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 utilizes 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.

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.

Multi-group classification arises in many prediction and decision-making problems, including applications in epidemiology, genomics, finance, and image recognition. Although classification methods have advanced considerably, much of the literature focuses on binary problems, and available extensions often provide limited flexibility for multi-group settings. Recent work has extended linear discriminant analysis to multiple groups, but more general methods are still needed to handle complex structures such as nonlinear decision boundaries and group-specific covariance patterns. We develop Multi-Group Quadratic Discriminant Analysis (MGQDA), a method for multi-group classification built on quadratic discriminant analysis. MGQDA projects high-dimensional predictors onto a lower-dimensional subspace, which enables accurate classification while capturing nonlinearity and heterogeneity in group-specific covariance structures. We derive theoretical guarantees, including variable selection consistency, to support the reliability of the procedure. In simulations and a gene-expression application, MGQDA achieves competitive or improved predictive performance compared with existing methods while selecting group-specific informative variables, indicating its practical value for high-dimensional multi-group classification problems. Supplementary materials for this article are available online.

ABSTRACT 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.

ABSTRACT Differential privacy has become a crucial tool for protecting sensitive information. In network data, both the existence of edges and their associated covariates may reveal private details, making their unprotected release a serious privacy concern. However, most existing approaches to edge privacy fail to account for the protection of edge-specific covariates. In this paper, we address this gap by proposing a unified framework for safeguarding both edges and edge-wise covariates in covariate-assisted network models. We introduce edge-covariate differential privacy, a privacy notion designed to simultaneously protect the presence of edges and their associated covariates. To assess its impact on network modeling, we investigate the fundamental privacy–utility tradeoff of parameter estimation under a joint latent space model. Our approach employs a mixed privatization mechanism that combines randomized response for edges with a Laplace mechanism for covariates. We establish asymptotic consistency and minimax optimality, up to logarithmic factors, for parameter estimation under this privacy constraint. Extensive simulation studies and an application to a real-world citation network demonstrate that our method achieves a favorable balance between strong privacy guarantees and estimation accuracy.

Risk management in many environmental settings requires an understanding of the mechanisms that drive extreme events. Useful metrics for quantifying such risk are extreme quantiles of response variables conditioned on predictor variables that describe, for example, climate, biosphere, and environmental states. Typically these quantiles lie outside the range of observable data and so, for estimation, require specification of parametric extreme value models within a regression framework. Classical approaches in this context use linear or additive relationships between predictor and response variables and suffer in either their predictive capabilities or computational efficiency; moreover, their simplicity is unlikely to capture the truly complex structures that lead to the creation of extreme wildfires. In this paper, we propose a new methodological framework for performing extreme quantile regression using artificial neutral networks, which are able to capture complex non-linear relationships and scale well to high-dimensional data. The “black box” nature of neural networks means that they lack the desirable trait of interpretability often favored by practitioners; thus, we combine linear and additive regression methodology with deep learning to create partially interpretable neural networks that can be used for statistical inference but retain high prediction accuracy. To complement this methodology, we further propose a novel point process model for extreme values which overcomes the finite lower-endpoint problem associated with the generalized extreme value class of distributions. Efficacy of our unified framework is illustrated on U.S. wildfire data with a high-dimensional predictor set and we illustrate vast improvements in predictive performance over linear and spline-based regression techniques. Our model is used to quantify the spatially varying effect of temperature and drought on wildfire extremes and occurrences across the U.S., as well as identify high risk regions.

In this article, we introduce EMbru, a novel method to perform inference in spatio-temporal Hawkes models that combines a Bayesian version of Expectation-Maximization (EM) method with the Bayesian Integrated Nested Laplace Approximation (INLA) method, offering an advantage over EM by incorporating uncertainty into the estimates, but also a large computational time reduction over Markov Chain Monte Carlo methods. To assess the performance of EMbru, we conduct a simulation study comparing it with both the EM and inlabru implementations in terms of estimation accuracy and computational time. Additionally, to demonstrate its applicability, we analyze data on rat sightings in urban environments and earthquake data, incorporating a covariate into the background rate in the latter case to evaluate its flexibility and generalization capacity. The results indicate that EMbru is a robust and efficient alternative for Bayesian inference on spatio-temporal Hawkes processes.

The Heckman selection model is one of the most well-known econometric models in the analysis of data with sample selection. This model is designed to rectify sample selection biases based on the assumption of bivariate normal error terms. However, real data diverge from this assumption in the presence of heavy tails and/or atypical observations. Recently, this assumption has been relaxed via a more flexible Student’s t-distribution, which has appealing statistical properties. This article introduces a novel Heckman selection model using a bivariate contaminated normal distribution for the error terms. We present an efficient Expectation Conditional Maximization algorithm for parameter estimation with closed-form expressions at the E-step based on truncated multinormal distribution formulas. The point identifiability of the proposed model is also discussed, and its properties have been examined. Through simulation studies, we compare our proposed model with the normal and Student’s t counterparts and investigate the finite-sample properties and the variation in missing rate. Results obtained from two real data analyses showcase the usefulness and effectiveness of our model. The proposed algorithms are implemented in the R package HeckmanEM.

Functional data classification has gained increasing utility in the modern statistical learning era. In this article, we investigate the generalization ability and the Fisher consistency of the smoothed score (SS) classifier on the intrinsic infinite-dimensional functional data both theoretically and numerically. Formulating the empirical risk minimization based on a regularized smoothed non-convex loss function, we first establish a rigorous error bound on the misclassification rate. The theoretical results reveal a tradeoff between the choice of a tuning parameter and the size of a candidate function class. Additionally, a nonregular convergence rate of the SS estimation is derived in L 2 norm that aligns with h n − ( 1 − ν ) n − μ 2 ( μ + 1 ) , as the bandwidth h n of the smoothed loss is shrunk to 0. By projecting the functional data onto one specific direction over a reproducing kernel Hilbert space where the estimated function is expected to deliver desirable performance, we address the problem of slope function estimation. Computationally, we tackle the nonconvex optimization by developing an efficient proximal gradient algorithm. Finally, the finite sample results in simulation studies as well as a real data analysis from the ADNI study demonstrate the favorable performance of the proposed method compared with some popular classifiers in terms of prediction and estimation.

We introduce a modification of Random Forests to estimate functions when unobserved confounding variables are present. The technique is tailored for high-dimensional settings with many observed covariates. We employ spectral deconfounding techniques to minimize a deconfounded version of the least squares objective, resulting in the Spectrally Deconfounded Random Forests (SDForests). We demonstrate how the omitted variable bias in estimating a direct effect approaches zero, assuming dense confounding and high-dimensional data. We compare the performance of SDForests with that of classical Random Forests in a simulation study and a semi-synthetic setting using single-cell gene expression data. Empirical results suggest that SDForests outperform classical Random Forests in estimating the direct regression function, even if the theoretical assumptions are not perfectly met, and that SDForests and classical Random Forests have comparable performance in the non-confounded case. We provide an R-Package for SDForest, and supplementary materials for this article are available online.