Sequential Co-Sparse Factor Regression

In multivariate regression models, a sparse singular value decomposition of the regression component matrix is appealing for reducing dimensionality and facilitating interpretation. However, the recovery of such a decomposition remains very challenging, largely due to the simultaneous presence of orthogonality constraints and co-sparsity regularization. By delving into the underlying statistical data-generation mechanism, we reformulate the problem as a supervised co-sparse factor analysis, and develop an efficient computational procedure, named sequential factor extraction via co-sparse unit-rank estimation (SeCURE), that completely bypasses the orthogonality requirements. At each step, the problem reduces to a sparse multivariate regression with a unit-rank constraint. Nicely, each sequentially extracted sparse and unit-rank coefficient matrix automatically leads to co-sparsity in its pair of singular vectors. Each latent factor is thus a sparse linear combination of the predictors and may influence only a subset of responses. The proposed algorithm is guaranteed to converge, and it ensures efficient computation even with incomplete data and/or when enforcing exact orthogonality is desired. Our estimators enjoy the oracle properties asymptotically; a non-asymptotic error bound further reveals some interesting finite-sample behaviors of the estimators. The efficacy of SeCURE is demonstrated by simulation studies and two applications in genetics. Supplementary materials for this article are available online.     

Panel‐based stratified cluster sampling and analysis for photovoltaic outdoor measurements

We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.     

Power and reversal power links for binary regressions: An application for motor insurance policyholders

In binary regression, symmetric links such as logit and probit are usually considered as standard. However, in the presence of unbalancing of ones and zeros, these links can be inappropriate and inflexible to fit the skewness in the response curve and likely to lead to misspecification. This is the case of covering some type of insurance, where it can be observed that the probability of a given binary response variable approaches zero at different rates than it approaches one. Furthermore, when usual links are considered, there is not a skewness parameter associated with the distribution chosen that, regardless of the linear predictor, is easily interpreted. In order to overcome such problems, a proposal for the construction of a set of new skew links is developed in this paper, where some of their properties are discussed. In this context, power links and their reversal versions are presented. A Bayesian inference approach using MCMC is developed for the presented models. The methodology is illustrated considering a sample of motor insurance policyholders selected randomly by gender. Results suggest that the proposed link functions are more appropriate than other alternative link functions commonly used in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Prediction of human-Streptococcus pneumoniae protein-protein interactions using logistic regression

Streptococcus pneumoniae is a major cause of mortality in children under five years old. In recent years, the emergence of antibiotic-resistant strains of S. pneumoniae increases the threat level of this pathogen. For that reason, the exploration of S. pneumoniae protein virulence factors should be considered in developing new drugs or vaccines, for instance by the analysis of host-pathogen protein-protein interactions (HP-PPIs). In this research, prediction of protein-protein interactions was performed with a logistic regression model with the number of protein domain occurrences as features. By utilizing HP-PPIs of three different pathogens as training data, the model achieved 57–77 % precision, 64–75 % recall, and 96–98 % specificity. Prediction of human-S. pneumoniae protein-protein interactions using the model yielded 5823 interactions involving thirty S. pneumoniae proteins and 324 human proteins. Pathway enrichment analysis showed that most of the pathways involved in the predicted interactions are immune system pathways. Network topology analysis revealed β-galactosidase (BgaA) as the most central among the S. pneumoniae proteins in the predicted HP-PPI networks, with a degree centrality of 1.0 and a betweenness centrality of 0.451853. Further experimental studies are required to validate the predicted interactions and examine their roles in S. pneumoniae infection.     

Galois G-covering of quotients of linear categories

In this paper, we introduce the notion of G-liftable ideals, which extends the liftable ideas defined by Assem and Le Meur. We characterize the G-liftable ideals and construct the Galois G-coverings of quotients of categories associated to the G-liftable ideals. In particular, we study the behavior of G-liftable admissible ideals under Galois G-coverings. Furthermore, we show that the ideals generated by finite dimensional projective modules over a locally bounded linear categories are admissible G-liftable ideals. As an application, we provide a reduction technique for dealing with the existence of Serre functors in the stable categories of Gorenstein projective objects.     

Quantum Bayesian computation

Quantum Bayesian computation is an emerging field that levers the computational gains available from quantum computers. They promise to provide an exponential speed-up in Bayesian computation. Our article adds to the literature in three ways. First, we describe how quantum von Neumann measurement provides quantum versions of popular machine learning algorithms such as Markov chain Monte Carlo and deep learning that are fundamental to Bayesian learning. Second, we describe quantum data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Third, we show how quantum algorithms naturally calculate Bayesian quantities of interest such as posterior distributions and marginal likelihoods. Our goal then is to show how quantum algorithms solve statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes and stochastic gradient descent. On the empirical side, we apply a quantum FFT algorithm to Chicago house price data. Finally, we conclude with directions for future research.     

Data-driven optimal tracking control of switched linear systems

This paper addresses the optimal tracking control for switched linear systems with unknown dynamics. We convert the problem into an optimal control problem of the augmented switched systems. In view of the augmented systems, we propose a data-driven switched linear quadratic regular algorithm for obtaining the optimal switching signal under unknown system dynamics. It is proved that the optimal switching signal will not cause Zeno behavior and can make the system stable. Besides, with the proposed algorithm, we just need to identify an autonomous system instead of the original systems, which has fewer parameters to be determined. A numerical example is given to illustrate the validity of the main results.     

The representation problem of constrained linear elasticity

The title problem is given the following explicit solution: = _D S|D, where the elasticity tensor in the constrained case is the restriction to the constraint subspace D of a corresponding unconstrained elasticity tensor S, followed by composition with the orthogonal projection _D on D.     

高维线性插值方法及其在3维温度场计算中的应用

通过分析1维和2维线性插值可以推导出任意斜角直线坐标系下n维线性插值的一般计算公式以及有唯一解的条件,这一结论能够应用于三维温度场计算。可以将n维插值问题归结如下:已知n 1维空间中的n 1个点的坐标以及第n 2个点的n个坐标分量xn 2,1,x n 2,2,,xn 2,n,求解该点的第n 1个坐标分量xn 2,n 1。根据线性插值定义,第n 2个点位于前n 1个点所确定的n维超平面上。根据这一条件列写方程、求解方程可得到插值xn 2,n 1。n维插值问题有唯一解的条件是已知的n 1个点在n维空间中构成的多面体的体积不为0。推导过程在斜角直线坐标系中完成,因而结论具有较大普适性。