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大型数据集中的快速稳健模型选择AI 解读

Large datasets are increasingly common in many research fields. In particular, in the linear regression context, it is often the case that a huge number of potential covariates are available to explain a response variable, and the first step of a reasonable statistical analysis is to reduce the number of covariates. This can be done in a forward selection procedure that includes selecting the variable to enter, deciding to retain it or stop the selection, and estimating the…

半监督加性模型中的传播评分AI 解读

This article presents a semisupervised modeling framework that combines feature-based (x) data and graph-based (G) data for classification/regression of the response Y. In this semisupervised setting, Y is observed for a subset of the observations (labeled) and missing for the remainder (unlabeled). The Propagated Scoring algorithm proposed for fitting this model is a semisupervised fixed-point regularization approach that essentially extends the generalized additive model…

用于学习与试验设计的动态树AI 解读

Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in online application settings. We create a sequential tree model whose state changes in time with the accumulation of new data, and provide particle learning algorithms that allow for the efficient online posterior filtering of tree states. A major advantage of tree regression is that it allows for the use of very simple models within each…

析因设计下高维回归系数的检验AI 解读

We propose simultaneous tests for coefficients in high-dimensional linear regression models with factorial designs. The proposed tests are designed for the “large p, small n” situations where the conventional F-test is no longer applicable. We derive the asymptotic distribution of the proposed test statistic under the high-dimensional null hypothesis and various scenarios of the alternatives, which allow power evaluations. We also evaluate the power of the F-test for models…

有偏抽样设计中参数可识别性与估计的统一框架AI 解读

Based on the odds ratio representation of a joint density, we propose a unified framework to study parameter identifiability in biased sampling designs. It is shown that most of these designs encountered in practice can be reformulated within the proposed framework and, as a result, the question of parameter identifiability can be largely clarified. Estimation of the identifiable parameters is considered and traditional results on the equivalence of the prospective and…

利用检验功效增强多重决策并控制族错误率与错误发现率AI 解读

Improved procedures, in terms of smaller missed discovery rates (MDR), for performing multiple hypotheses testing with weak and strong control of the family-wise error rate (FWER) or the false discovery rate (FDR) are developed and studied. The improvement over existing procedures such as the Šidák procedure for FWER control and the Benjamini–Hochberg (BH) procedure for FDR control is achieved by exploiting possible differences in the powers of the individual tests. Results…

高维稀疏模型中的 ℓ1 惩罚分位数回归AI 解读

We consider median regression and, more generally, a possibly infinite collection of quantile regressions in high-dimensional sparse models. In these models, the number of regressors p is very large, possibly larger than the sample size n, but only at most s regressors have a nonzero impact on each conditional quantile of the response variable, where s grows more slowly than n. Since ordinary quantile regression is not consistent in this case, we consider ℓ1-penalized…

流形上的回归：外微分估计AI 解读

Collinearity and near-collinearity of predictors cause difficulties when doing regression. In these cases, variable selection becomes untenable because of mathematical issues concerning the existence and numerical stability of the regression coefficients, and interpretation of the coefficients is ambiguous because gradients are not defined. Using a differential geometric interpretation, in which the regression coefficients are interpreted as estimates of the exterior…

高维多元回归中的支持集并集恢复AI 解读

In multivariate regression, a K-dimensional response vector is regressed upon a common set of p covariates, with a matrix B∗ ∈ ℝp × K of regression coefficients. We study the behavior of the multivariate group Lasso, in which block regularization based on the ℓ1 ∕ ℓ2 norm is used for support union recovery, or recovery of the set of s rows for which B∗ is nonzero. Under high-dimensional scaling, we show that the multivariate group Lasso exhibits a threshold for the recovery…

半参数变系数部分线性模型的新型高效估计与变量选择方法AI 解读

The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the semiparametric varying-coefficient partially linear model. We first study quantile regression estimates for the nonparametric varying-coefficient functions and the parametric regression coefficients. To achieve nice efficiency properties, we…

借助降维估计对主要关注参数进行推断AI 解读

Summary As high dimensional data become routinely available in applied sciences, sufficient dimension reduction has been widely employed and its research has received considerable attention. However, with the majority of sufficient dimension reduction methodology focusing on the dimension reduction step, complete analysis and inference after dimension reduction have yet to receive much attention. We couple the strategy of sufficient dimension reduction with a flexible…

半参数广义线性模型中快速稳定的限制极大似然与边际似然估计AI 解读

Summary Recent work by Reiss and Ogden provides a theoretical basis for sometimes preferring restricted maximum likelihood (REML) to generalized cross-validation (GCV) for smoothing parameter selection in semiparametric regression. However, existing REML or marginal likelihood (ML) based methods for semiparametric generalized linear models (GLMs) use iterative REML or ML estimation of the smoothing parameters of working linear approximations to the GLM. Such indirect schemes…

