Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso

The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that data are drawn identically from a generating distribution. Introducing sparsity and sparse-difference inducing priors, we relax these assumptions and propose a novel regularized M-estimator to jointly estimate both the graph and changepoint structure. The resulting estimator possesses the ability to therefore favor sparse dependency structures and/or smoothly evolving graph structures, as required. Moreover, our approach extends current methods to allow estimation of changepoints that are grouped across multiple dependencies in a system. An efficient algorithm for estimating structure is proposed. We study the empirical recovery properties in a synthetic setting. The qualitative effect of grouped changepoint estimation is then demonstrated by applying the method on a genetic time-course dataset. Supplementary material for this article is available online.     

基于岭回归和SVM的高维特征选择与肽QSAR建模

岭回归估计权重绝对值在一定程度上体现了对应特征作用大小, 据此发展了基于岭回归(RR)和支持向量机(SVM)的高维特征选择算法. 对苦味二肽(BTT)和细胞毒性T淋巴细胞(CTL)表位9 肽两个肽体系, 以氨基酸的531 个物理化学性质参数直接表征肽结构, 各获得1062、4779 个初始特征; 对训练集, 初始特征以岭回归排序后序贯引入, 当SVM留一法交叉测试(LOOCV)的均方误差(MSE)显著上扬时终止, 最后以多轮末尾淘汰进一步精筛, 分别获得7、18个物理化学意义明确的保留特征. 基于保留特征与支持向量回归(SVR), 对训练集建立定量构效关系(QSAR)模型, 预测独立测试集, 其拟合精度、留一法交叉测试精度、独立预测精度均优于现有文献报道结果. 新方法运行速度快, 选取的特征物理化学意义明确, 解释性强, 在肽、蛋白质定量构效关系建模等高维数据回归预测领域有较广泛应用前景.     

Forecasting mortality rate improvements with a high-dimensional VAR

Forecasting mortality rates is a problem which involves the analysis of high-dimensional time series. Most of usual mortality models propose to decompose the mortality rates into several latent factors to reduce this complexity. These approaches, in particular those using cohort factors, have a good fit, but they are less reliable for forecasting purposes. One of the major challenges is to determine the spatial–temporal dependence structure between mortality rates given a relatively moderate sample size. This paper proposes a large vector autoregressive (VAR) model fitted on the differences in the log-mortality rates, ensuring the existence of long-run relationships between mortality rate improvements. Our contribution is threefold. First, sparsity, when fitting the model, is ensured by using high-dimensional variable selection techniques without imposing arbitrary constraints on the dependence structure. The main interest is that the structure of the model is directly driven by the data, in contrast to the main factor-based mortality forecasting models. Hence, this approach is more versatile and would provide good forecasting performance for any considered population. Additionally, our estimation allows a one-step procedure, as we do not need to estimate hyper-parameters. The variance–covariance matrix of residuals is then estimated through a parametric form. Secondly, our approach can be used to detect nonintuitive age dependence in the data, beyond the cohort and the period effects which are implicitly captured by our model. Third, our approach can be extended to model the several populations in long run perspectives, without raising issue in the estimation process. Finally, in an out-of-sample forecasting study for mortality rates, we obtain rather good performances and more relevant forecasts compared to classical mortality models using the French, US and UK data. We also show that our results enlighten the so-called cohort and period effects for these populations.     

Stability of Zernike coefficients solved by the covariance matrix method in the analysis of the wave front aberration

The deduction of Zernike coefficients is usually influenced by the finite number of sampling dots on interferogram and their inherited measurement errors. In this paper, a simplified Gram-Schmidt method for solving the Zernike polynomial with the higher fitting precision is presented and used to analyze the wave front aberrations for the circle interference fringe of the fine polished aluminum disk surface captured by a Twyman-Green interferometer system. We find the stability of the Zernike coefficients changes with changing the Zernike term, which has lead to the wrong expression for the wave front aberration. By analyzing the condition number of the coefficients matrix and the fitting precision of the method, it is indicated that the instability can be avoided when the Zernike term is lower than 14. Such an analysis will be valuable in solving the Zernike polynomial for the wave front aberration analysis in optical testing.     

