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RBF 核高斯过程最大似然估计的精确渐近理论AI 解读

Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the…

连续处理随机政策变动下的双重差分AI 解读

Treatment effects of stochastic policy shifts quantify differences in outcomes across counterfactual scenarios with varying treatment distributions. Stochastic policy shifts may be of interest in settings where it is unrealistic or infeasible to deterministically manipulate treatments. In this paper, methods are developed to draw inference about stochastic policy effects under difference-in-differences (DiD) designs with a continuous treatment. The proposed causal estimand…

网络依赖与干扰下双重差分的高效非参数估计AI 解读

Differences-in-differences (DiD) is a causal inference method for observational longitudinal data that assumes parallel expected potential outcome trajectories between treatment groups under the counterfactual scenario where all units receive a specific treatment. In this paper DiD is extended to allow for: (i) non-identically distributed treatment effects and exposure probabilities; (ii) interference, where treatment of one unit can affect outcomes in neighboring units; and…

纵向数据的层级概率主成分分析AI 解读

In many longitudinal studies, a large number of variables are measured repeatedly over time, with substantial missing data. Existing methods, such as probabilistic principal component analysis (PPCA), are ill-equipped to handle such incomplete, high-dimensional longitudinal data, as they fail to account for the nested sources of variation and temporal dependency inherent in repeated measures. We introduce hierarchical probabilistic principal component analysis (HPPCA), a…

具有领先—滞后效应的时间序列高斯过程及其生物数据应用AI 解读

Investigating the relationship, particularly the lead-lag effect, between time series is a common question across various disciplines, especially when uncovering biological process. However, analyzing time series presents several challenges. Firstly, due to technical reasons, the time points at which observations are made are not at uniform inintervals. Secondly, some lead-lag effects are transient, necessitating time-lag estimation based on a limited number of time points.…