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London : Reproductive Health Matters, 1993-2018.

London : Reproductive Health Matters, 1993-2018.

London : Reproductive Health Matters, 1993-2018.

London : Reproductive Health Matters, 1993-2018.

London : Reproductive Health Matters, 1993-2018.

Pac-12 Networks' Yogi Roth and Ashley Adamson talk with Hall of Fame player and Pac-12 Networks talent Bill Walton during Thursday's Pac-12 Perspective podcast.

Ming Yu, Varun Gupta, Mladen Kolar.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 413--457.

Abstract:
We study the problem of recovery of matrices that are simultaneously low rank and row and/or column sparse. Such matrices appear in recent applications in cognitive neuroscience, imaging, computer vision, macroeconomics, and genetics. We propose a GDT (Gradient Descent with hard Thresholding) algorithm to efficiently recover matrices with such structure, by minimizing a bi-convex function over a nonconvex set of constraints. We show linear convergence of the iterates obtained by GDT to a region within statistical error of an optimal solution. As an application of our method, we consider multi-task learning problems and show that the statistical error rate obtained by GDT is near optimal compared to minimax rate. Experiments demonstrate competitive performance and much faster running speed compared to existing methods, on both simulations and real data sets.

Sihai Dave Zhao, Yet Tien Nguyen.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 110--142.

Abstract:
It is frequently of interest to identify simultaneous signals, defined as features that exhibit statistical significance across each of several independent experiments. For example, genes that are consistently differentially expressed across experiments in different animal species can reveal evolutionarily conserved biological mechanisms. However, in some problems the test statistics corresponding to these features can have complicated or unknown null distributions. This paper proposes a novel nonparametric false discovery rate control procedure that can identify simultaneous signals even without knowing these null distributions. The method is shown, theoretically and in simulations, to asymptotically control the false discovery rate. It was also used to identify genes that were both differentially expressed and proximal to differentially accessible chromatin in the brains of mice exposed to a conspecific intruder. The proposed method is available in the R package github.com/sdzhao/ssa.

Mikael Escobar-Bach, Yuri Goegebeur, Armelle Guillou.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1773--1795.

Abstract:
We consider bias-corrected estimation of the stable tail dependence function in the regression context. To this aim, we first estimate the bias of a smoothed estimator of the stable tail dependence function, and then we subtract it from the estimator. The weak convergence, as a stochastic process, of the resulting asymptotically unbiased estimator of the conditional stable tail dependence function, correctly normalized, is established under mild assumptions, the covariate argument being fixed. The finite sample behaviour of our asymptotically unbiased estimator is then illustrated on a simulation study and compared to two alternatives, which are not bias corrected. Finally, our methodology is applied to a dataset of air pollution measurements.

Daniel R. Kowal, Antonio Canale.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1744--1772.

Abstract:
We propose a simple yet powerful framework for modeling integer-valued data, such as counts, scores, and rounded data. The data-generating process is defined by Simultaneously Transforming and Rounding (STAR) a continuous-valued process, which produces a flexible family of integer-valued distributions capable of modeling zero-inflation, bounded or censored data, and over- or underdispersion. The transformation is modeled as unknown for greater distributional flexibility, while the rounding operation ensures a coherent integer-valued data-generating process. An efficient MCMC algorithm is developed for posterior inference and provides a mechanism for adaptation of successful Bayesian models and algorithms for continuous data to the integer-valued data setting. Using the STAR framework, we design a new Bayesian Additive Regression Tree model for integer-valued data, which demonstrates impressive predictive distribution accuracy for both synthetic data and a large healthcare utilization dataset. For interpretable regression-based inference, we develop a STAR additive model, which offers greater flexibility and scalability than existing integer-valued models. The STAR additive model is applied to study the recent decline in Amazon river dolphins.

Ryoya Oda, Hirokazu Yanagihara.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1386--1412.

Abstract:
We put forward a variable selection method for selecting explanatory variables in a normality-assumed multivariate linear regression. It is cumbersome to calculate variable selection criteria for all subsets of explanatory variables when the number of explanatory variables is large. Therefore, we propose a fast and consistent variable selection method based on a generalized $C_{p}$ criterion. The consistency of the method is provided by a high-dimensional asymptotic framework such that the sample size and the sum of the dimensions of response vectors and explanatory vectors divided by the sample size tend to infinity and some positive constant which are less than one, respectively. Through numerical simulations, it is shown that the proposed method has a high probability of selecting the true subset of explanatory variables and is fast under a moderate sample size even when the number of dimensions is large.

