This study proposes a novel forecasting model for time series based on the improvement in interpolating input data and the Bi-directional Long Short-Term Memory (BiLSTM) algorithm, with significant contributions both in theory and application. First, the time series is divided into clusters with an appropriate number based on an improved cluster self-updating (ICSU) algorithm. In the ICSU algorithm, the number of clusters is automatically determined depending on the mean and standard deviation of the pairwise distances of the elements. The fuzzy relationship between the elements and the clusters is established, which is then used to interpolate the original time series. The interpolated series is used as input data for the BiLSTM model. By combining these improvements, an efficient forecasting model for time series is developed. The model details the implementation steps, addresses convergence issues, and can be applied to real-world series using a program developed in Matlab software. The effectiveness of the proposed forecasting model is demonstrated by comparison with the existing models, including those based on statistical methods and deep learning, through the M3-Competition dataset with 3,003 series and M4-Competition dataset with 100,000 series. Specific applications on real economic datasets also show the advantages of this model.
The crucial role of gene regulation in embryonic development necessitates the association analysis of gene expression along cell lineage trees. However, due to cell division and differentiation, gene expression data measured on cells from a cell lineage tree possess certain spatial and temporal characteristics. These inherent natures of the tree-shaped data pose challenges in quantifying gene association. Traditional vector-based association measures do not fit well to such non-IID context. In this article, a geometric statistic is introduced to measure tree association. We analyzed its theoretical properties. A normalization algorithm for robust estimation of the geometric statistic is also proposed. Extensive simulations demonstrate that the geometric statistic provides a precise measure of tree association. Real data analyses conducted on gene expression on cell lineage trees of Caenorhabditis elegans showed its effectiveness. Supplementary materials for this article are available online.
Representative Learning (RepL) is a distributed learning framework in which nodes transmit pseudo data, called representatives, instead of model parameters or gradients. These representatives retain the original data format while encoding key statistical features, enabling them to support asynchronous communication and heterogeneous tasks. This paper introduces two new representative constructions: the Transformed Mean Representative (TMR), which generalizes the mean representative by incorporating model-specific link functions; and the Anchored Score-Matching Representative (Anchored-SMR), which modifies score-matching equations to ensure uniqueness and stability. Anchored-SMR is further extended to accommodate general smooth loss functions with optional non-smooth penalties. We analyze RepL in decentralized, asynchronous systems where gradients and models from other nodes may be delayed or misaligned. Theoretical results and extensive simulations demonstrate that the proposed representatives maintain accuracy and convergence under heterogeneity and asynchrony, offering a scalable and interpretable alternative to gradient-based distributed optimization.
This paper adopts a latent forest model for mixed data analysis. Unlike traditional latent tree model, the adopted model is more flexible with several trees, and observed variables are allowed to appear as internal nodes. This model can capture more complex potential mechanisms behind data. We address the latent structural learning and the parameter estimation for this model. For structural learning, we propose a consistent bottom-up algorithm and provide a theoretical guarantee on a finite sample size bound for the exact structural recovery. For parameter estimation, we introduce a moment estimator algorithm and demonstrate that the estimator is asymptotically normal. The simulation studies indicate that our algorithms performed well for learning the mixed latent forest model. The real data analysis shows that the learned model captured the hierarchical structure and latent information behind the Changchun mayor hotline data.
This paper introduces a novel kernel variable importance measure (KvIM) based on the maximum mean discrepancy (MMD). KvIM can effectively measure the importance of each individual dimension in contributing to the distributional difference by constructing weighted MMD and applying perturbations to evaluate changes in MMD through assigned weights. KvIM has several notable advantages: it is nonparametric and model-free, accounts for dependencies among dimensions, and is suitable for high-dimensional data. We establish the consistency of the empirical KvIM under general conditions, along with its theoretical properties in high-dimensional settings. Furthermore, we apply KvIM to classification problems and streaming datasets, proposing a KvIM-enhanced classification approach and an online KvIM. These applications demonstrate the practical utility of the proposed KvIM in diverse scenarios, as justified through extensive numerical experiments.
Doubly interval-censoring occurs frequently in infectious disease data, but the nonparametric estimators suitable for doubly interval-censored observed data are not well known. We develop a nonparametric estimator for the distribution function of doubly interval-censored data. Our proposed method analyzes the distributions of the incubation period and the infections simultaneously, and we derive its estimator based on the Bayesian and maximum likelihood methods. The simulation study suggests that this estimator is consistent. The usefulness of the proposed method is shown by a practical example using the reports of the novel coronavirus disease.
