每日简报

稳健效应量指标的渐近分布AI 解读

The Robust Effect Size Index (RESI) is a recently proposed standardized effect size to quantify association strength across models. However, its confidence interval construction has relied on computationally intensive bootstrap procedures. We establish a general theorem for the asymptotic distribution of the RESI using a Taylor expansion that accommodates a broad class of models. Simulations under various linear and logistic regression settings show that RESI and its CI have…

向量值分布强化学习的策略评估：希尔伯特空间嵌入方法AI 解读

We propose Kernel Embedding Distributional Reinforcement Learning (KE-DRL) an offline method to estimate kernel mean embeddings of conditional multivariate return distributions from observed offline trajectories with continuous state-action inputs and vector-valued rewards. KE-DRL approximates the conditional embedding and estimates its a finite-dictionary representation coefficients through a maximum mean discrepancy Bellman criterion. For a regular class of return…

黎曼环境流：从受损数据中同时学习流形与生成模型AI 解读

Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or linearly corrupted measurements can be observed. Moreover, latent structures, such as manifold geometries, present in the data are important to extract for further downstream scientific analysis. In this work, we introduce Riemannian…

BASTION：趋势与季节性分解的贝叶斯框架AI 解读

We introduce BASTION (Bayesian Adaptive Seasonality and Trend DecompositION), a flexible Bayesian framework for decomposing time series into trend and multiple seasonality components. We cast the decomposition as a penalized nonparametric regression and establish formal conditions under which the trend and seasonal components are uniquely identifiable, an issue only treated informally in the existing literature. BASTION offers three key advantages over existing decomposition…

纯跳半鞅中即期波动率的非参数推断AI 解读

We provide a comprehensive analysis of spot volatility inference in pure-jump semimartingales under two asymptotic settings: fixed-$k$, where each local window uses a fixed number of observations, and large-$k$, where this number grows with sampling frequency. For both active- and possibly inactive-jump settings, we derive generally nonstandard, typically non-Gaussian limit distributions and establish valid inference, including when the jump-activity index is consistently…

个体随机实地试验中常用估计量隐含的疫苗效力目标量AI 解读

We review vaccine efficacy (VE) estimands for susceptibility in individual randomized trials with natural (unmeasured) exposure, where individual responses are measured as time from vaccination until an event (e.g., disease from the infectious agent). Common VE estimands are written as $1-θ$, where $θ$ is some ratio effect measure (e.g., ratio of incidence rates, cumulative incidences, hazards, or odds) comparing outcomes under vaccination versus control. Although the ratio…

多变量函数型时间序列的图形主成分分析AI 解读

In this paper, we consider multivariate functional time series with a two-way dependence structure: a serial dependence across time points and a graphical interaction among the multiple functions within each time point. We develop the notion of dynamic weak separability, a more general condition than those assumed in literature, and use it to characterize the two-way structure in multivariate functional time series. Based on the proposed weak separability, we develop a…

半参数有效的经验高阶影响函数估计量AI 解读

Robins et al. (2008, 2017) applied the theory of higher order influence functions (HOIFs) to derive an estimator of the mean $ψ$ of an outcome Y in a missing data model with Y missing at random conditional on a vector X of continuous covariates; their estimator, in contrast to previous estimators, is semiparametric efficient under the minimal conditions of Robins et al. (2009b), together with an additional (non-minimal) smoothness condition on the density g of X, because the…

通过因果表征学习构建可解释的深度生成模型AI 解读

Recent developments in generative artificial intelligence (AI) rely on machine learning techniques such as deep learning and generative modeling to achieve state-of-the-art performance across wide-ranging domains. These methods' surprising performance is due in part to their ability to learn implicit "representations" of complex, multi-modal data. Unfortunately, deep neural networks are notoriously black boxes that obscure these representations, making them difficult to…

多维异质性动态非线性面板的去偏推断AI 解读

We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the limiting distribution of the point estimator is not centered at zero, and that test statistics do not follow their standard asymptotic distributions as in the absence of the fixed effects. To address the problem, we develop an analytical…

含交互固定效应的异质面板门限回归AI 解读

This paper introduces unit-specific heterogeneity in panel data threshold regression. We develop the asymptotic theory for models with heterogeneous thresholds, heterogeneous slope coefficients, and interactive fixed effects. The estimation methodology employs the Common Correlated Effects approach, which is able to handle heterogeneous parameters while maintaining computational simplicity. We also propose a semi-homogeneous model with heterogeneous slopes but a common…

因子分析中的最大软惩罚似然估计AI 解读

Estimation in exploratory factor analysis often yields estimates on the boundary of the parameter space. Such occurrences, known as Heywood cases, are characterised by non-positive variance estimates and can cause issues in numerical optimisation procedures or convergence failures, which, in turn, can lead to misleading inferences, particularly regarding factor scores and model selection. We derive sufficient conditions on the model and a penalty to the log-likelihood…

多项式对数边际密度与 Tweedie 公式：何时存在贝叶斯解释？AI 解读

Motivated by Tweedie's formula for the Compound Decision problem, we examine the theoretical foundations of empirical Bayes estimators that directly model the marginal density $m(y)$. Our main result shows that polynomial log-marginals of degree $k \ge 3 $ cannot arise from any valid prior distribution in exponential family models, while quadratic forms correspond exactly to Gaussian priors. This provides theoretical justification for why certain empirical Bayes decision…