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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…

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…