Wiener integrals, Malliavin calculus and covariance measure structure

We introduce the notion of covariance measure structure for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of variations and we make Gaussian assumptions only when necessary. Our main examples are finite quadratic variation processes with stationary increments and the bifractional Brownian motion.     

Synthesis and Characterization of a Novel 3D Organic–Inorganic Hybrid Framwork Templated by Keggin Anions

A novel 3D compound, {K₃H₂[Cu(Gly)₂]₃BW₁₂O₄₀}·10H₂O 1 (Gly = glycine), has been synthesized and characterized by elemental analyses, IR, TG analyses, cyclic voltammetry, and single-crystal X-ray diffraction. Compound 1 contains square-grid layers constructed by potassium cations and copper-glycine coordination complexes, the [BW₁₂O₄₀]^4? anions as templates are accommodated in the square grids by connecting with the K atoms. The K atoms link [BW₁₂O₄₀]^4? anions from different layers together to yield a 3D novel structure. The crystal data for compounds 1: monoclinic, space group p2(1)/n, a = 18.832(4) Å, b = 16.488(3) Å, c = 20.570(4) Å, β = 106.21(3)°, V = 6133(2) Å³, Z = 4.     

Pre-Envelope Covariance Differential Equations For White and Nonwhite Input Processes

The pre-envelope process is a complex process whose statistics are strictly related to the statistics of the envelope of a given process. The paper deals with the evaluation of the covariances of the pre-envelope output process of classically and nonclassically damped linear systems subjected to stationary and nonstationary white and nonwhite pre-envelope input process. More precisely, the pre-envelope covariances for nonwhite complex input processes are evaluated as solution of a set of first order differential equations. Furthermore, in the paper the pre-envelope of the white input process is defined, and for such input the pre-envelope covariance differential equations are determined by means of an extension to the complex field of the stochastic differential calculus. Sommario.Il processo 'pre-inviluppo' é un processo complesso i cui parametri statistici sono strettamente legati a quelli del processo 'inviluppo'. Il lavoro riguarda la valutazione delle covarianze del processo pre–inviluppo della risposta di sistemi dinamici classicamente e non classicamente smorzati soggetti a processi pre–inviluppo bianchi e filtrati, stazionari e non stazionari. Piprecisamente, nel caso di un processo filtrato pre–inviluppo le covarianze della risposta sono valutate come soluzione di un sistema di equazioni differenziali del primo ordine. Inoltre, nel lavoro definito il processo pre–inviluppo di un processo bianco e per tale caso sono presentate le equazioni differenziali delle covarianze della risposta ottenute attraverso l'estensione al campo complesso del classico calcolo differenziale stocastico.     

基于序列特征筛选与支持向量回归预测蛋白质折叠速率

折叠速率预测对阐明蛋白质折叠机理意义重大.本文收集了115条目前已知折叠速率的蛋白质样本(包括二态、多态和混态蛋白),为了较全面地表征蛋白质分子的一级结构信息,提取序列长度、氨基酸残基多尺度组分、成对残基k-space特征与基于残基物理化学性质的地统计学关联总共9357维特征.经改进的二元矩阵重排过滤器和多轮末尾淘汰非线性筛选,获得23个物理化学意义明确的保留特征,建立的非线性支持向量回归模型Jackknife交叉验证的相关系数R=0.95,优于文献报道及其他参比特征选择方法.支持向量回归解释体系表明折叠速率与保留描述符的非线性回归极显著,分析了各保留描述符对折叠速率的影响,结果表明蛋白质折叠速率与序列长度、中短程关联特征、三联体残基组份特征等密切相关.     

Example of a Gaussian Self-Similar Field With Stationary Rectangular Increments That Is Not a Fractional Brownian Sheet

We consider anisotropic self-similar random fields, in particular, the fractional Brownian sheet (fBs). This Gaussian field is an extension of fractional Brownian motion. It is well known that the fractional Brownian motion is a unique Gaussian self-similar process with stationary increments. The main result of this article is an example of a Gaussian self-similar field with stationary rectangular increments that is not an fBs. So we proved that the structure of self-similar Gaussian fields can be substantially more involved then the structure of self-similar Gaussian processes. In order to establish the main result, we prove some properties of covariance function for self-similar fields with rectangular increments. Also, using Lamperti transformation, we obtain properties of covariance function for the corresponding stationary fields.