Pac-12 Networks' Ashley Adamson catches up with Oregon's "Big 3" of Sabrina Ionescu, Ruthy Hebard and Satou Sabally to hear how they're adjusting to the new world without sports while still preparing for the WNBA Draft on April 17. They also share how they're staying hungry for basketball during the hiatus.

South Carolina coach Dawn Staley believes her top-ranked Gamecocks are the women's basketball national champions, even without an NCAA Tournament trophy to put in their display case due to the pandemic-shortened season. The NCAA decided against officially crowning champions after its signature tournaments were called off due to the coronavirus pandemic that has sent much of the world into lock down. Staley spoke from her home where she's spent the past month managing her program and ensuring her players don't linger too much on what they missed.

Mississippi State hired former Old Dominion women’s basketball coach Nikki McCray-Penson to replace Vic Schaefer as the Bulldogs’ head coach. Athletic director John Cohen called McCray-Penson “a proven winner who will lead one of the best programs in the nation” on the department’s website. McCray-Penson, a former Tennessee star and Women’s Basketball Hall of Famer, said it’s been a dream to coach in the Southeastern Conference and she’s “grateful and blessed for this incredible honor and opportunity.”

Eunji Lim.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 2053--2097.

Abstract:
We study the asymptotic behavior of the least squares estimators when the model is possibly misspecified. We consider the setting where we wish to estimate an unknown function $f_{*}:(0,1)^{d} ightarrow mathbb{R}$ from observations $(X,Y),(X_{1},Y_{1}),cdots ,(X_{n},Y_{n})$; our estimator $hat{g}_{n}$ is the minimizer of $sum _{i=1}^{n}(Y_{i}-g(X_{i}))^{2}/n$ over $gin mathcal{G}$ for some set of functions $mathcal{G}$. We provide sufficient conditions on the metric entropy of $mathcal{G}$, under which $hat{g}_{n}$ converges to $g_{*}$ as $n ightarrow infty $, where $g_{*}$ is the minimizer of $|g-f_{*}| riangleq mathbb{E}(g(X)-f_{*}(X))^{2}$ over $gin mathcal{G}$. As corollaries of our theorem, we establish $|hat{g}_{n}-g_{*}| ightarrow 0$ as $n ightarrow infty $ when $mathcal{G}$ is the set of monotone functions or the set of convex functions. We also make a connection between the convergence rate of $|hat{g}_{n}-g_{*}|$ and the metric entropy of $mathcal{G}$. As special cases of our finding, we compute the convergence rate of $|hat{g}_{n}-g_{*}|^{2}$ when $mathcal{G}$ is the set of bounded monotone functions or the set of bounded convex functions.

Gwenaëlle Castellan, Anthony Cousien, Viet Chi Tran.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 50--81.

Abstract:
Global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the Sobol indices of order 1 which are commonly-used indicators based on a decomposition of the output’s variance. In a deterministic framework, when the same inputs always give the same outputs, these indices are usually estimated by replicated simulations of the model. In a stochastic framework, when the response given a set of input parameters is not unique due to randomness in the model, metamodels are often used to approximate the mean and dispersion of the response by deterministic functions. We propose a new non-parametric estimator without the need of defining a metamodel to estimate the Sobol indices of order 1. The estimator is based on warped wavelets and is adaptive in the regularity of the model. The convergence of the mean square error to zero, when the number of simulations of the model tend to infinity, is computed and an elbow effect is shown, depending on the regularity of the model. Applications in Epidemiology are carried to illustrate the use of non-parametric estimators.

Alexandre Mösching, Lutz Dümbgen.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 24--49.

Abstract:
We consider bivariate observations $(X_{1},Y_{1}),ldots,(X_{n},Y_{n})$ such that, conditional on the $X_{i}$, the $Y_{i}$ are independent random variables. Precisely, the conditional distribution function of $Y_{i}$ equals $F_{X_{i}}$, where $(F_{x})_{x}$ is an unknown family of distribution functions. Under the sole assumption that $xmapsto F_{x}$ is isotonic with respect to stochastic order, one can estimate $(F_{x})_{x}$ in two ways: (i) For any fixed $y$ one estimates the antitonic function $xmapsto F_{x}(y)$ via nonparametric monotone least squares, replacing the responses $Y_{i}$ with the indicators $1_{[Y_{i}le y]}$. (ii) For any fixed $eta in (0,1)$ one estimates the isotonic quantile function $xmapsto F_{x}^{-1}(eta)$ via a nonparametric version of regression quantiles. We show that these two approaches are closely related, with (i) being more flexible than (ii). Then, under mild regularity conditions, we establish rates of convergence for the resulting estimators $hat{F}_{x}(y)$ and $hat{F}_{x}^{-1}(eta)$, uniformly over $(x,y)$ and $(x,eta)$ in certain rectangles as well as uniformly in $y$ or $eta$ for a fixed $x$.