Identifying influential variables in high-dimensional matrix-valued data while controlling the false discovery rate (FDR) is a critical challenge in modern data science. We propose a novel, model-free procedure specifically designed for simultaneous row and column selection in matrix predictor regression. Our approach uses folding selection subspaces (FSS) to formulate structured hypotheses and employs data splitting to construct mirror statistics from FSS estimators. This design bypasses restrictive model specification and the need for p-value computation. Key theoretical contributions include establishing the asymptotic distribution of FSS estimators and proving the mirror statistic is asymptotically symmetric with respect to zero under the null hypothesis. Using the symmetry, we develop a multiple hypothesis testing procedure with data-driven thresholds that provably controls the FDR for row and column at the desired level asymptotically. The framework is further extended to control element-wise FDR under specific structural assumptions. Extensive simulations and a real data analysis demonstrate the superior performance of the proposed method over existing approaches across various settings.
The hypervolume under the receiver operating characteristic (ROC) manifold, referred to as HUM, is a critical metric for evaluating the performance in multi-classification problems. Nevertheless, its practical applicability is constrained by the polynomial time complexity of the standard implementation. This paper introduces a new fast algorithm for computing HUM value based on probability assessment vectors. Compared with the HUM value based on ordered response with a single marker, it poses unique challenges due to its complicated sample space. Inspired by the method of incomplete U-statistic, we propose a sampling-based algorithm for approximating HUM values. Theoretically, the approximation error diminishes inversely with computational time and becomes asymptotically negligible within quasi-linear computational complexity. Furthermore, we introduce a generalized definition of HUM to accommodate the discrete data, which fits well with our sampling-based method. Additionally, we present inference procedures applicable when probability assessment vectors are either known or estimated. The performance of the proposed procedures is evaluated through simulation studies. We also apply the method to two real-world applications to show its practical utility. Supplementary materials for this article are available online.
Mixture regression models are widely employed for analyzing heterogeneous data. Currently, network-based heterogeneity analysis methods predominantly focus on unsupervised learning, intending to uncover subgroup structures within data and estimate multiple graphs/networks. However, in many real-world scenarios, there is a significant emphasis on both prediction performance of the model and meaningful interpretation of the identified subgroups. In this study, we propose a supervised heterogeneous Gaussian graphical model that accommodates both continuous and discrete response variables. A high-dimensional expectation-conditional-maximization (ECM) algorithm is developed for estimation. We provide a non-asymptotic statistical analysis of the outputs generated from the ECM algorithm. Additionally, numerical studies are conducted to demonstrate the superior performance of our approach, which is further illustrated through an analysis of spectrometric data. Supplementary materials are available online.
Traditional distributed methods rely on two fundamental assumptions: completeness, which assumes that datasets across local machines be fully observed, and randomness, which stipulates that data be randomly distributed across these machines. Violating these assumptions can significantly impair the statistical efficiency of distributed estimators or even render them inconsistent. In this paper, we focus on distributed estimation for data that is non-randomly and non-uniformly distributed, and contains missing values. Depending on whether the local Hessian matrix can be transformed, we propose two Communication-efficient Pilot One-step Update (CPOU) methods. These methods integrate pilot sampling to guarantee estimator consistency, inverse probability weighting (IPW) to reduce bias arising from missing data, and one-step updating to ensure that the efficiency of the proposed estimators is comparable to that of the global estimator. Theoretical analysis and empirical studies demonstrate the good performance of the proposed methods. Supplementary materials for this article are available online.
Partially linear single-index models prove to be flexible in facilitating various types of relationships between the outcome and covariates. However, their validity is hampered by the presence of measurement error in covariates, a feature commonly encountered in applications. In this article, we explore the use of such models to handle data subject to measurement error. In addition, with multivariate covariates, often a few of them are informative while most of them are not. In this article, we propose the three stage procedure to eliminate measurement error effects and select important variables for both the linear predictor term and the single-index part. To implement the proposed method efficiently, we develop a boosting algorithm to select variables and estimate the parameters without handling non-differentiable penalty functions. Theoretical results, including consistency and asymptotic normality of the estimator, are established to justify the validity of the proposed method. Numerical studies, including simulation and data analysis, are conducted to assess the finite sample performance of the proposed method. Supplementary materials for this article are available online.
While generalized additive models are widely used to estimate smooth nonlinear relationships between responses and covariates, their application to temporal data analysis is limited, as the smooth functions may fail to accurately capture temporal evolution in the data and may yield unstable out-of-sample predictions. To address this limitation, dynamic generalized additive models have been proposed, which comprise two components: a generalized additive component and a component of random effects that evolve according to latent stochastic processes. The model falls within the scope of non-Gaussian state space models. For posterior inference in a Bayesian perspective of the model, Markov chain Monte Carlo algorithms require many iterations to converge, particularly in cases involving high-dimensional non-Gaussian time series observations. Therefore, we employ a variational inference scheme to obtain reasonable results efficiently. Specifically for the coefficients of the spline bases and the random effects, a Gaussian variational approximation is assumed. The optimization of the evidence lower bound is performed using a coordinate ascent variational inference algorithm. The proposed variational approach is more efficient than several competing methods in the dynamic generalized additive model framework. We apply the method to study death counts as a function of observed predictors and temporally dependent multivariate random effects that incorporate dependence structures among geographical locations and among causes of death, using an Italian mortality dataset from January 2015 to December 2020.
Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with corresponding covariates across multiple studies. In this paper, we introduce factor models designed to jointly analyze multiple studies by extracting study-shared and specified factors. Our factor models account for heterogeneous noises and overdispersion among counts with augmented covariates. We propose an efficient and speedy variational estimation procedure for estimating model parameters, along with a novel criterion for selecting the optimal number of factors and the rank of regression coefficient matrix. The consistency and asymptotic normality of estimators are systematically investigated by connecting variational likelihood and profile M-estimation. Extensive simulations and an analysis of a single-cell sequencing dataset are conducted to demonstrate the effectiveness of the proposed multi-study Poisson factor model.
Estimation of treatment effects is one of the crucial research problems in causal inference, and there are multiple treatment effects depending on the purpose of research targets or researchers' interests, which include but are not limited to the average treatment effect (ATE) and the quantile treatment effect (QTE). In this study, we aim to propose the statistical functional and cumulative distribution function structure, which leads to a flexible and robust estimator and covers some frequent treatment effects. In addition, our approach also takes variable selection into account, so that informative and network structure in confounders can be identified and implemented in our estimation procedure. The theoretical properties, including variable selection consistency and asymptotic normality of the statistical functional estimator, are established. Some common treatment effects estimations are also conducted in numerical studies, and the results reveal that the proposed estimator generally outperforms the existing methods and is more efficient than its competitors.
Complex spatial datasets defined on non-Euclidean domains with intricate geometry and dependence structures are fostering new frontiers in statistics. For such data, traditional spatial models developed for Euclidean settings may be inadequate, motivating approaches that explicitly account for the underlying domain geometry and locally varying dependencies. In this paper, we address the modeling of random functions over broad and complex domains by adopting low-rank spatial regression models. The underlying spatial field is represented in a reduced-dimensional subspace, obtained through a basis expansion in the corresponding functional space. These models leverage the prototypical structures of manifolds and graphs, allowing for spectral representations of the data using eigenfunctions of the graph Laplacian and the Laplace-Beltrami operator. This framework is extended to non-linear spatial regression models using a feed-forward neural networks, which can effectively handle non-Euclidean domains with complex geometries, dependencies, and manifold structures. We illustrate the proposed approach through four applications, each involving distinct types of data with increasing levels of complexity in terms of spatial domain and process characteristics. The results demonstrate the usefulness of the proposed models in accommodating intricacies of irregularly shaped spatial domains or manifold structures.
We introduce a general family of stochastic dispersion mixed Poisson spatial-temporal regression models for climate-related claim counts. The proposed framework can account for overdispersion caused by unobserved heterogeneity stemming from geographical differences and long-term climate patterns. The model is constructed based on a mixing between alternative base distributions: the Poisson, zero-inflated Poisson, and Hurdle Poisson distributions and unit mean continuous prior, or mixing distributions. Spatial variability is accommodated by linking the mean functions of the base distributions through a spatial adjacency matrix, with covariates also included. The temporal component is defined by an intensity process that quantifies heteroskedasticity over time and controls spatial effects for each region. Four versions of the mean function are presented: the spatial effect is combined with the risk characteristic either additively or multiplicatively, and the spatial adjacency matrix is either known a priori or learned during model training. A lasso regularizer is added when the spatial adjacency matrix is learned to reduce overfitting and remove spurious spatial-temporal associations between regions. The model is calibrated by maximizing the likelihood using a novel regularized Expectation-Maximization algorithm. The model's implementation is demonstrated using climate-related claim data from a Greek property insurance company for the period 2012-2022. Supplemental materials and code are available online.
Discrete choice experiments (DCEs) are popular in business, marketing, health sciences, and many other fields. Panel mixed logit models are a special case of generalized linear mixed models that are natural choices for analyzing data arising from such experiments. In this article, we propose techniques for identifying optimal designs for panel mixed logit models. Here the information matrix does not have a closed form expression and is computationally intensive to evaluate numerically, which to date has made finding designs under these models using search algorithms difficult. To overcome this difficulty, we propose using alternative forms of the information matrix based on penalized quasi-likelihood (PQL), marginal quasi-likelihood (MQL) and the method of simulated moments (MSM). Our simulation results suggest that PQL is the best option when a design with a very high efficiency is required, but that the significantly faster MQL may be acceptable in many cases. We use the proposed methods to search for D-optimal designs for two nontrivial DCE examples reported in literature with a large number of attributes and choice sets, which would be prohibitively expensive using existing techniques. All approaches are implemented in an R package.