In this paper, we extend the methodology developed for Support Vector Machines (SVM) using the $ell_2$-norm ($ell_2$-SVM) to the more general case of $ell_p$-norms with $p>1$ ($ell_p$-SVM). We derive second order cone formulations for the resulting dual and primal problems. The concept of kernel function, widely applied in $ell_2$-SVM, is extended to the more general case of $ell_p$-norms with $p>1$ by defining a new operator called multidimensional kernel. This object gives rise to reformulations of dual problems, in a transformed space of the original data, where the dependence on the original data always appear as homogeneous polynomials. We adapt known solution algorithms to efficiently solve the primal and dual resulting problems and some computational experiments on real-world datasets are presented showing rather good behavior in terms of the accuracy of $ell_p$-SVM with $p>1$.

We consider the problem of jointly estimating multiple inverse covariance matrices from high-dimensional data consisting of distinct classes. An $ell_2$-penalized maximum likelihood approach is employed. The suggested approach is flexible and generic, incorporating several other $ell_2$-penalized estimators as special cases. In addition, the approach allows specification of target matrices through which prior knowledge may be incorporated and which can stabilize the estimation procedure in high-dimensional settings. The result is a targeted fused ridge estimator that is of use when the precision matrices of the constituent classes are believed to chiefly share the same structure while potentially differing in a number of locations of interest. It has many applications in (multi)factorial study designs. We focus on the graphical interpretation of precision matrices with the proposed estimator then serving as a basis for integrative or meta-analytic Gaussian graphical modeling. Situations are considered in which the classes are defined by data sets and subtypes of diseases. The performance of the proposed estimator in the graphical modeling setting is assessed through extensive simulation experiments. Its practical usability is illustrated by the differential network modeling of 12 large-scale gene expression data sets of diffuse large B-cell lymphoma subtypes. The estimator and its related procedures are incorporated into the R-package rags2ridges.

High dimensional data often contain multiple facets, and several clustering patterns can co-exist under different variable subspaces, also known as the views. While multi-view clustering algorithms were proposed, the uncertainty quantification remains difficult --- a particular challenge is in the high complexity of estimating the cluster assignment probability under each view, and sharing information among views. In this article, we propose an approximate Bayes approach --- treating the similarity matrices generated over the views as rough first-stage estimates for the co-assignment probabilities; in its Kullback-Leibler neighborhood, we obtain a refined low-rank matrix, formed by the pairwise product of simplex coordinates. Interestingly, each simplex coordinate directly encodes the cluster assignment uncertainty. For multi-view clustering, we let each view draw a parameterization from a few candidates, leading to dimension reduction. With high model flexibility, the estimation can be efficiently carried out as a continuous optimization problem, hence enjoys gradient-based computation. The theory establishes the connection of this model to a random partition distribution under multiple views. Compared to single-view clustering approaches, substantially more interpretable results are obtained when clustering brains from a human traumatic brain injury study, using high-dimensional gene expression data.

We consider the skill rating problem for multiplayer games, that is how to infer player skills from game outcomes in multiplayer games. We formulate the problem as a minimization problem $arg min_{s} s^T Delta s$ where $Delta$ is a positive semidefinite matrix and $s$ a real-valued function, of which some entries are the skill values to be inferred and other entries are constrained by the game outcomes. We leverage graph-based semi-supervised learning (SSL) algorithms for this problem. We apply our algorithms on several data sets of multiplayer games and obtain very promising results compared to Elo Duelling (see Elo, 1978) and TrueSkill (see Herbrich et al., 2006).. As we leverage graph-based SSL algorithms and because games can be seen as relations between sets of players, we then generalize the approach. For this aim, we introduce a new finite model, called hypernode graph, defined to be a set of weighted binary relations between sets of nodes. We define Laplacians of hypernode graphs. Then, we show that the skill rating problem for multiplayer games can be formulated as $arg min_{s} s^T Delta s$ where $Delta$ is the Laplacian of a hypernode graph constructed from a set of games. From a fundamental perspective, we show that hypernode graph Laplacians are symmetric positive semidefinite matrices with constant functions in their null space. We show that problems on hypernode graphs can not be solved with graph constructions and graph kernels. We relate hypernode graphs to signed graphs showing that positive relations between groups can lead to negative relations between individuals.

We consider the problem of unveiling the implicit network structure of node interactions (such as user interactions in a social network), based only on high-frequency timestamps. Our inference is based on the minimization of the least-squares loss associated with a multivariate Hawkes model, penalized by $ell_1$ and trace norm of the interaction tensor. We provide a first theoretical analysis for this problem, that includes sparsity and low-rank inducing penalizations. This result involves a new data-driven concentration inequality for matrix martingales in continuous time with observable variance, which is a result of independent interest and a broad range of possible applications since it extends to matrix martingales former results restricted to the scalar case. A consequence of our analysis is the construction of sharply tuned $ell_1$ and trace-norm penalizations, that leads to a data-driven scaling of the variability of information available for each users. Numerical experiments illustrate the significant improvements achieved by the use of such data-driven penalizations.