Aurélie Fischer, Dominique Picard.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1648--1689.

Abstract:
In this paper, we consider the estimation of a change-point for possibly high-dimensional data in a Gaussian model, using a maximum likelihood method. We are interested in how dimension reduction can affect the performance of the method. We provide an estimator of the change-point that has a minimax rate of convergence, up to a logarithmic factor. The minimax rate is in fact composed of a fast rate —dimension-invariant— and a slow rate —increasing with the dimension. Moreover, it is proved that considering the case of sparse data, with a Sobolev regularity, there is a bound on the separation of the regimes above which there exists an optimal choice of dimension reduction, leading to the fast rate of estimation. We propose an adaptive dimension reduction procedure based on Lepski’s method and show that the resulting estimator attains the fast rate of convergence. Our results are then illustrated by a simulation study. In particular, practical strategies are suggested to perform dimension reduction.

Karl Ewald, Ulrike Schneider.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 944--969.

Abstract:
We derive expressions for the finite-sample distribution of the Lasso estimator in the context of a linear regression model in low as well as in high dimensions by exploiting the structure of the optimization problem defining the estimator. In low dimensions, we assume full rank of the regressor matrix and present expressions for the cumulative distribution function as well as the densities of the absolutely continuous parts of the estimator. Our results are presented for the case of normally distributed errors, but do not hinge on this assumption and can easily be generalized. Additionally, we establish an explicit formula for the correspondence between the Lasso and the least-squares estimator. We derive analogous results for the distribution in less explicit form in high dimensions where we make no assumptions on the regressor matrix at all. In this setting, we also investigate the model selection properties of the Lasso and show that possibly only a subset of models might be selected by the estimator, completely independently of the observed response vector. Finally, we present a condition for uniqueness of the estimator that is necessary as well as sufficient.

Ran Dai, Hyebin Song, Rina Foygel Barber, Garvesh Raskutti.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 801--834.

Abstract:
We study the bias of the isotonic regression estimator. While there is extensive work characterizing the mean squared error of the isotonic regression estimator, relatively little is known about the bias. In this paper, we provide a sharp characterization, proving that the bias scales as $O(n^{-eta /3})$ up to log factors, where $1leq eta leq 2$ is the exponent corresponding to Hölder smoothness of the underlying mean. Importantly, this result only requires a strictly monotone mean and that the noise distribution has subexponential tails, without relying on symmetric noise or other restrictive assumptions.

The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error controlled under some user-specified level $alpha$. This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people have clear priorities among the two error types. Recently, Tong, Feng, and Li (2018) proposed a nonparametric umbrella algorithm that adapts all scoring-type classification methods (e.g., logistic regression, support vector machines, random forest) to respect the given type I error (i.e., conditional probability of classifying a class $0$ observation as class $1$ under the 0-1 coding) upper bound $alpha$ with high probability, without specific distributional assumptions on the features and the responses. Universal the umbrella algorithm is, it demands an explicit minimum sample size requirement on class $0$, which is often the more scarce class, such as in rare disease diagnosis applications. In this work, we employ the parametric linear discriminant analysis (LDA) model and propose a new parametric thresholding algorithm, which does not need the minimum sample size requirements on class $0$ observations and thus is suitable for small sample applications such as rare disease diagnosis. Leveraging both the existing nonparametric and the newly proposed parametric thresholding rules, we propose four LDA-based NP classifiers, for both low- and high-dimensional settings. On the theoretical front, we prove NP oracle inequalities for one proposed classifier, where the rate for excess type II error benefits from the explicit parametric model assumption. Furthermore, as NP classifiers involve a sample splitting step of class $0$ observations, we construct a new adaptive sample splitting scheme that can be applied universally to NP classifiers, and this adaptive strategy reduces the type II error of these classifiers. The proposed NP classifiers are implemented in the R package nproc.