具有动态条件相关性的广义多元门限 GARCH 模型AI 解读

We introduce a new multivariate GARCH model with multivariate thresholds in conditional correlations and develop a two-step estimation procedure that is feasible in large dimensional applications. Optimal threshold functions are estimated endogenously from the data and the model conditional covariance matrix is ensured to be positive definite. We study the empirical performance of our model in two applications using U.S. stock and bond market data. In both applications our…

多元计数数据的动态因子模型：股票市场交易活动应用AI 解读

We propose a dynamic factor model for the analysis of multivariate time series count data. Our model allows for idiosyncratic as well as common serially correlated latent factors in order to account for potentially complex dynamic interdependence between series of counts. The model is estimated under alternative count distributions (Poisson and negative binomial). Maximum likelihood estimation requires high-dimensional numerical integration in order to marginalize the joint…

分层马尔可夫正态混合模型及金融资产收益应用AI 解读

Motivated by the common problem of constructing predictive distributions for daily asset returns over horizons of one to several trading days, this article introduces a new model for time series. This model is a generalization of the Markov normal mixture model in which the mixture components are themselves normal mixtures, and it is a specific case of an artificial neural network model with two hidden layers. The article uses the model to construct predictive distributions…

高维数据模型选择的复合似然贝叶斯信息准则AI 解读

For high-dimensional data sets with complicated dependency structures, the full likelihood approach often leads to intractable computational complexity. This imposes difficulty on model selection, given that most traditionally used information criteria require evaluation of the full likelihood. We propose a composite likelihood version of the Bayes information criterion (BIC) and establish its consistency property for the selection of the true underlying marginal model. Our…

利用全变差惩罚估计多个变点AI 解读

We propose a new approach for dealing with the estimation of the location of change-points in one-dimensional piecewise constant signals observed in white noise. Our approach consists in reframing this task in a variable selection context. We use a penalized least-square criterion with a ℓ1-type penalty for this purpose. We explain how to implement this method in practice by using the LARS / LASSO algorithm. We then prove that, in an appropriate asymptotic framework, this…

高维自适应非线性交互结构的变量选择AI 解读

Numerous penalization based methods have been proposed for fitting a traditional linear regression model in which the number of predictors, p, is large relative to the number of observations, n. Most of these approaches assume sparsity in the underlying coefficients and perform some form of variable selection. Recently, some of this work has been extended to nonlinear additive regression models. However, in many contexts one wishes to allow for the possibility of…

利用成对 Copula 分解序列依赖的纵向数据建模AI 解读

Copulas have proven to be very successful tools for the flexible modeling of cross-sectional dependence. In this paper we express the dependence structure of continuous-valued time series data using a sequence of bivariate copulas. This corresponds to a type of decomposition recently called a “vine” in the graphical models literature, where each copula is entitled a “pair-copula.” We propose a Bayesian approach for the estimation of this dependence structure for longitudinal…

函数型预测变量的最具预测力设计点AI 解读

We suggest a way of reducing the very high dimension of a functional predictor, X, to a low number of dimensions chosen so as to give the best predictive performance. Specifically, if X is observed on a fine grid of design points t1,…, tr, we propose a method for choosing a small subset of these, say ti1,…, tik, to optimize the prediction of a response variable, Y. The values tij are referred to as the most predictive design points, or covariates, for a given value of k, and…

非齐次平面泊松过程强度的 Voronoi 估计量AI 解读

The Voronoi estimator may be defined for any location as the inverse of the area of the corresponding Voronoi cell. We investigate the statistical properties of this estimator for the intensity of an inhomogeneous Poisson process, and demonstrate it is approximately unbiased with a gamma sampling distribution. We also introduce the centroidal Voronoi estimator, a simple extension based on spatial regularization of the point pattern. Simulations show the Voronoi estimator has…

坐标无关的稀疏充分降维与变量选择AI 解读

Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is large. The standard SDR methods suffer because the estimated linear combinations usually consist of all original predictors, making it difficult to interpret. In this paper, we propose a unified method—coordinate-independent sparse…

多核学习中的稀疏性AI 解读

The problem of multiple kernel learning based on penalized empirical risk minimization is discussed. The complexity penalty is determined jointly by the empirical L2 norms and the reproducing kernel Hilbert space (RKHS) norms induced by the kernels with a data-driven choice of regularization parameters. The main focus is on the case when the total number of kernels is large, but only a relatively small number of them is needed to represent the target function, so that the…

Markowitz 问题及线性约束二次规划的高维效应：风险低估AI 解读

We first study the properties of solutions of quadratic programs with linear equality constraints whose parameters are estimated from data in the high-dimensional setting where p, the number of variables in the problem, is of the same order of magnitude as n, the number of observations used to estimate the parameters. The Markowitz problem in Finance is a subcase of our study. Assuming normality and independence of the observations we relate the efficient frontier computed…