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高维动态线性回归中基于迭代融合 Lasso 的结构突变检测与变量选择AI 解读

We aim to develop a time series modeling methodology tailored to high-dimensional environments, addressing two critical challenges: variable selection from a large pool of candidates, and the detection of structural break points, where the model's parameters shift. This effort centers on formulating a least squares estimation problem with regularization constraints, drawing on techniques such as Fused LASSO and AdaLASSO, which are well-established in machine learning. Our…

利用因子模型学习公平决策：年金定价应用AI 解读

Fairness-aware statistical learning is essential for mitigating discrimination against protected attributes such as gender, race, and ethnicity in data-driven decision-making. This is particularly critical in high-stakes applications like insurance underwriting and annuity pricing, where biased business decisions can have significant financial and social consequences. Factor models are commonly used in these domains for risk assessment and pricing; however, their predictive…

高维稳健线性回归的递归在线得分估计与统计推断AI 解读

This paper introduces a novel framework for estimation and inference in penalized M-estimators applied to robust high-dimensional linear regression models. Traditional methods for high-dimensional statistical inference, which predominantly rely on convex likelihood-based approaches, struggle to address the nonconvexity inherent in penalized M-estimation with nonconvex objective functions. Our proposed method extends the recursive online score estimation (ROSE) framework of…

偏序集合上的模型选择AI 解读

In problems such as variable selection and graph estimation, models are characterized by Boolean logical structure such as presence or absence of a variable or an edge. Consequently, false positive error or false negative error can be specified as the number of variables/edges that are incorrectly included or excluded in an estimated model. However, there are several other problems such as ranking, clustering, and causal inference in which the associated model classes do not…

理解最佳子集选择：两种复杂性视角AI 解读

We consider the problem of best subset selection (BSS) under high-dimensional sparse linear regression model. Recently, Guo et al. (2020) showed that the model selection performance of BSS depends on a certain identifiability margin, a measure that captures the model discriminative power of BSS under a general correlation structure that is robust to the design dependence, unlike its computational surrogates such as LASSO, SCAD, MCP, etc. Expanding on this, we further broaden…

连续时间靶向极大似然与高度自适应 Lasso 的干预特定复发事件期望次数估计AI 解读

Longitudinal settings involving outcome, competing risks and censoring events occurring and recurring in continuous time are common in medical research, but are often analyzed with methods that do not allow for taking post-baseline information into account. In this work, we define statistical and causal target parameters via the g-computation formula by carrying out interventions directly on the product integral representing the observed data distribution in a…

树正则化贝叶斯潜类别分析：改善小规模亚群中弱分离膳食模式的亚型识别AI 解读

Dietary patterns synthesize multiple related diet components, which can be used by nutrition researchers to examine diet-disease relationships. Latent class models (LCMs) have been used to derive dietary patterns from dietary intake assessment, where each class profile represents the probabilities of exposure to a set of diet components. However, LCM-derived dietary patterns can exhibit strong similarities, or weak separation, resulting in numerical and inferential…

连续字典混合模型的离网学习AI 解读

We consider a general non-linear model where the signal is a finite mixture of an unknown, possibly increasing, number of features issued from a continuous dictionary parameterized by a real non-linear parameter. The signal is observed with Gaussian (possibly correlated) noise in either a continuous or a discrete setup. We propose an off-the-grid optimization method, that is, a method which does not use any discretization scheme on the parameter space, to estimate both the…

广义岭回归：在非正交线性回归模型中的应用AI 解读

This paper analyzes the possibilities of using the generalized ridge regression to mitigate multicollinearity in a multiple linear regression model. For this purpose, we obtain the expressions for the estimated variance, the coefficient of variation, the coefficient of correlation, the variance inflation factor and the condition number. The results obtained are illustrated with two numerical examples.

支配超平面正则化用于多元计数回归的变量选择AI 解读

Identifying relevant factors that influence the multinomial counts in compositional data is difficult in high dimensional settings due to the complex associations and overdispersion. Multivariate count models such as the Dirichlet-multinomial (DM), negative multinomial, and generalized DM accommodate overdispersion but are difficult to optimize due to their non-concave likelihood functions. Further, for the class of regression models that associate covariates to the…

含节点同质性与节点效应的有向网络模型中的正则化与选择AI 解读

This article introduces a regularization and selection methods for directed networks with nodal homophily and nodal effects. The proposed approach not only preserves the statistical efficiency of the resulting estimator, but also ensures that the selection of nodal homophily and nodal effects is scalable with large-scale network data and multiple nodal features. In particular, we propose a directed random network model with nodal homophily and nodal effects, which includes…

带预测变量图结构的稀疏 Fréchet 充分降维AI 解读

Fréchet regression has received considerable attention to model metric-space valued responses that are complex and non-Euclidean data, such as probability distributions and vectors on the unit sphere. However, existing Fréchet regression literature focuses on the classical setting where the predictor dimension is fixed, and the sample size goes to infinity. This paper proposes sparse Fréchet sufficient dimension reduction with graphical structure among high-dimensional…