Tensor Train decomposition is used across many branches of machine learning. We present T3F—a library for Tensor Train decomposition based on TensorFlow. T3F supports GPU execution, batch processing, automatic differentiation, and versatile functionality for the Riemannian optimization framework, which takes into account the underlying manifold structure to construct efficient optimization methods. The library makes it easier to implement machine learning papers that rely on the Tensor Train decomposition. T3F includes documentation, examples and 94% test coverage.

Dual first-order methods are essential techniques for large-scale constrained convex optimization. However, when recovering the primal solutions, we need $T(epsilon^{-2})$ iterations to achieve an $epsilon$-optimal primal solution when we apply an algorithm to the non-strongly convex dual problem with $T(epsilon^{-1})$ iterations to achieve an $epsilon$-optimal dual solution, where $T(x)$ can be $x$ or $sqrt{x}$. In this paper, we prove that the iteration complexity of the primal solutions and dual solutions have the same $Oleft(frac{1}{sqrt{epsilon}} ight)$ order of magnitude for the accelerated randomized dual coordinate ascent. When the dual function further satisfies the quadratic functional growth condition, by restarting the algorithm at any period, we establish the linear iteration complexity for both the primal solutions and dual solutions even if the condition number is unknown. When applied to the regularized empirical risk minimization problem, we prove the iteration complexity of $Oleft(nlog n+sqrt{frac{n}{epsilon}} ight)$ in both primal space and dual space, where $n$ is the number of samples. Our result takes out the $left(log frac{1}{epsilon} ight)$ factor compared with the methods based on smoothing/regularization or Catalyst reduction. As far as we know, this is the first time that the optimal $Oleft(sqrt{frac{n}{epsilon}} ight)$ iteration complexity in the primal space is established for the dual coordinate ascent based stochastic algorithms. We also establish the accelerated linear complexity for some problems with nonsmooth loss, e.g., the least absolute deviation and SVM.

A new strategy for probabilistic graphical modeling is developed that draws parallels to community detection analysis. The method jointly estimates an undirected graph and homogeneous communities of nodes. The structure of the communities is taken into account when estimating the graph and at the same time, the structure of the graph is accounted for when estimating communities of nodes. The procedure uses a joint group graphical lasso approach with community detection-based grouping, such that some groups of edges co-occur in the estimated graph. The grouping structure is unknown and is estimated based on community detection algorithms. Theoretical derivations regarding graph convergence and sparsistency, as well as accuracy of community recovery are included, while the method's empirical performance is illustrated in an fMRI context, as well as with simulated examples.

We consider the problem of clustering and completing a set of tensors with missing data that are drawn from a union of low-rank tensor spaces. In the clustering problem, given a partially sampled tensor data that is composed of a number of subtensors, each chosen from one of a certain number of unknown tensor spaces, we need to group the subtensors that belong to the same tensor space. We provide a geometrical analysis on the sampling pattern and subsequently derive the sampling rate that guarantees the correct clustering under some assumptions with high probability. Moreover, we investigate the fundamental conditions for finite/unique completability for the union of tensor spaces completion problem. Both deterministic and probabilistic conditions on the sampling pattern to ensure finite/unique completability are obtained. For both the clustering and completion problems, our tensor analysis provides significantly better bound than the bound given by the matrix analysis applied to any unfolding of the tensor data.

Raj Kamal Maurya, Yogesh Mani Tripathi.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 345--369.

Abstract:
We consider estimation of the multicomponent stress-strength reliability under progressive Type II censoring under the assumption that stress and strength variables follow Burr XII distributions with a common shape parameter. Maximum likelihood estimates of the reliability are obtained along with asymptotic intervals when common shape parameter may be known or unknown. Bayes estimates are also derived under the squared error loss function using different approximation methods. Further, we obtain exact Bayes and uniformly minimum variance unbiased estimates of the reliability for the case common shape parameter is known. The highest posterior density intervals are also obtained. We perform Monte Carlo simulations to compare the performance of proposed estimates and present a discussion based on this study. Finally, two real data sets are analyzed for illustration purposes.

