Computational Statistics & Data Analysis最新文献

For multivariate nonparametric regression, doubly penalized ANOVA modeling (DPAM) has recently been proposed, using hierarchical total variations (HTVs) and empirical norms as penalties on the component functions such as main effects and multi-way interactions in a functional ANOVA decomposition of the underlying regression function. The two penalties play complementary roles: the HTV penalty promotes sparsity in the selection of basis functions within each component function, whereas the empirical-norm penalty promotes sparsity in the selection of component functions. To facilitate large-scale training of DPAM using backfitting or block minimization, two suitable primal-dual algorithms are developed, including both batch and stochastic versions, for updating each component function in single-block optimization. Existing applications of primal-dual algorithms are intractable for DPAM with both HTV and empirical-norm penalties. The validity and advantage of the stochastic primal-dual algorithms are demonstrated through extensive numerical experiments, compared with their batch versions and a previous active-set algorithm, in large-scale scenarios.

Mixed membership models are an extension of finite mixture models, where each observation can partially belong to more than one mixture component. A probabilistic framework for mixed membership models of high-dimensional continuous data is proposed with a focus on scalability and interpretability. The novel probabilistic representation of mixed membership is based on convex combinations of dependent multivariate Gaussian random vectors. In this setting, scalability is ensured through approximations of a tensor covariance structure through multivariate eigen-approximations with adaptive regularization imposed through shrinkage priors. Conditional weak posterior consistency is established on an unconstrained model, allowing for a simple posterior sampling scheme while keeping many of the desired theoretical properties of our model. The model is motivated by two biomedical case studies: a case study on functional brain imaging of children with autism spectrum disorder (ASD) and a case study on gene expression data from breast cancer tissue. These applications highlight how the typical assumption made in cluster analysis, that each observation comes from one homogeneous subgroup, may often be restrictive in several applications, leading to unnatural interpretations of data features.

To address the challenges in estimating parameters of the widely applied Student-Lévy process, the study introduces two distinct methods: a likelihood-based approach and a data-driven approach. A two-step quasi-likelihood-based method is initially proposed, countering the non-closed nature of the Student-Lévy process's distribution function under convolution. This method utilizes the limiting properties observed in high-frequency data, offering estimations via a quasi-likelihood function characterized by asymptotic normality. Additionally, a novel neural-network-based parameter estimation technique is advanced, independent of high-frequency observation assumptions. Utilizing a CNN-LSTM framework, this method effectively processes sparse, local jump-related data, extracts deep features, and maps these to the parameter space using a fully connected neural network. This innovative approach ensures minimal assumption reliance, end-to-end processing, and high scalability, marking a significant advancement in parameter estimation techniques. The efficacy of both methods is substantiated through comprehensive numerical experiments, demonstrating their robust performance in diverse scenarios.

Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are not robust against outliers (i.e., against erroneous or extreme data points). A difference in trends in the bulk of the data and the outliers thus yields skewed inference and predictions. To address this problem, robust methods have been introduced. The most commonly applied robust method is frequentist and consists in an estimator which is derived from a modification of the derivative of the log-likelihood. The objective is to propose an alternative approach which is modelling-based and thus fundamentally different. Such an approach allows for an understanding and interpretation of the modelling, and it can be applied for both frequentist and Bayesian statistical analyses. The proposed approach possesses appealing theoretical and empirical properties.

Modelling the first-order intensity function is one of the main aims in point process theory. An appropriate model describes the first-order intensity as a nonparametric function of spatial covariates. A formal testing procedure is presented to assess the goodness-of-fit of this model, assuming an inhomogeneous Poisson point process. The test is based on a quadratic distance between two kernel intensity estimators. The asymptotic normality of the test statistic is proved and a bootstrap procedure to approximate its distribution is suggested. The proposal is illustrated with two applications to real data sets, and an extensive simulation study to evaluate its finite-sample performance.

