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通过模型平均实现多层网络迁移学习的框架AI 解读

Link prediction in multilayer networks is a key challenge in applications such as recommendation systems and protein-protein interaction prediction. While many techniques have been developed, most rely on assumptions about shared structures and require access to raw auxiliary data, limiting their practicality. To address these issues, we propose a novel transfer learning framework for multilayer networks using a bi-level model averaging method. A $K$-fold cross-validation…

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极端事件估计的分布鲁棒优化框架AI 解读

Conventional methods for extreme event estimation rely on well-chosen parametric models asymptotically justified from extreme value theory (EVT). These methods, while powerful and theoretically grounded, could however encounter a difficult bias-variance tradeoff that exacerbates especially when data size is too small, deteriorating the reliability of the tail estimation. In this paper, we study a framework based on the recently surging literature of distributionally robust…

真实模型包含在候选集中时最小二乘模型平均的渐近最优性AI 解读

Asymptotic optimality is a key theoretical property in model averaging. Due to technical difficulties, existing studies rely on restricted weight sets or on the assumption that there is no true model with fixed dimensions in the candidate set. The focus of this article is to overcome these difficulties by studying a class of least squares model averaging methods with nested candidate models, which includes Mallows model averaging (MMA) of Hansen (2007, Econometrica 75,…

高维暴露与高维中介模型的统计推断AI 解读

High-dimensional mediation analysis has gained increasing interest in various fields, particularly in genetic and medical research. Compared with existing works that focus mainly on high-dimensional mediators, this paper advocates a new framework of Partial Regularization-based Inference for Mediation Effects (PRIME) when both exposures and mediators are high-dimensional. Estimated direct and indirect effects are established using a group-wise partially penalized least…

基于稀疏张量分解的高维时间序列谱变点估计AI 解读

Abstract Multivariate time series may be subject to partial structural changes over certain frequency band, for instance, in neuroscience. We study the change point detection problem with high-dimensional time series, within the framework of frequency domain. The overarching goal is to locate all change points and delineate which series are activated by the change, over which frequencies. In practice, the number of activated series per change and frequency could span from a…

因子调整的模型平均AI 解读

We propose a model averaging method for high-dimensional regression with highly correlated covariates. We use a factor structure to model the covariate dependence, allowing the covariates to be decomposed into two uncorrelated or weakly correlated latent components: common factors and idiosyncratic components. The number of common factors is allowed to diverge. We average estimators from factor-adjusted candidate models with augmented predictors composed of estimated common…

风险价值与期望损失联合回归的最优模型平均AI 解读

Since the implementation of the Basel III Accord, expected shortfall (ES) has gained increasing attention from regulators as a complement to value-at-risk (VaR). The problem of elicitability for ES makes jointly modeling VaR and ES a popular method to study ES. In this article, we develop model averaging for joint VaR and ES regression models that selects the two weight vectors by minimizing a jackknife criterion. We show the large sample properties of the estimators under…

异质处理效应与异方差下的模型平均估计AI 解读

The primary focus of this article is to capture heterogeneous treatment effects measured by the conditional average treatment effect. A model averaging estimation scheme is proposed with multiple candidate linear regression models under heteroskedastic errors, and the properties of this scheme are explored analytically. First, it is shown that our proposal is asymptotically optimal in the sense of achieving the lowest possible squared error. Second, the convergence of the…

加性模型下异质处理效应估计量的模型平均AI 解读

We consider spline-based additive models for estimation of conditional treatment effects. To handle the uncertainty due to variable selection, we propose a method of model averaging with weights obtained by minimizing a J -fold cross-validation criterion, in which a nearest neighbor matching is used to approximate the unobserved potential outcomes. We show that the proposed method is asymptotically optimal in the sense of achieving the lowest possible squared loss in some…

基于交叉验证与一般损失函数的统一最优模型平均AI 解读

Studying unified model averaging estimation for situations with complicated data structures, we propose a novel model averaging method based on cross-validation ( MACV). MACV unifies a large class of new and existing model averaging estimators and covers a very general class of loss functions. Furthermore, to reduce the computational burden caused by the conventional leave-subject/one-out cross validation, we propose a SEcond-order-Approximated Leave-one/subject-out ( SEAL)…

从模型选择到模型平均：嵌套线性模型的比较AI 解读

Model selection (MS) and model averaging (MA) are two popular approaches when many candidate models exist. Theoretically, the estimation risk of an oracle MA is not larger than that of an oracle MS because the former is more flexible, but a foundational issue is this: Does MA offer a substantial improvement over MS? Recently, seminal work by Peng and Yang (2022) has answered this question under nested models with linear orthonormal series expansion. In the current paper, we…

通过最优模型平均改进张量回归AI 解读

Tensors have broad applications in neuroimaging, data mining, digital marketing, etc. CANDECOMP/PARAFAC (CP) tensor decomposition can effectively reduce the number of parameters to gain dimensionality-reduction and thus plays a key role in tensor regression. However, in CP decomposition, there is uncertainty about which rank to use. In this article, we develop a model averaging method to handle this uncertainty by weighting the estimators from candidate tensor regression…