Uttam Bandyopadhyay, Shirsendu Mukherjee, Atanu Biswas.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 291--303.

Abstract:
In adaptive crossover design, our goal is to allocate more patients to a promising treatment sequence. The present work contains a very simple three period crossover design for two competing treatments where the allocation in period 3 is done on the basis of the data obtained from the first two periods. Assuming normality of response variables we use a reliability functional for the choice between two treatments. We calculate the allocation proportions and their standard errors corresponding to the possible treatment combinations. We also derive some asymptotic results and provide solutions on related inferential problems. Moreover, the proposed procedure is compared with a possible competitor. Finally, we use a data set to illustrate the applicability of the proposed design.

Zhengwei Liu, Qi Li, Fukang Zhu.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 251--272.

Abstract:
To predict time series of counts with small values and remarkable fluctuations, an available model is the $r$ states random environment process based on the negative binomial thinning operator and the geometric marginal. However, we argue that the aforementioned model may suffer from the following two drawbacks. First, under the condition of no prior information, the overdispersed property of the geometric distribution may cause the predictions fluctuate greatly. Second, because of the constraints on the model parameters, some estimated parameters are close to zero in real-data examples, which may not objectively reveal the correlation relationship. For the first drawback, an $r$ states random environment process based on the binomial thinning operator and the Poisson marginal is introduced. For the second drawback, we propose a generalized $r$ states random environment integer-valued autoregressive model based on the binomial thinning operator to model fluctuations of data. Yule–Walker and conditional maximum likelihood estimates are considered and their performances are assessed via simulation studies. Two real-data sets are conducted to illustrate the better performances of the proposed models compared with some existing models.

David A. C. Mollinedo.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 188--201.

Abstract:
We consider the stochastic transport equation with a possibly unbounded Hölder continuous vector field. Well-posedness is proved, namely, we show existence, uniqueness and strong stability of $W^{1,p}$-weak solutions.

Abedin Haidari, Amir T. Payandeh Najafabadi, Narayanaswamy Balakrishnan.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 150--166.

Abstract:
Consider two parallel systems, say $A$ and $B$, with respective lifetimes $T_{1}$ and $T_{2}$ wherein independent component lifetimes of each system follow exponentiated generalized gamma distribution with possibly different exponential shape and scale parameters. We show here that $T_{2}$ is smaller than $T_{1}$ with respect to the usual stochastic order (reversed hazard rate order) if the vector of logarithm (the main vector) of scale parameters of System $B$ is weakly weighted majorized by that of System $A$, and if the vector of exponential shape parameters of System $A$ is unordered mojorized by that of System $B$. By means of some examples, we show that the above results can not be extended to the hazard rate and likelihood ratio orders. However, when the scale parameters of each system divide into two homogeneous groups, we verify that the usual stochastic and reversed hazard rate orders can be extended, respectively, to the hazard rate and likelihood ratio orders. The established results complete and strengthen some of the known results in the literature.

Wesley Bertoli, Katiane S. Conceição, Marinho G. Andrade, Francisco Louzada.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 4, 826--860.

Abstract:
The primary goal of this paper is to introduce the zero-modified Poisson–Lindley regression model as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros in the presence of covariates. The zero-modification is incorporated by considering that a zero-truncated process produces positive observations and consequently, the proposed model can be fitted without any previous information about the zero-modification present in a given dataset. A fully Bayesian approach based on the g-prior method has been considered for inference concerns. An intensive Monte Carlo simulation study has been conducted to evaluate the performance of the developed methodology and the maximum likelihood estimators. The proposed model was considered for the analysis of a real dataset on the number of bids received by $126$ U.S. firms between 1978–1985, and the impact of choosing different prior distributions for the regression coefficients has been studied. A sensitivity analysis to detect influential points has been performed based on the Kullback–Leibler divergence. A general comparison with some well-known regression models for discrete data has been presented.

Glaura C. Franco, Helio S. Migon, Marcos O. Prates.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 4, 756--781.

Abstract:
Observation and parameter driven models are commonly used in the literature to analyse time series of counts. In this paper, we study the characteristics of a variety of models and point out the main differences and similarities among these procedures, concerning parameter estimation, model fitting and forecasting. Alternatively to the literature, all inference was performed under the Bayesian paradigm. The models are fitted with a latent AR($p$) process in the mean, which accounts for autocorrelation in the data. An extensive simulation study shows that the estimates for the covariate parameters are remarkably similar across the different models. However, estimates for autoregressive coefficients and forecasts of future values depend heavily on the underlying process which generates the data. A real data set of bankruptcy in the United States is also analysed.

