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同根异叶：面板数据中的时间序列与横截面方法AI 解读

One dominant approach to evaluate the causal effect of a treatment is through panel data analysis, whereby the behaviors of multiple units are observed over time. The information across time and units motivates two general approaches: (i) horizontal regression (i.e., unconfoundedness), which exploits time series patterns, and (ii) vertical regression (e.g., synthetic controls), which exploits cross‐sectional patterns. Conventional wisdom often considers the two approaches to…

奇异性、模型误设与EM算法的收敛速度AI 解读

A line of recent work has analyzed the behavior of the Expectation-Maximization (EM) algorithm in the well-specified setting, in which the population likelihood is locally strongly concave around its maximizing argument. Examples include suitably separated Gaussian mixture models and mixtures of linear regressions. We consider over-specified settings in which the number of fitted components is larger than the number of components in the true distribution. Such mis-specified…

EM 算法的统计保证：从总体到有限样本分析AI 解读

The EM algorithm is a widely used tool in maximum-likelihood estimation in incomplete data problems. Existing theoretical work has focused on conditions under which the iterates or likelihood values converge, and the associated rates of convergence. Such guarantees do not distinguish whether the ultimate fixed point is a near global optimum or a bad local optimum of the sample likelihood, nor do they relate the obtained fixed point to the global optima of the idealized…

正则化对谱聚类的影响AI 解读

The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et al. [Ann. Statist. 41 (2013) 2097–2122]. Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the stochastic block model (SBM), and its extensions, previous results on spectral clustering relied on the minimum degree of the graph being sufficiently large for its good performance. By examining the scenario…

稀疏有向无环图马尔可夫等价类上的可逆MCMCAI 解读

Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with currently known algorithms, sampling over such classes is only feasible for graphs with fewer than approximately 20 vertices. In this paper, we design reversible…

因果推断中忠实性假设的几何结构AI 解读

Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform or…

随机实验中通过后分层调整处理效应估计AI 解读

Summary Experimenters often use post-stratification to adjust estimates. Post-stratification is akin to blocking, except that the number of treated units in each stratum is a random variable because stratification occurs after treatment assignment. We analyse both post-stratification and blocking under the Neyman–Rubin model and compare the efficiency of these designs. We derive the variances for a post-stratified estimator and a simple difference-in-means estimator under…

谱聚类与高维随机块模型AI 解读

Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of highly connected actors form an essential feature in the structure of several empirical networks. Spectral clustering is a popular and computationally feasible method to discover these communities. The stochastic blockmodel [Social Networks…

用于分组与层级变量选择的复合绝对惩罚族AI 解读

Extracting useful information from high-dimensional data is an important focus of today’s statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and empirically. With the virtues of both regularization and sparsity, the L1-penalized squared error minimization method Lasso has been popular in regression models and beyond. In this paper, we combine different norms including L1 to form an…

高维数据稀疏表示的Lasso型恢复AI 解读

The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables pn is potentially much larger than the number of samples n. However, it was recently discovered that the sparsity pattern of the Lasso estimator can only be asymptotically identical to the true sparsity pattern if the design matrix satisfies the so-called irrepresentable condition. The latter condition can easily be violated in the…

Boosting is one of the most significant advances in machine learning for classification and regression. In its original and computationally flexible version, boosting seeks to minimize empirically a loss function in a greedy fashion. The resulting estimator takes an additive function form and is built iteratively by applying a base estimator (or learner) to updated samples depending on the previous iterations. An unusual regularization technique, early stopping, is employed…

关于提升方法论文的讨论及作者回应AI 解读

Discussions of: "Process consistency for AdaBoost" [Ann. Statist. 32 (2004), no. 1, 13-29] by W. Jiang; "On the Bayes-risk consistency of regularized boosting methods" [ibid., 30-55] by G. Lugosi and N. Vayatis; and "Statistical behavior and consistency of classification methods based on convex risk minimization" [ibid., 56-85] by T. Zhang. Includes rejoinders by the authors.

三篇关于提升法的论文：导言AI 解读

The notion of boosting originated in the Machine Learning literature in the 1980's [VALIANT, L.G. (1984). A theory of the learnable. In Proc. 16th Annual ACM Symposium on Theory of Computing 436-445. ACM Press, New York]. The goal of boosting is to improve the generalization performance of weak (or base) learning algorithms by combining them in a certain way. The first algorithm of this type was discovered by Schapire [SCHAPIRE, R.E. (1990). The strength of weak…

采用平方损失的提升方法AI 解读

This article investigates a computationally simple variant of boosting, L2Boost, which is constructed from a functional gradient descent algorithm with the L2-loss function. Like other boosting algorithms, L2Boost uses many times in an iterative fashion a prechosen fitting method, called the learner. Based on the explicit expression of refitting of residuals of L2Boost, the case with (symmetric) linear learners is studied in detail in both regression and classification. In…

Bagging 的理论分析AI 解读

Bagging is one of the most effective computationally intensive procedures to improve on unstable estimators or classifiers, useful especially for high dimensional data set problems. Here we formalize the notion of instability and derive theoretical results to analyze the variance reduction effect of bagging (or variants thereof) in mainly hard decision problems, which include estimation after testing in regression and decision trees for regression functions and classifiers.…

This article reviews the principle of minimum description length (MDL) for problems of model selection. By viewing statistical modeling as a means of generating descriptions of observed data, the MDL framework discriminates between competing models based on the complexity of each description. This approach began with Kolmogorov's theory of algorithmic complexity, matured in the literature on information theory, and has recently received renewed attention within the…

依赖数据的上确界范数密度估计及其 Gibbs 采样应用AI 解读

This paper investigates the density estimation problem in the $L^\infty$ norm for dependent data. It is shown that the iid optimal minimax rates are also optimal for smooth classes of stationary sequences satisfying certain $\beta$-mixing (or absolutely regular) conditions. Moreover, for given $\beta$-mixing coefficients, bounds on uniform convergence rates of kernel estimators are computed in terms of the mixing coefficients. The rates and the bounds obtained are not only…