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Mondrian 树与森林的极小极大最优速率AI 解读

Introduced by Breiman (Mach. Learn. 45 (2001) 5–32), Random Forests are widely used classification and regression algorithms. While being initially designed as batch algorithms, several variants have been proposed to handle online learning. One particular instance of such forests is the Mondrian forest (In Adv. Neural Inf. Process. Syst. (2014) 3140–3148; In Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS) (2016)), whose…

非齐次随机图的双样本假设检验AI 解读

The study of networks leads to a wide range of high-dimensional inference problems. In many practical applications, one needs to draw inference from one or few large sparse networks. The present paper studies hypothesis testing of graphs in this high-dimensional regime, where the goal is to test between two populations of inhomogeneous random graphs defined on the same set of $n$ vertices. The size of each population $m$ is much smaller than $n$, and can even be a constant…

变分后验分布的收敛率AI 解读

We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood and variational class that characterize the convergence rates. Under similar “prior mass and testing” conditions considered in the literature, the rate is found to be the sum of two terms. The first term stands for the convergence rate of the true posterior distribution, and the second term is contributed by…

双重切片辅助的高维删失数据充分降维AI 解读

This paper provides a unified framework and an efficient algorithm for analyzing high-dimensional survival data under weak modeling assumptions. In particular, it imposes neither parametric distributional assumption nor linear regression assumption. It only assumes that the survival time $T$ depends on a high-dimensional covariate vector $\mathbf{X}$ through low-dimensional linear combinations of covariates $\Gamma ^{T}\mathbf{X}$. The censoring time is allowed to be…

贝叶斯回归树与森林的后验集中AI 解读

Since their inception in the 1980s, regression trees have been one of the more widely used nonparametric prediction methods. Tree-structured methods yield a histogram reconstruction of the regression surface, where the bins correspond to terminal nodes of recursive partitioning. Trees are powerful, yet susceptible to overfitting. Strategies against overfitting have traditionally relied on pruning greedily grown trees. The Bayesian framework offers an alternative remedy…

依赖观测下高维线性回归的模型选择AI 解读

We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. To prevent OGA from overfitting, we introduce a high-dimensional Akaike’s information criterion (HDAIC) to determine the number of OGA iterations. A key contribution of this work is to show that OGA, used in conjunction…

使用 ReLU 深度神经网络的非参数回归AI 解读

Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of convergence (up to $\log n$-factors) under a general composition assumption on the regression function. The framework includes many well-studied structural constraints such as (generalized) additive models. While there is a lot of flexibility…

通过去噪矩方法最优估计高斯混合分布AI 解读

The method of moments (Philos. Trans. R. Soc. Lond. Ser. A 185 (1894) 71–110) is one of the most widely used methods in statistics for parameter estimation, by means of solving the system of equations that match the population and estimated moments. However, in practice and especially for the important case of mixture models, one frequently needs to contend with the difficulties of non-existence or nonuniqueness of statistically meaningful solutions, as well as the high…

大维情形下乘法相关结构的估计AI 解读

We propose a Kronecker product model for correlation or covariance matrices in the large dimensional case. The number of parameters of the model increases logarithmically with the dimension of the matrix. We propose a minimum distance (MD) estimator based on a log-linear property of the model, as well as a one-step estimator, which is a one-step approximation to the quasi-maximum likelihood estimator (QMLE). We establish rates of convergence and central limit theorems (CLT)…

非参数工具变量回归及其他病态模型中的诚实置信集AI 解读

Abstract This article develops inferential methods for a very general class of ill-posed models in econometrics encompassing the nonparametric instrumental variable regression, various functional regressions, and the density deconvolution. We focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles et al. (2011, Econometrica 79, 1541–1565). Since it is impossible to have inferential methods based on the central…

用收缩方法、实时扩散指数与模型组合预测利率AI 解读

Summary In the context of predicting the term structure of interest rates, we explore the marginal predictive content of real‐time macroeconomic diffusion indexes extracted from a “data rich” real‐time data set, when used in dynamic Nelson–Siegel (NS) models of the variety discussed in Svensson (NBER technical report, 1994; NSS) and Diebold and Li ( Journal of Econometrics , 2006, 130 , 337–364; DNS). Our diffusion indexes are constructed using principal component analysis…

模型简化与变量选择：复现 Hendry 的英国通胀模型AI 解读

Summary In this paper, we revisit the well‐known UK inflation model by Hendry ( Journal of Applied Econometrics , 2001, 16 , 255–275. We replicate the results in a narrow sense using the gretl and PcGive programs. In a wide sense, we extend the study of model uncertainty using the Bayesian averaging of classical estimates (BACE) approach as an automatic model reduction strategy. We consider three different specifications to compare BACE variable selection with Hendry's…