Yair Y. Shaki.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 3, 532--548.

Abstract:
We consider a Jackson network in a general heavy traffic diffusion regime with the $alpha$-parametrization . We also assume that each customer may abandon the system while waiting. We show that in this regime the queue-length process converges to a multi-dimensional regulated Ornstein–Uhlenbeck process.

Christian Olivera, Ciprian Tudor.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 3, 520--531.

Abstract:
Via a special transform and by using the techniques of the Malliavin calculus, we analyze the density of the solution to a stochastic differential equation with unbounded drift.

Yong-Chao Zhang, Na Zhang.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 1, 184--191.

Abstract:
We investigate the equivalence of dynamic and static asset allocations in the case where the price process of a risky asset is driven by a Poisson process. Under some mild conditions, we obtain a necessary and sufficient condition for the equivalence of dynamic and static asset allocations. In addition, we provide a simple sufficient condition for the equivalence.

Julie Josse, Susan Holmes.

Source: Statistics Surveys, Volume 10, 132--167.

Abstract:
Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based coefficients are being used by different research communities. Scientists use these coefficients to test whether two random vectors are linked. Once it has been ascertained that there is such association through testing, then a next step, often ignored, is to explore and uncover the association’s underlying patterns. This article provides a survey of various measures of dependence between random vectors and tests of independence and emphasizes the connections and differences between the various approaches. After providing definitions of the coefficients and associated tests, we present the recent improvements that enhance their statistical properties and ease of interpretation. We summarize multi-table approaches and provide scenarii where the indices can provide useful summaries of heterogeneous multi-block data. We illustrate these different strategies on several examples of real data and suggest directions for future research.

Jonathan R. Bradley, Noel Cressie, Tao Shi.

Source: Statistics Surveys, Volume 10, 100--131.

Abstract:
In this article, we review and compare a number of methods of spatial prediction, where each method is viewed as an algorithm that processes spatial data. To demonstrate the breadth of available choices, we consider both traditional and more-recently-introduced spatial predictors. Specifically, in our exposition we review: traditional stationary kriging, smoothing splines, negative-exponential distance-weighting, fixed rank kriging, modified predictive processes, a stochastic partial differential equation approach, and lattice kriging. This comparison is meant to provide a service to practitioners wishing to decide between spatial predictors. Hence, we provide technical material for the unfamiliar, which includes the definition and motivation for each (deterministic and stochastic) spatial predictor. We use a benchmark dataset of $mathrm{CO}_{2}$ data from NASA’s AIRS instrument to address computational efficiencies that include CPU time and memory usage. Furthermore, the predictive performance of each spatial predictor is assessed empirically using a hold-out subset of the AIRS data.

José A. Ferreira.

Source: Statistics Surveys, Volume 9, 106--208.

Abstract:
This article provides a concise and essentially self-contained exposition of some of the most important models and non-parametric methods for the analysis of observational data, and a substantial number of illustrations of their application. Although for the most part our presentation follows P. Rosenbaum’s book, “Observational Studies”, and naturally draws on related literature, it contains original elements and simplifies and generalizes some basic results. The illustrations, based on simulated data, show the methods at work in some detail, highlighting pitfalls and emphasizing certain subjective aspects of the statistical analyses.

Aki Vehtari, Janne Ojanen.

Source: Statistics Surveys, Volume 8, , 1--1.

Abstract:
Errata for “A survey of Bayesian predictive methods for model assessment, selection and comparison” by A. Vehtari and J. Ojanen, Statistics Surveys , 6 (2012), 142–228. doi:10.1214/12-SS102.

Aki Vehtari, Janne Ojanen

Source: Statist. Surv., Volume 6, 142--228.

Abstract:
To date, several methods exist in the statistical literature for model assessment, which purport themselves specifically as Bayesian predictive methods. The decision theoretic assumptions on which these methods are based are not always clearly stated in the original articles, however. The aim of this survey is to provide a unified review of Bayesian predictive model assessment and selection methods, and of methods closely related to them. We review the various assumptions that are made in this context and discuss the connections between different approaches, with an emphasis on how each method approximates the expected utility of using a Bayesian model for the purpose of predicting future data.

