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Deep neural network (DNN) techniques have demonstrated significant advantages over regression and some other techniques. In recent studies, DNN-based analysis has been conducted on data with high-dimensional input such as omics measurements. In such analysis, regularization, in particular penalization, has been applied to regularize estimation and distinguish relevant input variables from irrelevant ones. A unique challenge arises from the "lack of information" attributable to high dimensionality of input and limited size of training data. For many data/studies, there exist other data/studies that may be relevant and can potentially provide additional information to boost performance. In this study, we conduct integrative analysis of multiple independent datasets/studies, with the goal of borrowing information across each other and improving overall performance. Significantly different from regression-based integrative analysis (where alignment can be easily achieved based on covariates), alignment across multiple DNNs can be nontrivial. We develop ANNI, an A ligned D NN technique for I ntegrative analysis with high-dimensional input. Penalization is applied for regularized estimation, selection of important input variables, and, equally importantly, information borrowing across multiple DNNs. An effective computational algorithm is developed. Extensive simulations demonstrate competitive performance of the proposed technique. The analysis of cancer omics data further establishes its practical utility. [Display omitted] [ABSTRACT FROM AUTHOR]

A brain–computer interface (BCI) is a system which provides direct communication between the mind of a person and the outside world by using only brain activity (EEG). The event-related potential (ERP)-based BCI problem consists of a binary pattern recognition. Linear discriminant analysis (LDA) is widely used to solve this type of classification problems, but it fails when the number of features is large relative to the number of observations. In this work we propose a penalized version of the sparse discriminant analysis (SDA), called generalized sparse discriminant analysis (GSDA), for binary classification. This method inherits both the discriminative feature selection and classification properties of SDA and it also improves SDA performance through the addition of Kullback–Leibler class discrepancy information. The GSDA method is designed to automatically select the optimal regularization parameters. Numerical experiments with two real ERP-EEG datasets show that, on one hand, GSDA outperforms standard SDA in the sense of classification performance, sparsity and required computing time, and, on the other hand, it also yields better overall performances, compared to well-known ERP classification algorithms, for single-trial ERP classification when insufficient training samples are available. Hence, GSDA constitute a potential useful method for reducing the calibration times in ERP-based BCI systems. [ABSTRACT FROM AUTHOR]

In this study, we propose two types of sieve estimators, based on least squares (LS), for probability distributions that are mixtures of a finite number of discrete atoms and a continuous distribution under the framework of measurement error models. This research is motivated by the maximum likelihood (ML) sieve estimator developed in Lee et al. (2013). We obtain two types of LS sieve estimators through minimizing the distance between the empirical distribution/characteristic functions and the model distribution/characteristic functions. The LS estimators outperform the ML sieve estimator in several aspects: (1) they need much less computational time; (2) they give smaller integrated mean squared error; (3) the characteristic function based LS estimator is more robust against mis-specification of the error distribution. We also use roughness penalization to improve the smoothness of the resulting estimators and reduce the estimation variance. As an application of our proposed LS estimators, we use the Framingham Heart Study data to investigate the distribution of genetic effects on body mass index. Finally asymptotic properties of the LS estimators are investigated. [ABSTRACT FROM AUTHOR]

Inspired by the legacy of the Netflix contest, we provide an overview of what has been learned--from our own efforts, and those of others--concerning the problems of collaborative filtering and recommender systems. The data set consists of about 100 million movie ratings (from 1 to 5 stars) involving some 480 thousand users and some 18 thousand movies; the associated ratings matrix is about 99% sparse. The goal is to predict ratings that users will give to movies; systems which can do this accurately have significant commercial applications, particularly on the world wide web. We discuss, in some detail, approaches to "baseline" modeling, singular value decomposition (SVD), as well as kNN (nearest neighbor) and neural network models; temporal effects, cross-validation issues, ensemble methods and other considerations are discussed as well. We compare existing models in a search for new models, and also discuss the mission-critical issues of penalization and parameter shrinkage which arise when the dimensions of a parameter space reaches into the millions. Although much work on such problems has been carried out by the computer science and machine learning communities, our goal here is to address a statistical audience, and to provide a primarily statistical treatment of the lessons that have been learned from this remarkable set of data. [ABSTRACT FROM AUTHOR]

This work discusses geometric optimization problems governed by stationary Navier-Stokes equations. Optimal domains are proved to exist under the assumption that the family of admissible domains is bounded and satisfies the Lipschitz condition with a uniform constant, and in the absence of the uniqueness property for the state system. Through the parametrization of the admissible shapes by continuous functions defined on a larger universal domain, the optimization parameter becomes a control, i.e. an element of that family of continuous functions. The approximating extension technique via the penalization of the Navier-Stokes equation enables the approximation of the associated shape optimization problem by an optimal control problem. Results on existence and uniqueness are proved for the approximating problem and a gradient-type algorithm is indicated. [ABSTRACT FROM AUTHOR]

The EM algorithm is a special case of a more general algorithm called the MM algorithm. Specific MM algorithms often have nothing to do with missing data. The first M step of an MM algorithm creates a surrogate function that is optimized in the second M step. In minimization, MM stands for majorize--minimize; in maximization, it stands for minorize--maximize. This two-step process always drives the objective function in the right direction. Construction of MM algorithms relies on recognizing and manipulating inequalities rather than calculating conditional expectations. This survey walks the reader through the construction of several specific MM algorithms. The potential of the MM algorithm in solving high-dimensional optimization and estimation problems is its most attractive feature. Our applications to random graph models, discriminant analysis and image restoration showcase this ability. [ABSTRACT FROM AUTHOR]

This work discusses geometric optimization problems governed by stationary Navier-Stokes equations. Optimal domains are proved to exist under the assumption that the family of admissible domains is bounded and satisfies the Lipschitz condition with a uniform constant, and in the absence of the uniqueness property for the state system. Through the parametrization of the admissible shapes by continuous functions defined on a larger universal domain, the optimization parameter becomes a control, i.e. an element of that family of continuous functions. The approximating extension technique via the penalization of the Navier-Stokes equation enables the approximation of the associated shape optimization problem by an optimal control problem. Results on existence and uniqueness are proved for the approximating problem and a gradient-type algorithm is indicated. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this report is to review the contemporary research in amblyopia treatment and how it will affect clinical practice patterns. Methods: Topics addressed include prescribing the optimal refractive correction, the most effective treatment, duration and intensity of treatment, regression after treatment, the upper age for treatment, and the chance of the amblyope losing his or her sound eye. Results and Conclusions: The optimal refractive correction is best determined with cycloplegic retinoscopy; pharmacologic penalization can be as effective as patching in children with moderate amblyopia; less-intense treatment regimens have been found to be as effective as more-intense treatment regimens; regression can occur in as many as 25% of all treated patients; some older amblyopes can be treated successfully; and the amblyope has a higher chance of becoming blind than the nonamblyope. [Copyright &y& Elsevier]

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