模型不确定性与参数不稳定性下的股票收益预测AI 解读

Summary We compare several representative sophisticated model averaging and variable selection techniques of forecasting stock returns. When estimated traditionally, our results confirm that the simple combination of individual predictors is superior. However, sophisticated models improve dramatically once we combine them with the historical average and take parameter instability into account. An equal weighted combination of the historical average with the standard…

建模研究间异质性以提高基因特征选择与临床预测的可重复性AI 解读

In the genomic era, the identification of gene signatures associated with disease is of significant interest. Such signatures are often used to predict clinical outcomes in new patients and aid clinical decision-making. However, recent studies have shown that gene signatures are often not replicable. This occurrence has practical implications regarding the generalizability and clinical applicability of such signatures. To improve replicability, we introduce a novel approach…

无需插补的块缺失多模态数据最优稀疏线性预测AI 解读

In modern scientific research, data are often collected from multiple modalities. Since different modalities could provide complementary information, statistical prediction methods using multi-modality data could deliver better prediction performance than using single modality data. However, one special challenge for using multi-modality data is related to block-missing data. In practice, due to dropouts or the high cost of measures, the observations of a certain modality…

GAP：两样本稀疏推断的信息汇聚通用框架AI 解读

Yin Xiaa, T. Tony Caib & Wenguang Sunc*a Department of Statistics, School of Management, Fudan University, Shanghai, China; b Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA; c Department of Data Sciences and Operations, University of Southern California, Los Angeles, CAColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available…

大型有向无环图的似然比检验AI 解读

Inference of directional pairwise relations between interacting units in a directed acyclic graph (DAG), such as a regulatory gene network, is common in practice, imposing challenges because of lack of inferential tools. For example, inferring a specific gene pathway of a regulatory gene network is biologically important. Yet, frequentist inference of directionality of connections remains largely unexplored for regulatory models. In this article, we propose constrained…

基于稀疏随机投影的整体定性处理效应检验AI 解读

In contrast to the classical "one size fits all" approach, precision medicine proposes the customization of individualized treatment regimes to account for patients' heterogeneity in response to treatments. Most of existing works in the literature focused on estimating optimal individualized treatment regimes. However, there has been less attention devoted to hypothesis testing regarding the existence of overall qualitative treatment effects, especially when there is a large…

复杂分组高维多响应模型的典型相关搜索特征选择AI 解读

High-dimensional multiresponse models with complex group structures in both the response variables and the covariates arise from current researches in important fields such as genetics and medicine. However, no enough research has been done on such models. One of a few researches, if not the only one, is the article by Li, Nan, and Zhu where the sparse group Lasso approach is extended to such models. In this article, we propose a novel approach named the sequential canonical…

用 D 概率比较和加权不完美模型AI 解读

), relying on evaluating parametric models relative to a nonparametric Bayesian reference using Kullback-Leibler divergence. D-probabilities are useful in goodness-of-fit assessments, in comparing imperfect models, and in providing model weights to be used in model aggregation. D-probabilities avoid some of the disadvantages of Bayesian model probabilities, such as large sensitivity to prior choice, and tend to place higher weight on a greater diversity of models. In an…

空间滞后模型中空间权重矩阵的估计与选择AI 解读

Spatial econometric models allow for interactions among variables through the specification of a spatial weight matrix. Practitioners often face the risk of misspecification of such a matrix. In many problems a number of potential specifications exist, such as geographic distances, or various economic quantities among variables. We propose estimating the best linear combination of these specifications, added with a potentially sparse adjustment matrix. The coefficients in…

基于正则化奇异值分解的时间序列季节调整AI 解读

We propose a new seasonal adjustment method based on the Regularized Singular Value Decomposition (RSVD) of the matrix obtained by reshaping the seasonal time series data. The method is flexible enough to capture two kinds of seasonality: the fixed seasonality that does not change over time and the time-varying seasonality that varies from one season to another. RSVD represents the time-varying seasonality by a linear combination of several seasonal patterns. The right…

高维假设检验的灵活框架AI 解读

Summary Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high dimensional regime where the number of parameters exceeds the number of samples (p > n). To make informative inference, we assume that the model is approximately sparse, i.e. the effect of covariates on the response can be well approximated by conditioning on a relatively small number of covariates whose identities are unknown. We develop…

高维广义线性模型的拟合优度检验AI 解读

Summary We propose a family of tests to assess the goodness of fit of a high dimensional generalized linear model. Our framework is flexible and may be used to construct an omnibus test or directed against testing specific non-linearities and interaction effects, or for testing the significance of groups of variables. The methodology is based on extracting left-over signal in the residuals from an initial fit of a generalized linear model. This can be achieved by predicting…