多门限变量自回归模型的最小二乘估计AI 解读

Most threshold models to-date contain a single threshold variable. However, in many empirical applications, models with multiple threshold variables may be needed and are the focus of this article. For the sake of readability, we start with the Two-Threshold-Variable Autoregressive (2-TAR) model and study its Least Squares Estimation (LSE). Among others, we show that the respective estimated thresholds are asymptotically independent. We propose a new method, namely the…

利用可能部分共享参数的多样本模型进行预测AI 解读

We consider prediction based on a main model. When the main model shares partial parameters with several other helper models, we make use of the additional information. Specifically, we propose a Model Averaging Prediction (MAP) procedure that takes into account data related to the main model as well as data related to the helper models. We allow the data related to different models to follow different structures, as long as they share some common covariate effect. We show…

基于前向验证的最优模型平均AI 解读

In this paper, noting that the prediction of time series follows the temporal order of data, we propose a frequentist model averaging method based on forward-validation. Our method also considers the uncertainty of the window size in estimation, i.e., we allow the sample size to vary among candidate models. We establish the asymptotic optimality of our method in the sense of achieving the lowest possible squared prediction risk. We also prove that if there exists one or more…

高维生存数据的秩驱动贪心模型平均AI 解读

Model averaging is an effective way to enhance prediction accuracy. However, most previous works focus on low-dimensional settings with completely observed responses. To attain an accurate prediction for the risk effect of survival data with high-dimensional predictors, we propose a novel method: rank-based greedy (RG) model averaging. Specifically, adopting the transformation model with splitting predictors as working models, we doubly use the smooth concordance index…

可扩展的频率学派模型平均方法AI 解读

Frequentist model averaging is an effective technique to handle model uncertainty. However, calculation of the weights for averaging is extremely difficult, if not impossible, even when the dimension of the predictor vector, p, is moderate, because we may have 2p candidate models. The exponential size of the candidate model set makes it difficult to estimate all candidate models, and brings additional numeric errors when calculating the weights. This article proposes a…

惩罚化时变模型平均AI 解读

This paper proposes a new penalized time-varying model averaging method to determine optimal time-varying combination weights for candidate models, which avoids over-fitting and yields sparseness from various potential predictive variables. The asymptotic optimality and convergence rate of the selected weights are derived even when all candidate models are misspecified, and the consistency and normality of the proposed time-varying model averaging estimator are obtained when…

基于 K 折交叉验证的模型平均预测AI 解读

This paper considers the model averaging prediction in a quasi-likelihood framework that allows for parameter uncertainty and model misspecification. We propose an averaging prediction that selects the data-driven weights by minimizing a K-fold cross-validation. We provide two theoretical justifications for the proposed method. First, when all candidate models are misspecified, we show that the proposed averaging prediction using K-fold cross-validation weights is…

核平均估计量AI 解读

The issue of bandwidth selection is a fundamental model selection problem stemming from the uncertainty about the smoothness of the regression. In this article, we advocate a model averaging approach to circumvent the problem caused by this uncertainty. Our new approach involves averaging across a series of Nadaraya-Watson kernel estimators each under a different bandwidth, with weights for these different estimators chosen such that a least-squares cross-validation…

参数维数增长的时间序列模型平均预测AI 解读

An important problem with the model averaging approach is the choice of weights. In this paper, a generalized Mallows model averaging (GMMA) criterion for choosing weights is developed in the context of an infinite order autoregressive (AR(∞)) process. The GMMA method adapts to the circumstances in which the dimensions of candidate models can be large and increase with the sample size. The GMMA method is shown to be asymptotically optimal in the sense of achieving the lowest…

时变模型平均AI 解读

Structural changes often occur in economics and finance due to changes in preferences, technologies, institutional arrangements, policies, crises, etc. Improving forecast accuracy of economic time series with structural changes is a long-standing problem. Model averaging aims at providing an insurance against selecting a poor forecast model. All existing model averaging approaches in the literature are designed with constant (non-time-varying) combination weights. Little…

最小二乘模型平均渐近最优性的新研究AI 解读

In this article, we present a comprehensive study of asymptotic optimality of least squares model averaging methods. The concept of asymptotic optimality is that in a large-sample sense, the method results in the model averaging estimator with the smallest possible prediction loss among all such estimators. In the literature, asymptotic optimality is usually proved under specific weights restriction or using hardly interpretable assumptions. This article provides a new…

Summary In this paper, we develop a model averaging method to estimate a high-dimensional covariance matrix, where the candidate models are constructed by different orders of polynomial functions. We propose a Mallows-type model averaging criterion and select the weights by minimizing this criterion, which is an unbiased estimator of the expected in-sample squared error plus a constant. Then, we prove the asymptotic optimality of the resulting model average covariance…