Jeffrey Picka

Source: Statist. Surv., Volume 6, 74--112.

Abstract:
This paper gives an overview of statistical inference for disordered sphere packing processes. These processes are used extensively in physics and engineering in order to represent the internal structure of composite materials, packed bed reactors, and powders at rest, and are used as initial arrangements of grains in the study of avalanches and other problems involving powders in motion. Packing processes are spatial processes which are neither stationary nor ergodic. Classical spatial statistical models and procedures cannot be applied to these processes, but alternative models and procedures can be developed based on ideas from statistical physics. Most of the development of models and statistics for sphere packings has been undertaken by scientists and engineers. This review summarizes their results from an inferential perspective.

Scott H. Holan, Robert Lund, Ginger Davis

Source: Statist. Surv., Volume 4, 232--274.

Abstract:
Autoregressive moving-average (ARMA) difference equations are ubiquitous models for short memory time series and have parsimoniously described many stationary series. Variants of ARMA models have been proposed to describe more exotic series features such as long memory autocovariances, periodic autocovariances, and count support set structures. This review paper enumerates, compares, and contrasts the common variants of ARMA models in today’s literature. After the basic properties of ARMA models are reviewed, we tour ARMA variants that describe seasonal features, long memory behavior, multivariate series, changing variances (stochastic volatility) and integer counts. A list of ARMA variant acronyms is provided.

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Application and use of deep learning algorithms for different healthcare applications is gaining interest at a steady pace. However, use of such algorithms can prove to be challenging as they require large amounts of training data that capture different possible variations. This makes it difficult to use them in a clinical setting since in most health applications researchers often have to work with limited data. Less data can cause the deep learning model to over-fit. In this paper, we ask how can we use data from a different environment, different use-case, with widely differing data distributions. We exemplify this use case by using single-sensor accelerometer data from healthy subjects performing activities of daily living - ADLs (source dataset), to extract features relevant to multi-sensor accelerometer gait data (target dataset) for Parkinson's disease classification. We train the pre-trained model using the source dataset and use it as a feature extractor. We show that the features extracted for the target dataset can be used to train an effective classification model. Our pre-trained source model consists of a convolutional autoencoder, and the target classification model is a simple multi-layer perceptron model. We explore two different pre-trained source models, trained using different activity groups, and analyze the influence the choice of pre-trained model has over the task of Parkinson's disease classification.

Segmentation of cardiac images, particularly late gadolinium-enhanced magnetic resonance imaging (LGE-MRI) widely used for visualizing diseased cardiac structures, is a crucial first step for clinical diagnosis and treatment. However, direct segmentation of LGE-MRIs is challenging due to its attenuated contrast. Since most clinical studies have relied on manual and labor-intensive approaches, automatic methods are of high interest, particularly optimized machine learning approaches. To address this, we organized the "2018 Left Atrium Segmentation Challenge" using 154 3D LGE-MRIs, currently the world's largest cardiac LGE-MRI dataset, and associated labels of the left atrium segmented by three medical experts, ultimately attracting the participation of 27 international teams. In this paper, extensive analysis of the submitted algorithms using technical and biological metrics was performed by undergoing subgroup analysis and conducting hyper-parameter analysis, offering an overall picture of the major design choices of convolutional neural networks (CNNs) and practical considerations for achieving state-of-the-art left atrium segmentation. Results show the top method achieved a dice score of 93.2% and a mean surface to a surface distance of 0.7 mm, significantly outperforming prior state-of-the-art. Particularly, our analysis demonstrated that double, sequentially used CNNs, in which a first CNN is used for automatic region-of-interest localization and a subsequent CNN is used for refined regional segmentation, achieved far superior results than traditional methods and pipelines containing single CNNs. This large-scale benchmarking study makes a significant step towards much-improved segmentation methods for cardiac LGE-MRIs, and will serve as an important benchmark for evaluating and comparing the future works in the field.

