq data in order to more accurately cluster cells. We demonstrate the effectiveness of our method with extensive simulation studies and applications to three real scRNA-seq datasets.