Subgroup analysis for modeling longitudinal data with heterogeneity across all individuals has drawn attention in the modern statistical learning. In this paper, we focus on heterogeneous quantile regression model and propose to achieve variable selection, heterogeneous subgrouping and parameter estimation simultaneously, by using the smoothed generalized estimating equations in conjunction with the multi-directional separation penalty. The proposed method allows individuals to be divided into multiple subgroups for different heterogeneous covariates such that estimation efficiency can be gained through incorporating individual correlation structure and sharing information within subgroups. A data-driven procedure based on a modified BIC is applied to estimate the number of subgroups. Theoretical properties of the oracle estimator given the underlying true subpopulation information are firstly provided and then it is shown that the proposed estimator is equivalent to the oracle estimator under some conditions. The finite-sample performance of the proposed estimators is studied through simulations and an application to an AIDS dataset is also presented.

Missing data arise commonly in applications, and research on this topic has received extensive attention in the past few decades. Various inference methods have been developed under different missing data mechanisms, including missing at random and missing not at random. The assessment of a feasible missing data mechanism is, however, difficult due to the lack of validation data. The problem is further complicated by the presence of spurious variables in covariates. Focusing on missingness in the response variable, a unified modeling scheme is proposed by utilizing the parametric generalized additive model to characterize various types of missing data processes. Taking the generalized linear model to facilitate the dependence of the response on the associated covariates, the concurrent estimation and variable selection procedures are developed using regularized likelihood, and the asymptotic properties for the resultant estimators are rigorously established. The proposed methods are appealing in their flexibility and generality; they circumvent the need of assuming a particular missing data mechanism that is required by most available methods. Empirical studies demonstrate that the proposed methods result in satisfactory performance in finite sample settings. Extensions to accommodating missingness in both the response and covariates are also discussed.

The ability to interpret machine learning models has become increasingly important as their usage in data science continues to rise. Most current interpretability methods are optimized to work on either (i) a global scale, where the goal is to rank features based on their contributions to overall variation in an observed population, or (ii) the local level, which aims to detail on how important a feature is to a particular individual in the data set. In this work, a new operator is proposed called the “GlObal And Local Score” (GOALS): a simple post hoc approach to simultaneously assess local and global feature variable importance in nonlinear models. Motivated by problems in biomedicine, the approach is demonstrated using Gaussian process regression where the task of understanding how genetic markers are associated with disease progression both within individuals and across populations is of high interest. Detailed simulations and real data analyses illustrate the flexible and efficient utility of GOALS over state-of-the-art variable importance strategies.

Clustering is part of unsupervised analysis methods that group samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to infer the variables that significantly separate the estimated clusters from each other. However, data-driven hypotheses are thus used for the inference process because the hypotheses are derived from the clustering results. This double use of the data leads traditional hypothesis test to fail to control the Type I error rate particularly because of uncertainty in the clustering process and the potential artificial differences it could create. Three novel statistical hypothesis tests are introduced, each designed to account for the clustering process. These tests efficiently control the Type I error rate by identifying only variables that contain a true signal separating groups of observations. The proposed tests were applied in two distinct contexts: animal ecology and immunology, demonstrating the relevance of the results with real datasets.

Subgroup identification is crucial in dealing with the heterogeneous population and has wide applications in various areas, such as clinical trials and market segmentation. With the prevalence of multi-source data, there is a practical need to identify subgroups based on multi-source data. This paper proposes a working-independence pseudo-loglikelihood and integrates the parameters of each source into a pairwise fusion penalty for simultaneous parameter estimation and subgroup identification. To implement the proposed method, an alternating direction method of multipliers (ADMM) algorithm is derived. Furthermore, the weak oracle properties of parameter estimation are established, illustrating the latent subgroups can be consistently identified. Finally, numerical simulations and an analysis of a randomized trial on reduced nicotine standards for cigarettes are conducted to evaluate the performance of the proposed method.