In recent years, multi-access edge computing (MEC) is a key enabler for handling the massive expansion of Internet of Things (IoT) applications and services. However, energy consumption of a MEC network depends on volatile tasks that induces risk for energy demand estimations. As an energy supplier, a microgrid can facilitate seamless energy supply. However, the risk associated with energy supply is also increased due to unpredictable energy generation from renewable and non-renewable sources. Especially, the risk of energy shortfall is involved with uncertainties in both energy consumption and generation. In this paper, we study a risk-aware energy scheduling problem for a microgrid-powered MEC network. First, we formulate an optimization problem considering the conditional value-at-risk (CVaR) measurement for both energy consumption and generation, where the objective is to minimize the loss of energy shortfall of the MEC networks and we show this problem is an NP-hard problem. Second, we analyze our formulated problem using a multi-agent stochastic game that ensures the joint policy Nash equilibrium, and show the convergence of the proposed model. Third, we derive the solution by applying a multi-agent deep reinforcement learning (MADRL)-based asynchronous advantage actor-critic (A3C) algorithm with shared neural networks. This method mitigates the curse of dimensionality of the state space and chooses the best policy among the agents for the proposed problem. Finally, the experimental results establish a significant performance gain by considering CVaR for high accuracy energy scheduling of the proposed model than both the single and random agent models.

We focus on estimating emph{a priori} generalization error of two-layer ReLU neural networks (NNs) trained by mean squared error, which only depends on initial parameters and the target function, through the following research line. We first estimate emph{a priori} generalization error of finite-width two-layer ReLU NN with constraint of minimal norm solution, which is proved by cite{zhang2019type} to be an equivalent solution of a linearized (w.r.t. parameter) finite-width two-layer NN. As the width goes to infinity, the linearized NN converges to the NN in Neural Tangent Kernel (NTK) regime citep{jacot2018neural}. Thus, we can derive the emph{a priori} generalization error of two-layer ReLU NN in NTK regime. The distance between NN in a NTK regime and a finite-width NN with gradient training is estimated by cite{arora2019exact}. Based on the results in cite{arora2019exact}, our work proves an emph{a priori} generalization error bound of two-layer ReLU NNs. This estimate uses the intrinsic implicit bias of the minimum norm solution without requiring extra regularity in the loss function. This emph{a priori} estimate also implies that NN does not suffer from curse of dimensionality, and a small generalization error can be achieved without requiring exponentially large number of neurons. In addition the research line proposed in this paper can also be used to study other properties of the finite-width network, such as the posterior generalization error.

We study the interplay of two important issues on Bayesian model selection (BMS): censoring and model misspecification. We consider additive accelerated failure time (AAFT), Cox proportional hazards and probit models, and a more general concave log-likelihood structure. A fundamental question is what solution can one hope BMS to provide, when (inevitably) models are misspecified. We show that asymptotically BMS keeps any covariate with predictive power for either the outcome or censoring times, and discards other covariates. Misspecification refers to assuming the wrong model or functional effect on the response, including using a finite basis for a truly non-parametric effect, or omitting truly relevant covariates. We argue for using simple models that are computationally practical yet attain good power to detect potentially complex effects, despite misspecification. Misspecification and censoring both have an asymptotically negligible effect on (suitably-defined) false positives, but their impact on power is exponential. We portray these issues via simple descriptions of early/late censoring and the drop in predictive accuracy due to misspecification. From a methods point of view, we consider local priors and a novel structure that combines local and non-local priors to enforce sparsity. We develop algorithms to capitalize on the AAFT tractability, approximations to AAFT and probit likelihoods giving significant computational gains, a simple augmented Gibbs sampler to hierarchically explore linear and non-linear effects, and an implementation in the R package mombf. We illustrate the proposed methods and others based on likelihood penalties via extensive simulations under misspecification and censoring. We present two applications concerning the effect of gene expression on colon and breast cancer.