利用共享因子结构与非凸惩罚改进矩阵补全AI 解读

This article investigates the problem of noisy low-rank matrix completion with a shared factor structure, leveraging the auxiliary information from the missing indicator matrix to enhance prediction accuracy. Despite decades of development in matrix completion, the potential relationship between observed data and missing indicators has largely been overlooked. To address this gap, we propose a joint modeling framework for the observed data and missing indicators within the…

基于极值尾部估计的非参数治愈模型AI 解读

In survival analysis, the estimation of the proportion of subjects who will never experience the event of interest, termed the cure rate, has received considerable attention recently. Its estimation can be a particularly difficult task when follow-up is not sufficient, that is when the censoring mechanism has a smaller support than the distribution of the target data. In the latter case, non-parametric estimators were recently proposed using extreme value methodology,…

平衡回归中的变量选择及其在微生物组成分数据中的应用AI 解读

Compositional data, where only relative abundances are available, are common in microbiome and other high-throughput sequencing studies. Log ratios between groups of variables serve as key biomarkers in these settings. However, selecting predictive log ratios is a combinatorial challenge, and existing greedy search-based methods are computationally expensive, limiting their applicability to high-dimensional data. We introduce the supervised log ratio (SLR) method, a novel…

因果推断中多类处理效应的统一估计方法AI 解读

In this paper, we introduce a unified estimator to analyze various treatment effects in causal inference, including but not limited to the average treatment effect (ATE) and the quantile treatment effect (QTE). The proposed estimator is developed under 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…

Sparklen：面向高维霍克斯过程的 Python 统计学习工具包AI 解读

This paper introduces Sparklen, a statistical learning toolkit for Hawkes processes in Python, designed to bring together efficiency and ease of use. The purpose of this package is to provide the Python community with a complete suite of cutting-edge tools specifically tailored for the study of exponential Hawkes processes, with a particular focus on highdimensional framework. It includes state-of-the-art estimation tools with built-in support for incorporating…

重审希尔伯特空间学习中的一般源条件AI 解读

In Learning Theory, the smoothness assumption on the target function (known as source condition) is a key factor in establishing theoretical convergence rates for an estimator. The existing general form of the source condition, as discussed in learning theory literature, has traditionally been restricted to a class of functions that can be expressed as a product of an operator monotone function and a Lipschitz continuous function. In this note, we remove these restrictions…

分布偏差影响留一交叉验证AI 解读

Cross-validation is a common method for estimating the predictive performance of machine learning models. In a data-scarce regime, where one typically wishes to maximize the number of instances used for training the model, an approach called "leave-one-out cross-validation" is often used. In this design, a separate model is built for predicting each data instance after training on all other instances. Since this results in a single test instance available per model trained,…

当 n < p 时的主成分分析：挑战与解决方案AI 解读

Principal Component Analysis is a key technique for reducing the complexity of high-dimensional data while preserving its fundamental data structure, ensuring models remain stable and interpretable. This is achieved by transforming the original variables into a new set of uncorrelated variables (principal components) based on the covariance structure of the original variables. However, since the traditional maximum likelihood covariance estimator does not accurately converge…

以预测为中心的不确定性量化：基于MMD的方法AI 解读

Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised Bayesian methodologies have been proposed for inference with misspecified models, but these are typically associated with vanishing parameter uncertainty as more data are observed. In the context of a misspecified deterministic mathematical…

多视图正交投影回归及其在多组学整合中的应用AI 解读

Multi-omics integration offers novel insights into complex biological mechanisms by utlizing the fused information from various omics datasets. However, the inherent within- and inter-modality correlations in multi-omics data present significant challenges for traditional variable selection methods, such as Lasso regression. These correlations can lead to multicollinearity, compromising the stability and interpretability of selected variables. To address these problems, we…

删失与隐藏混杂下高维随机试验和真实世界数据的整合分析AI 解读

In this study, we focus on estimating the heterogeneous treatment effect (HTE) for survival outcome. The outcome is subject to censoring and the number of covariates is high-dimensional. We utilize data from both the randomized controlled trial (RCT), considered as the gold standard, and real-world data (RWD), possibly affected by hidden confounding factors. To achieve a more efficient HTE estimate, such integrative analysis requires great insight into the data generation…

混合模型迹回归中的正则化参数估计AI 解读

We introduce mixed model trace regression (MMTR), a mixed model linear regression extension for scalar responses and high-dimensional matrix-valued covariates. MMTR's fixed effects component is equivalent to trace regression, with an element-wise lasso penalty imposed on the regression coefficients matrix to facilitate the estimation of a sparse mean parameter. MMTR's key innovation lies in modeling the covariance structure of matrix-variate random effects as a Kronecker…