Co-training is a well-known semi-supervised learning approach which trains classifiers on two or more different views and exchanges pseudo labels of unlabeled instances in an iterative way. During the co-training process, pseudo labels of unlabeled instances are very likely to be false especially in the initial training, while the standard co-training algorithm adopts a 'draw without replacement' strategy and does not remove these wrongly labeled instances from training stages. Besides, most of the traditional co-training approaches are implemented for two-view cases, and their extensions in multi-view scenarios are not intuitive. These issues not only degenerate their performance as well as available application range but also hamper their fundamental theory. Moreover, there is no optimization model to explain the objective a co-training process manages to optimize. To address these issues, in this study we design a unified self-paced multi-view co-training (SPamCo) framework which draws unlabeled instances with replacement. Two specified co-regularization terms are formulated to develop different strategies for selecting pseudo-labeled instances during training. Both forms share the same optimization strategy which is consistent with the iteration process in co-training and can be naturally extended to multi-view scenarios. A distributed optimization strategy is also introduced to train the classifier of each view in parallel to further improve the efficiency of the algorithm. Furthermore, the SPamCo algorithm is proved to be PAC learnable, supporting its theoretical soundness. Experiments conducted on synthetic, text categorization, person re-identification, image recognition and object detection data sets substantiate the superiority of the proposed method.

An important problem in the field of Topological Data Analysis is defining topological summaries which can be combined with traditional data analytic tools. In recent work Bubenik introduced the persistence landscape, a stable representation of persistence diagrams amenable to statistical analysis and machine learning tools. In this paper we generalise the persistence landscape to multiparameter persistence modules providing a stable representation of the rank invariant. We show that multiparameter landscapes are stable with respect to the interleaving distance and persistence weighted Wasserstein distance, and that the collection of multiparameter landscapes faithfully represents the rank invariant. Finally we provide example calculations and statistical tests to demonstrate a range of potential applications and how one can interpret the landscapes associated to a multiparameter module.

We consider a setting where multiple players sequentially choose among a common set of actions (arms). Motivated by an application to cognitive radio networks, we assume that players incur a loss upon colliding, and that communication between players is not possible. Existing approaches assume that the system is stationary. Yet this assumption is often violated in practice, e.g., due to signal strength fluctuations. In this work, we design the first multi-player Bandit algorithm that provably works in arbitrarily changing environments, where the losses of the arms may even be chosen by an adversary. This resolves an open problem posed by Rosenski et al. (2016).

Jun Zhang, Yujie Gai, Xia Cui, Gaorong Li.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 370--393.

Abstract:
This paper studies the measure of symmetry or asymmetry of a continuous variable under the multiplicative distortion measurement errors setting. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. First, two direct plug-in estimation procedures are proposed, and the empirical likelihood based confidence intervals are constructed to measure the symmetry or asymmetry of the unobserved variable. Next, we propose four test statistics for testing whether the unobserved variable is symmetric or not. The asymptotic properties of the proposed estimators and test statistics are examined. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators and test statistics. These methods are applied to analyze a real dataset for an illustration.

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.

Victor Coscrato, Rafael Izbicki, Rafael B. Stern.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 230--250.

Abstract:
Despite its common practice, statistical hypothesis testing presents challenges in interpretation. For instance, in the standard frequentist framework there is no control of the type II error. As a result, the non-rejection of the null hypothesis $(H_{0})$ cannot reasonably be interpreted as its acceptance. We propose that this dilemma can be overcome by using agnostic hypothesis tests, since they can control the type I and II errors simultaneously. In order to make this idea operational, we show how to obtain agnostic hypothesis in typical models. For instance, we show how to build (unbiased) uniformly most powerful agnostic tests and how to obtain agnostic tests from standard p-values. Also, we present conditions such that the above tests can be made logically coherent. Finally, we present examples of consistent agnostic hypothesis tests.

Andreas Anastasiou, Robert E. Gaunt.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 136--149.

Abstract:
We use the delta method and Stein’s method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and its asymptotic multivariate normal distribution. Our bounds apply in situations in which the MLE can be written as a function of a sum of i.i.d. $t$-dimensional random vectors. We apply our general bound to establish a bound for the multivariate normal approximation of the MLE of the normal distribution with unknown mean and variance.