The $p$-tensor Curie-Weiss model is a two-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic has a linear term and a term with degree $p geq 2$. This is a special case of the tensor Ising model and the natural generalization of the matrix Curie-Weiss model, which provides a convenient mathematical abstraction for capturing, not just pairwise, but higher-order dependencies. In this paper we provide a complete description of the limiting properties of the maximum likelihood (ML) estimates of the natural parameters, given a single sample from the $p$-tensor Curie-Weiss model, for $p geq 3$, complementing the well-known results in the matrix ($p=2$) case (Comets and Gidas (1991)). Our results unearth various new phase transitions and surprising limit theorems, such as the existence of a 'critical' curve in the parameter space, where the limiting distribution of the ML estimates is a mixture with both continuous and discrete components. The number of mixture components is either two or three, depending on, among other things, the sign of one of the parameters and the parity of $p$. Another interesting revelation is the existence of certain 'special' points in the parameter space where the ML estimates exhibit a superefficiency phenomenon, converging to a non-Gaussian limiting distribution at rate $N^{frac{3}{4}}$. We discuss how these results can be used to construct confidence intervals for the model parameters and, as a byproduct of our analysis, obtain limit theorems for the sample mean, which provide key insights into the statistical properties of the model.

We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the learning process by adding the residuals of a system of Partial Differential Equations to the loss function. Our PINN is supervised with realistic ultrasonic surface acoustic wave data acquired at a frequency of 5 MHz. The ultrasonic surface wave data is represented as a surface deformation on the top surface of a metal plate, measured by using the method of laser vibrometry. The PINN is physically informed by the acoustic wave equation and its convergence is sped up using adaptive activation functions. The adaptive activation function uses a scalable hyperparameter in the activation function, which is optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The usage of adaptive activation function significantly improves the convergence, notably observed in the current study. We use PINNs to estimate the speed of sound of the metal plate, which we do with an error of 1\%, and then, by allowing the speed of sound to be space dependent, we identify and characterize the crack as the positions where the speed of sound has decreased. Our study also shows the effect of sub-sampling of the data on the sensitivity of sound speed estimates. More broadly, the resulting model shows a promising deep neural network model for ill-posed inverse problems.

Early detection of patients vulnerable to infections acquired in the hospital environment is a challenge in current health systems given the impact that such infections have on patient mortality and healthcare costs. This work is focused on both the identification of risk factors and the prediction of healthcare-associated infections in intensive-care units by means of machine-learning methods. The aim is to support decision making addressed at reducing the incidence rate of infections. In this field, it is necessary to deal with the problem of building reliable classifiers from imbalanced datasets. We propose a clustering-based undersampling strategy to be used in combination with ensemble classifiers. A comparative study with data from 4616 patients was conducted in order to validate our proposal. We applied several single and ensemble classifiers both to the original dataset and to data preprocessed by means of different resampling methods. The results were analyzed by means of classic and recent metrics specifically designed for imbalanced data classification. They revealed that the proposal is more efficient in comparison with other approaches.

This paper proposes a stochastic variant of the stable matching model from Rasulkhani and Chow [1] which allows microtransit operators to evaluate their operation policy and resource allocations. The proposed model takes into account the stochastic nature of users' travel utility perception, resulting in a probabilistic stable operation cost allocation outcome to design ticket price and ridership forecasting. We applied the model for the operation policy evaluation of a microtransit service in Luxembourg and its border area. The methodology for the model parameters estimation and calibration is developed. The results provide useful insights for the operator and the government to improve the ridership of the service.

In this paper we obtain the limit distribution for partial sums with a random number of terms following a class of mixed Poisson distributions. The resulting weak limit is a mixing between a normal distribution and an exponential family, which we call by normal exponential family (NEF) laws. A new stability concept is introduced and a relationship between {alpha}-stable distributions and NEF laws is established. We propose estimation of the parameters of the NEF models through the method of moments and also by the maximum likelihood method, which is performed via an Expectation-Maximization algorithm. Monte Carlo simulation studies are addressed to check the performance of the proposed estimators and an empirical illustration on financial market is presented.

An important component of every country's COVID-19 response is fast and efficient testing -- to identify and isolate cases, as well as for early detection of local hotspots. For many countries, producing a sufficient number of tests has been a serious limiting factor in their efforts to control COVID-19 infections. Group testing is a well-established mathematical tool, which can provide a serious and rapid improvement to this situation. In this note, we compare several well-established group testing schemes in the context of qPCR testing for COVID-19. We include example calculations, where we indicate which testing architectures yield the greatest efficiency gains in various settings. We find that for identification of individuals with COVID-19, array testing is usually the best choice, while for estimation of COVID-19 prevalence rates in the total population, Gibbs-Gower testing usually provides the most accurate estimates given a fixed and relatively small number of tests. This note is intended as a helpful handbook for labs implementing group testing methods.

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.